Development of Some Novel Spatial-Domain and Transform - ethesis

Development of Some Novel

Spatial-Domain and Transform-

Domain Digital Image Filters

A thesis submitted in fulfillment of the

requirements for the degree of Doctor of Philosophy

by

NILAMANI BHOI

Department of Electronics and Communication Engineering

National Institute of Technology Rourkela INDIA

January 2009

hellip dedicated to my loving parents

CERTFICATE

This is to certify that the thesis titled ldquoDDeevveellooppmmeenntt ooff SSoommee

NNoovveell SSppaattiiaall--DDoommaaiinn aanndd TTrraannssffoorrmm--DDoommaaiinn DDiiggiittaall IImmaaggee

FFiilltteerrssrdquo submitted to the National Institute of Technology Rourkela

(INDIA) by Nilamani Bhoi Roll No 50607001 for the award of the

degree of DDooccttoorr ooff PPhhiilloossoopphhyy iinn EElleeccttrroonniiccss aanndd CCoommmmuunniiccaattiioonn

EEnnggiinneeeerriinngg is a bona fide record of research work carried out by him

under my supervision and guidance

The candidate has fulfilled all the requirements

The thesis which is based on candidatersquos own work has not been

submitted elsewhere for a degreediploma

In my opinion the thesis is of standard required of a PhD degree in

Engineering

To the best of my knowledge Mr Bhoi bears a good moral

character and decent behavior

Dr Sukadev Meher

Asst Professor

Department of Electronics ampCommunication Engineering

National Institute of Technology

Rourkela-769008 (INDIA)

Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters

i

PREFACE

Digital Image Processing developed during last three decades has become a

very important subject in electronics and computer engineering Image restoration is

one of the many areas it encompasses Image deblurring and image denoising are the

two sub-areas of image restoration

When an image gets corrupted with noise during the processes of acquisition

transmission storage and retrieval it becomes necessary to suppress the noise quite

effectively without distorting the edges and the fine details in the image so that the

filtered image becomes more useful for display andor further processing

Two spatial-domain and three transform-domain digital image filters are

proposed in this doctoral thesis for efficient suppression of additive white Gaussian

noise (AWGN) The filters are tested on low moderate and high noise conditions and

they are compared with existing filters in terms of objective and subjective evaluation

Under low noise conditions though many filters are very good in terms of objective

evaluations the resulting output images of almost all filters give nearly equal visual

quality Hence efforts are made here to develop efficient filters for suppression of

AWGN under moderate and high noise conditions The execution time is taken into

account while developing filters for online and real-time applications such as

television photo-phone etc

Therefore the present research work may be treated as

(i) developmental work and

(ii) applied research work

I would be happy to see other researchers using the results reported in the thesis

for developing better image filters Moreover I will be contended to find these filters

implemented for practical applications in near future

Nilamani Bhoi


ii

ACKNOWLEDGEMENT

I express my indebtedness and gratefulness to my teacher and supervisor

Prof Sukadev Meher for his continuous encouragement and guidance I needed his

support guidance and encouragement throughout the research period I am obliged to

him for his moral support through all the stages during this doctoral research work I

am indebted to him for the valuable time he has spared for me during this work

I am thankful to Prof S K Patra Head Department of Electronics amp

Communication Engineering who provided all the official facilities to me I am also

thankful to other DSC members Prof G Panda and Prof B Majhi for their

continuous support during the doctoral research work

I would like to thank all my colleagues and friends MR Meher R Kulkarni

CS Rawat and Ratnakar Yadav for their company and cooperation during this

period

I take this opportunity to express my regards and obligation to my parents

whose support and encouragement I can never forget in my life

I would like to thank my wife Sima and son Pratik for their patience and

cooperation I canrsquot forget their help who have managed themselves during the tenure

of my Ph D work I duly acknowledge the constant moral support they provided

throughout

Lastly I am thankful to all those who have supported me directly or indirectly

during the doctoral research work

Nilamani Bhoi


iii

BIO-DATA OF THE CANDIDATE

Name of the candidate Nilamani Bhoi

Fatherrsquos Name Premaraj Bhoi

Present Address PhD Scholar

Dept of Electronics and

Communication Engg

National Institute of

Technology Rourkela-769008

Permanent Address AT-Budhikhamar

PO-Kalamati

Dist-Sambalpur-768111

ACADEMIC QUALIFICATION

(i) B E in Electrical Engineering University College of Engg Burla

Sambalur University BURLA Orissa INDIA

(ii) M E in Electronic Systems amp Tele-Communication Engineering

Jadavpur University Kolkata WestBengal INDIA

PUBLICATION

(i) Published 01 paper in International Journals

(ii) Communicated 02 papers to International Journals

(iii) Published 08 papers in National and International Conferences

Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filter iv

CONTENTS Page No

Certificate

Preface i

Acknowledgement ii

Bio-data of the Candidate iii

Contents iv

Abstract

vi

List of Abbreviations used x

List of Symbols used

xii

1 INTRODUCTION 1 Preview

11 Fundamentals of Digital Image Processing 3 12 Noise in Digital Images 8

13 Literature Review 12 14 Problem Statement 18

15 Image Metrics 19

16 Chapter-wise Organization of the Thesis 23 17 Conclusion 24

2 Study of Image Denoising Filters 25

Preview

21 Order Statistics Filter 27

22 Wiener and Lee Filter 29

23 Anisotropic Diffusion (AD) and Total Variation (TV)

Filters

32

24 Bilateral Filter 36

25 Non-local Means (NL-Means) Filter 38

26 Wavelet Domain Filters 42

27 Simulation Results 52

28 Conclusion 79

CONTENTS


v

3 Development of Novel Spatial-Domain Image Filters 81

Preview

31 Development of Adaptive Window Wiener Filter 84

32 Development of Circular Spatial Filter 89


34 Conclusion 122

4 Development of Transform-Domain Filters 124

Preview

41 Development of Gaussian Shrinkage based DCT-domain Filter

127

42 Development of Total Variation based DWT-domain Filter 133

43 Development of Region Merging based DWT-domain

Filter

137


45 Conclusion 167

5 Development of Some Color Image Denoising Filters 168

Preview

51 Multi-Channel Color Image Filtering 171

52 Multi-Channel Mean Filter 177

53 Multi-Channel LAWML Filter 179

54 Development of Multi-Channel Circular Spatial Filter 181

55 Development of Multi-Channel Region Merging based

DWT-domain Filter

183


57 Conclusion 209

6 Conclusion 211

Preview

61 Comparative Analysis 213

62 Conclusion 221

63 Scope for Future Work 222

References 223

Contribution by the Candidate 237

Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filter vi

Abstract

Some spatial-domain and transform-domain digital image filtering algorithms

have been developed in this thesis to suppress additive white Gaussian noise

(AWGN)

In many occasions noise in digital images is found to be additive in nature

with uniform power in the whole bandwidth and with Gaussian probability

distribution Such a noise is referred to as Additive White Gaussian Noise (AWGN)

It is difficult to suppress AWGN since it corrupts almost all pixels in an image The

arithmetic mean filter commonly known as Mean filter can be employed to suppress

AWGN but it introduces a blurring effect Image denoising is usually required to be

performed before display or further processing like segmentation feature extraction

object recognition texture analysis etc The purpose of denoising is to suppress the

noise quite efficiently while retaining the edges and other detailed features as much as

possible

In literature many efficient digital image filters are found that perform well

under low noise conditions But their performance is not so good under moderate and

high noise conditions Thus it is felt that there is sufficient scope to investigate and

develop quite efficient but simple algorithms to suppress moderate and high power

noise in an image

The filter-performances are usually compared in terms of peak-signal-to-noise

ratio (PSNR) mean squared error (MSE) and mean absolute error (MAE) These are

simply mathematically defined image metrics that take care of noise power level in

the whole image Large values of PSNR and small values of MSE indicate less noise

power in an image irrespective of the degradations undergone So the quality of an

image obtained from a filter can not be judged properly with these objective

evaluation image metrics (PSNR MSE MAE) Recently an image metric known as

universal quality index (UQI) is proposed in the literature that takes care of human

visual system (HVS) A higher value of UQI usually guarantees better subjective

evaluation automatically even if it is an objective evaluation measure So the filter

performance should be compared in terms of UQI values as well Further the image

Abstract


vii

denoising filters also degrade an original (noise-free) image This degradation is

termed as method noise In many applications the images are corrupted with very low

power AWGN Under such circumstances the method noise should also be evaluated

and considered while developing good filters The method noise is described as an

error voltage level in terms of its mean absolute value when the input to the filter is

noise-free In addition the execution time taken by a filter should be low for online

and real-time image processing applications

The present doctoral research work is focused on developing quite efficient

image denoising filters in spatial-domain and transform-domain to suppress AWGN

quite effectively without yielding much distortion and blurring The performances of

the developed filters are compared with the existing filters in terms of peak-signal-to-

noise ratio root-mean-squared error universal quality index method noise and

execution time

The approaches adopted and the novel filters designed are summarized here

(A) Spatial-Domain Filters Two novel spatial-domain image denoising filters

(i) Adaptive Window Wiener Filter (AWWF) and (ii) Circular Spatial Filter (CSF) are

developed

(i) Adaptive Window Wiener Filter (AWWF) The adaptive window Wiener filter

(AWWF) suppresses Gaussian noise under low and moderate noise conditions very

efficiently The work begins by using a mean filter on a noisy image to get the blurred

version of the image Using an edge detection algorithm the edges of the resulted

blurred image are found out Many edge detection algorithms are available in the

literature The Wiener filter of variable size is applied throughout the noisy image to

suppress the noise The window size is made bigger in homogenous and smooth

regions and is made smaller in edge and complex regions

(ii) Circular Spatial Filter (CSF) A novel circular spatial filter (CSF) is proposed

for suppressing additive white Gaussian noise (AWGN) In this method a circular

spatial-domain window whose weights are derived from two independent functions

(i) spatial distance and (ii) gray level distance is employed for filtering The proposed

filter is different from Bilateral filter and performs well under moderate and high

Abstract


viii

noise conditions The filter is also capable of retaining the edges and intricate details

of the image

(B) Transform-Domain Filters Three novel transform-domain filters (i)

Gaussian Shrinkage based DCT-domain Filter (GS-DCT) (ii) Total Variation based

DWT-domain Filter (TV-DWT) (iii) Region Merging based DWT-domain filter(RM-

DWT) are developed to suppress the Gaussian noise effectively

(i) Gaussian Shrinkage based DCT-domain Filter (GS-DWT) The proposed filter

presents a simple image denoising scheme by using an adaptive Gaussian smoothing

based thresholding in the discrete cosine transform (DCT) domain The edge pixel

density on the current sliding window decides the threshold level in the DCT domain

for removing the high frequency components eg noise Since the hard threshold

approach is discontinuous in nature and it tends to yield artifacts (like Gibbs

phenomenon) in the recovered image a method of associating Gaussian weights to

DCT coefficients is proposed This reduces artifacts and yields better PSNR values

(ii) Total Variation based DWT-domain Filter (TV-DWT) In the proposed filter

the total variation (TV) algorithm is applied on a noisy image decomposed in wavelet

domain for suppression of Gaussian noise After the decomposition process four

different energy bands low-low (LL) low-high (LH) high-low (HL) and high-high

(HH) are found The LL subband of a single decomposed noisy image is used to find

the horizontal vertical and diagonal edges Using the pixel position of horizontal

edges the corresponding wavelet coefficients in HL subband is retained thresholding

others to zero Adopting the same procedure the vertical and diagonal details of LH

and HH subbands are retained The method TV is applied to LL subband for one

iteration only Applying inverse wavelet transform on modified wavelet coefficients

we get back the image with little noise This small amount of noise can further be

suppressed using the TV algorithm for one iteration once again in the spatial-domain

(iii) Region Merging based DWT-domain Filter (RM-DWT) The proposed region

merging based DWT-domain (RM-DWT) filter introduces an image denoising

scheme with region merging approach in wavelet-domain In the proposed method

Abstract


ix

the wavelet transform is applied on the noisy image to yield the wavelet coefficients

in different subbands A region including the denoising point in the particular subband

is partitioned in order to get distinct sub-regions The signal-variance in a sub-region

is estimated by using maximum likelihood (ML) estimation It distinguishes a sub-

region with some non-zero ac signal power from a sub-region containing no ac signal

power The sub-regions containing some appreciable ac signal power are merged

together to get a large homogenous region However if the sub-region including

denoising point has no ac signal power this sub-region can be merged with other

likelihood sub-regions with zero ac signal power to get a homogenous region Now in

a large homogenous region in wavelet domain the signal variance is estimated with

better accuracy Using the estimated signal variance the wavelet coefficients of

original (noise-free) decomposed image in wavelet domain are estimated using the

minimum mean squared error (MMSE) estimator

Since the Circular Spatial Filter and Region Merging based DWT-Domain

Filter give very good performance in denoising gray-scale images two multi-channel

filters Multi-channel Circular Spatial Filter (MCSF) and Multi-channel Region

Merging based DWT-Domain Filter (MRM-DWT) are developed for suppression of

AWGN from color images The developed filters MCSF and MRM-DWT are based

on three-channel-processing (RGB- processing) and hence are necessarily 3-Channel

CSF and 3-Channel RM-DWT respectively

The AWWF perform well under moderate noise conditions The developed

circular spatial filter (CSF) suppresses AWGN efficiently under moderate and high

noise conditions The GS-DCT filter suppresses additive noise in DCT-domain and

works well when the noise power is moderate The developed filter TV-DWT takes

less execution time as compared to other filters When the noise power is low the

proposed wavelet-domain filter RM-DWT suppress additive noise effectively

Among all developed filters and existing filters CSF is found to be best for

suppressing AWGN

Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filter x

List of Abbreviations used

Abbreviations

1 AWGN Additive White Gaussian Noise

2 SPN Salt and Pepper Noise

3 RVIN Random Valued Impulse Noise

4 SN Speckle Noise

5 DCT Discrete Cosine Transform

6 CWT Continuous Wavelet Transform

7 DWT Discrete Wavelet Transform

8 LL Low-Low

9 LH Low-High

10 HL High-Low

11 HH High-High

12 PEP Percentage of Edge Pixels

13 ML Maximum Likelihood

14 SURE Steinrsquos Unbiased Risk Estimate

15 DS Directional Smoothing

16 MED Median

17 MSE Mean Squared Error

18 MAE Mean Absolute Error

19 RMSE Root Mean Squared Error

20 MMSE Minimum Mean Squared Error

21 PSNR Peak Signal to Noise Ratio



xi

22 CPSNR Color Peak Signal to Noise Ratio

23 UQI Universal Quality Index

24 HVS

Human Visual System

SOME IMPORTANT FILTERS AVAILABLE IN LITERATURE

25 MF Mean Filter

26 ATM Alpha Trimmed Mean

27 AD Anisotropic Diffusion

28 TV Total Variation

29 NL-Means Non-local Means

30 LAWML Locally Adaptive Window based Maximum Likelihood

31 M-MF Multi-Channel Mean Filter

32 M-LAWML Multi-Channel Locally Adaptive Window based

Maximum Likelihood

DEVELOPED FILTERS

33 AWWF Adaptive Window Wiener Filter

34 CSF Circular Spatial Filter

35 GS-DCT Gaussian Shrinkage based DCT

36 TV-DWT Total Variation based DWT

37 RM-DWT Region Merging based DWT

38 MCSF Multi-Channel Circular Spatial Filter

39 MRM-DWT Multi-Channel Region Merging based DWT

Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filter xii


Symbols

1 f(xy) Original (noise-free) Digital Image

with discrete spatial coordinates (xy)

2 η Random Variable Noise

3 fAWGN g Noisy Image Corrupted with AWGN

4 fSPN Image corrupted with Salt and Pepper Noise

5 fRVIN Image corrupted with Random-Valued Impulse Noise

6 ˆ ( )f x y Filtered Output Image

7 TE Execution Time

8 MN Method Noise

9 2

nσ Noise Variance

10 dg Gray-level Distance

11 ds Spatial Distance

12 cp Center Pixel its gray-scale value

13 wg Gray-level Kernel

14 wd Distance Kernel

15 L Total Number of Pixels in a Window

16 TU Universal Threshold

17 TSURE Threshold of SureShrink

18 TB Threshold of BayesShrink

19 TOS Threshold of OracleShrink

20 TOT Threshold of OracleThresh

21 ( )hTξ sdot Soft Thresholding Operation



xiii

22 ( )hT

ζ sdot Hard Thresholding Operation

23 F Original Decomposed Image in Wavelet-Domain

24 Y Noisy Decomposed Image in Wavelet-Domain

25 F Estimated (Filtered) Image Decomposed in Wavelet-Domain

26 Γ Shrinkage function for NeighShrink

27 N Neighborhood in Wavelet-Domain

28 C Color Space

Chapter 1

Introduction

Chapter-1 Introduction

Development of Some Novel Spatial-Domain and Transform-Domain Digital Image Filters 2

Preview

Image processing has got wide varieties of applications in computer vision

multimedia communication television broadcasting etc that demand very good

quality of images The quality of an image degrades due to introduction of additive

white Gaussian noise (AWGN) during acquisition transmission reception and

storage retrieval processes It is very much essential to suppress the noise in an image

and to preserve the edges and fine details as far as possible In the present research

work efforts are made to develop efficient spatial-domain and transform-domain

image filters that suppress noise quite effectively

The following topics are covered in this chapter

Fundamentals of Digital Image Processing

Noise in Digital Images

Literature Review

Problem Statement

Image Metrics

Chapter-wise Organization of the Thesis

Conclusion

1



11 Fundamentals of Digital Image Processing

Digital Image Processing usually refers to the processing of a 2-dimensional

(2-D) picture signal by a digital hardware The 2-D image signal might be a

photographic image text image graphic image (including synthetic image)

biomedical image (X-ray ultrasound etc) satellite image etc In a broader context it

implies processing of any 2-D signal using a dedicated hardware eg an application

specific integrated circuit (ASIC) or using a general-purpose computer implementing

some algorithms developed for the purpose

An image is a 2-D function (signal) ( )f x y where x and y are the spatial

(plane) coordinates The magnitude of f at any pair of coordinates (xy) is the

intensity or gray level of the image at that point In a digital image xy and the

magnitude of f are all finite and discrete quantities Each element of this matrix (2-D

array) is called a picture element or pixel Image processing refers to some algorithms

for processing a 2-D image signal ie to operate on the pixels directly (spatial-

domain processing) or indirectly (transform-domain processing) Such a processing

may yield another image or some attributes of the input image at the output

It is a hard task to distinguish between the domains of image processing and

any other related areas such as computer vision Though essentially not correct

image processing may be defined as a process where both input and output are

images At the high level of processing and after some preliminary processing it is

very common to perform some analysis judgment or decision making or perform

some mechanical operation (robot motion) These areas are the domains of artificial

intelligence (AI) computer vision robotics etc

Digital image processing has a broad spectrum of applications such as digital

television photo-phone remote sensing image transmission and storage for business

applications medical processing radar sonar and acoustic image processing



robotics and computer aided manufacturing (CAM) and automated quality control in

industries Fig 11 depicts a typical image processing system [12]

Most of the image-processing functions are implemented in software A

significant amount of basic image processing software is obtained commercially

Major areas of image processing are [126]

(i) Image Representation

(ii) Image Transformation

(iii) Image Enhancement

(iv) Image Restoration

(v) Color Image Processing

(vi) Transform-domain Processing

(vii) Image Compression

(viii) Morphological Image Processing

(ix) Image Representation and Description

(x) Object Recognition

Image processing begins with an image acquisition process Fig 12 illustrates

such a process When illumination energy is incident upon an object it reflects some

part of it depending on its surface-reflectance Thus the image created f(xy) is a 2-D

planar projection of a 3-D object in general and os directly proportional to the

illumination energy i(xy) incident on the object and the reflectance r(xy) of the

object Mathematically it may be expressed as

( ) ( ) ( )f x y K i x y r x y= (11)

where 0 ( )i x ylt lt infin (12)

0 ( ) 1r x ylt lt (13)

and K is a constant for the physical acquisition process

Under perfect ideal conditions the process-constant K is space-invariant and the

whole process of image acquisition is noise-free In fact both the assumptions are

invalid in any practical acquisition system Therefore a practical image contains some

distortion and noise and hence needs to undergo a process of restoration [2]



Fig 12 An example of image acquisition process

(a) illumination energy source (b) an object

(c) imaging system (d) 2-D planar image

(b)

(a)

(c)

(d)

Imaging

System

Sampler and

Quantizer

Digital Storage

System

Digital

Computer

Online

Buffer

Display

Device

Observe Digitize Store Refresh Process Output

Fig11 A typical digital image processing system

Object

Transmitter

Recorder



Image processing may be performed in the spatial-domain or in a transform-

domain To perform a meaningful and useful task a suitable transform eg discrete

Fourier transform (DFT) [1] discrete cosine transform (DCT) [1517] discrete

Hartley transform (DHT) [143-145] discrete wavelet transform (DWT) [10-1418-

21] etc may be employed Depending on the application a suitable transform is

used

Image enhancement techniques are used to highlight certain features of

interest in an image Two important examples of image enhancement are (i)

increasing the contrast and (ii) changing the brightness level of an image so that the

image looks better It is a subjective area of image processing On the other hand

image restoration is very much objective The restoration techniques are based on

mathematical and statistical models of image degradation Denoising (filtering) [4-5]

and deblurring [146-147] tasks come under this category

Image processing is characterized by specific solutions hence a technique that

works well in one area may totally be inadequate in another The actual solution to a

specific problem still requires a significant research and development

Image restoration [126148-149] is one of the prime areas of image

processing and its objective is to recover the images from degraded observations The

techniques involved in image restoration are oriented towards modeling the

degradations and then applying an inverse procedure to obtain an approximation of

the original image Hence it may be treated as a deconvolution operation

Depending on applications there are various types of imaging systems X-ray

Gamma ray ultraviolet and ultrasonic imaging systems are used in biomedical

instrumentation In astronomy the ultraviolet infrared and radio imaging systems are

used Sonic imaging is performed for geological exploration Microwave imaging is

employed for radar applications But the most commonly known imaging systems are

visible light imaging Such systems are employed for applications like remote

sensing microscopy measurements consumer electronics entertainment electronics

etc

The images acquired by optical electro-optical or electronic means are likely

to be degraded by the sensing environment The degradation may be in the form of

sensor noise blur due to camera misfocus relative object camera motion random



atmospheric turbulence and so on [1-2] The noise in an image may be due to a noisy

channel if the image is transmitted through a medium It may also be due to electronic

noise associated with a storage-retrieval system

Noise in an image is a very common problem An image gets corrupted with

different types of noise during the processes of acquisition transmission reception

and storage retrieval Noise may be classified as substitutive noise (impulsive noise

eg salt amp pepper noise random-valued impulse noise etc) and additive noise (eg

additive white Gaussian noise) The impulse noise of low and moderate noise

densities can be removed easily by simple denoising schemes available in the

literature The simple median filter [1360-61] works very nicely for suppressing

impulse noise of low density However now-a-days many denoising schemes [28-40]

are proposed which are efficient in suppressing impulse noise of moderate and high

noise densities In many occasions noise in digital images is found to be additive in

nature with uniform power in the whole bandwidth and with Gaussian probability



arithmetic mean filter commonly known as Mean filter [1-6] can be employed to

suppress AWGN but it introduces a blurring effect

Efficient suppression of noise in an image is a very important issue Denoising

finds extensive applications in many fields of image processing Image denoising is

usually required to be performed before display or further processing like texture

analysis [45-51] object recognition [52-55] image segmentation [56-58] etc

Conventional techniques of image denoising using linear and nonlinear techniques

have already been reported and sufficient literature is available in this area [1-6]

Recently various nonlinear and adaptive filters have been suggested for the

purpose The objectives of these schemes are to reduce noise as well as to retain the

edges and fine details of the original image in the restored image as much as possible

However both the objectives conflict each other and the reported schemes are not

able to perform satisfactorily in both aspects Hence still various research workers are

actively engaged in developing better filtering schemes using latest signal processing



techniques In this doctoral research work efforts have been made in developing

some novel filters to suppress AWGN quite efficiently

12 Noise in Digital Images

In this section various types of noise corrupting an image signal are studied

the sources of noise are discussed and mathematical models for the different types of

noise are presented

121 Sources of Noise

During acquisition transmission storage and retrieval processes an image

signal gets contaminated with noise Acquisition noise is usually additive white

Gaussian noise (AWGN) with very low variance In many engineering applications

the acquisition noise is quite negligible It is mainly due to very high quality sensors

In some applications like remote sensing biomedical instrumentation etc the

acquisition noise may be high enough But in such a system it is basically due to the

fact that the image acquisition system itself comprises of a transmission channel So if

such noise problems are considered as transmission noise then it may be concluded

that acquisition noise is negligible The acquisition noise is considered negligible due

to another fact that the human visual system (HVS) canrsquot recognize a large dynamic

range of image That is why an image is usually quantized at 256 levels Thus each

pixel is represented by 8 bits (1 byte) The present-day technology offers very high

quality sensors that donrsquot have noise level greater than half of the resolution of the

analog-to-digital converter (ADC) ie noise magnitude in time domain ( )8

22

1 Vtn sdotlt

where n(t) is the noise amplitude at any arbitrary instant of time t and V is the

maximum output of the sensor and is also equal to the maximum allowed input

voltage level for the ADC That is for V = 33 volts the noise amplitude should be

less than ~ 65 mV In many practical applications the acquisition noise level is much

below this margin Thus the acquisition noise need not be considered

Hence the researchers are mostly concerned with the noise in a transmission

system Usually the transmission channel is linear but dispersive due to a limited



bandwidth The image signal may be transmitted either in analog form or in digital

form

When an analog image signal is transmitted through a linear dispersive

channel the image edges (step-like or pulse like signal) get blurred and the image

signal gets contaminated with AWGN since no practical channel is noise free If the

channel is so poor that the noise variance is high enough to make the signal excurse to

very high positive or high negative value then the thresholding operation done at the

front end of the receiver will contribute to saturated max and min values Such noisy

pixels will be seen as white and black spots Therefore this type of noise is known as

salt and pepper noise (SPN) In essence if analog image signal is transmitted then the

signal gets corrupted with AWGN and SPN as well Thus there is an effect of mixed

noise

If the image signal is transmitted in digital form through a linear dispersive

channel then inter-symbol interference (ISI) takes place In addition the presence of

AWGN in a practical channel can not be ignored This makes the situation worse Due

to ISI and AWGN it may so happen that a lsquo1rsquo may be recognized as lsquo0rsquo and vice-

versa Under such circumstances the image pixel values have changed to some

random values at random positions in the image frame Such type of noise is known

as random-valued impulse noise (RVIN)

122 Mathematical Representation of Noise

The AWGN SPN and RVIN are mathematically represented below The

Gaussian noise is given by

( )ttn GAWGN η=)( (14)

( ) ( )AWGN G

f f x y x yηrArr = + (15)

where ( )tGη is a random variable that has a Gaussian probability distribution It is an

additive noise that is characterized by its variance 2σ where σ represents its

standard deviation In (15) the noisy image is represented as a sum of the original



uncorrupted image and the Gaussian distributed random noise Gη When the variance

of the random noise Gη is very low ( )G

x yη is zero or very close to zero at many

pixel locations Under such circumstances the noisy image AWGN

f is same or very

close to the original image ( )f x y at many pixel locations ( )x y

Let a digital image ( )f x y after being corrupted with SPN of density d be

represented by SPN

f (xy) Then the noisy image SPN

f (xy) is mathematically

represented as

SPN

with probability 1

( ) 0 2

1 2

f(xy) p d

f x y p d

p d

= minus

= = =

(16)

The impulse noise occurs at random locations ( )x y with a probability of d

The SPN and RVIN are substitutive in nature A digital image corrupted with RVIN

of density d RVIN

f (xy) is mathematically represented as

RVIN

with probability 1( )

( ) with probability

f(xy) p df x y

x y p dη

= minus=

=

(17)

Here ( )x yη represents a uniformly distributed random variable ranging

from 0 to 1 that replaces the original pixel value ( )f x y The noise magnitude at any

noisy pixel location (xy) is independent of the original pixel magnitude Therefore

the RVIN is truly substitutive

Another type of noise that may corrupt an image signal is the speckle noise

(SN) In some biomedical applications like ultrasonic imaging and a few engineering

applications like synthesis aperture radar (SAR) imaging such a noise is encountered



The SN is a signal dependent noise ie if the image pixel magnitude is high then the

noise is also high Therefore it is also known as multiplicative noise and is given by

( ) ( )tSttnSN

)( η= (18)

( ) ( ) ( ) ( ) SN

f x y f x y x y f x yηrArr = + (19)

where ( )tη is a random variable and ( )tS is the magnitude of the signal The noisy

digital image SN

f (xy) is represented mathematically in (19) The noise is

multiplicative since the imaging system transmits a signal to the object and the

reflected signal is recorded In the forward transmission path the signal gets

contaminated with additive noise in the channel Due to varying reflectance of the

surface of the object the reflected signal magnitude varies So also the noise varies

since the noise is also reflected by the surface of the object Noise magnitude is

therefore higher when the signal magnitude is higher Thus the speckle noise is

multiplicative in nature

The speckle noise is encountered only in a few applications like ultrasonic

imaging and SAR whereas all other types of noise ie AWGN SPN and RVIN

occur in almost all the applications The AWGN is the most common among all

Under very low noise variance it may look like RVIN In general some combinations

of AWGN SPN and RVIN may represent a practical noise Such type of noise is

known as mixed noise Some effective schemes are available in the literature [41-44]

for filtration of mixed noise

The proposed filters developed in subsequent chapters are meant for

suppression of AWGN To avoid ambiguity the noisy image is taken as g(xy) in the

subsequent chapters Thus the noisy image is expressed as

( ) ( ) ( )g x y f x y x yη= + (110)

where g(xy) is the same as fAWGN expressed in (15)



13 Literature Review

Noise introduced in an image is usually classified as substitutive (impulsive

noise eg salt amp pepper noise random-valued impulse noise etc) and additive

(eg additive white Gaussian noise) noise

The impulsive noise of low and moderate noise densities can be removed

easily by simple denoising schemes available in the literature The simple median

filter [3] works very nicely for suppressing impulsive noise of low density However

many efficient filters have been developed for removal of impulsive noise of

moderate and high noise densities Chen et al [28] have developed a nonlinear filter

called tri-state median filter for preserving image details while effectively

suppressing impulsive noise The standard median filter and the center weighted

median (CWM) filter are incorporated into noise detection framework to determine

whether a pixel is corrupted before applying the filtering operation A nonlinear non-

iterative multidimensional filter the peak-and-valley filter [29] is developed for

impulsive noise reduction The filter consists of a couple of conditional rules that

identify the noisy pixels and replace their gray level values in a single step F Russo

has developed an evolutionary neural fuzzy system for noise cancellation in image

data [30] The proposed approach combines the advantages of the fuzzy and neural

paradigms The network structure is designed to exploit the effectiveness of fuzzy

reasoning in removing noise without destroying the useful information in input data

Farbiz et al have proposed a fuzzy logic filter for image enhancement [31] It is able

to remove impulsive noise and smooth Gaussian noise Also it preserves edges and

image details H-L Eng and K-K Ma have proposed a noise adaptive soft-switching

(NASM) filter [32] A soft-switching noise-detection scheme is developed to classify

each pixel to be uncorrupted pixel isolated impulsive noise non-isolated impulsive

noise or image objectrsquos edge pixel lsquoNo filteringrsquo a standard median filter or the

proposed fuzzy weighted median filter is then employed according to respective

characteristic type identified T Chen and HR Wu have developed a scheme for

adaptive impulse detection using CWM filters [33] In addition to the removal of

noise from gray images some color image denoising filters [34-40] are also

developed for efficient removal of impulsive noise from color images



In many occasions noise in digital images is found to additive white Gaussian

noise (AWGN) with uniform power in the whole bandwidth and with Gaussian

probability distribution Traditionally AWGN is suppressed using linear spatial

domain filters such as Mean filter [1-6] Wiener filter [12962-64] etc Linear

techniques possess mathematical simplicity but have the disadvantage of yielding

blurring effect They also do not perform well in the presence of signal dependant

noise Nonlinear filters [4] are then developed to avoid the aforementioned

disadvantages The well known nonlinear mean filters such as harmonic mean

geometric mean Lp mean contra-harmonic mean proposed by Pitas et al [5] are

found to be good in preserving edges Another good edge preserving filter is Lee filter

[79] proposed by JS Lee In the flat parts of the signal the output of the Lee filter is

almost equal to the local signal mean But in the rapidly varying parts of signal the

output of the Lee filtering is almost equal to the observed signal value Thus the Lee

filtering can smooth noise and preserve edges efficiently Anisotropic diffusion [67-

68] is also a powerful filter where local image variation is measured at every point

and pixel values are averaged from neighborhoods whose size and shape depend on

local variation Diffusion methods average over extended regions by solving partial

differential equations and are therefore inherently iterative More iteration may lead

to instability where in addition to edges noise becomes prominent Rudin et al

proposed total variation (TV) filter which is also iterative in nature Later a simple

and noniterative scheme for edge preserving smoothing is proposed that is known as

Bilateral filter [70] Bilateral filter combines gray levels or colors based on both their

geometric closeness and their photometric similarity and prefers near values to

distant values in both domain and range A filter named non local means (NL-Means)

[88] is proposed which averages similar image pixels defined according to their local

intensity similarity

T Rabie [110] proposed a simple blind denoising filter based on the theory of

robust statistics Robust statistics addresses the problem of estimation when the

idealized assumptions about a system are occasionally violated The contaminating

noise in an image is considered as a violation of the assumption of spatial coherence

of the image intensities and is referred as an outlier system A denoised image is

estimated by fitting a spatially coherent stationary image model to the available noisy



data using a robust estimator-based regression method within an optimal size adaptive

window Another robust image denoising method based on the bi-weight mid-

regression is proposed by Hou et al [116] is found to be effective in suppressing

AWGN Kernel regression is a nonparametric class of regression method used for

image denoising [119]

F Russo [111] proposed a new method for automatic enhancement of noisy

images The most relevant feature of the proposed approach is a novel procedure for

automatic tuning that takes into account the histograms of the edge gradients

Fuzzy techniques can be applied to develop filters for suppression of additive

noise Ville et al [113] proposed a fuzzy filter for suppression of AWGN The filter

consists of two stages The first stage computes a fuzzy derivative for eight different

directions The second stage uses these fuzzy derivatives to perform fuzzy smoothing

by weighting the contributions of neighboring pixel values The filter can be applied

iteratively to effectively reduce high noise

Kervrann et al [114] developed a novel adaptive and patch-based approach

for image denoising and representation The method is based on a pointwise selection

of small image patches of fixed size in the variable neighborhood of each pixel This

method is general and can be applied under the assumption that there exist repetitive

patterns in a local neighborhood of a point

A novel method using adaptive principal components is proposed by Mureson

and Parks [115] for suppression of AWGN The method uses principal components on

a local image patches to derive a 2-D locally adaptive basis set The local principal

components provide the best local basis set and the largest eigenvector is in the

direction of the local image edge

Dabov et al [121] proposed a novel image denoising strategy based on an

enhancement sparse representation in transform-domain The enhancement of sparsity

is achieved by grouping similar 2-D image fragments (eg blocks) into 3-D data

arrays which is called as ldquogroupsrdquo Collaborative filtering is a special procedure

developed to deal with these 3-D groups The filter is realized with three successive

steps 3-D transformation of a group shrinkage of the transform spectrum and

inverse 3-D transformation



A spatial adaptive denoising method is developed by M Mignotte [122] which

is based on an averaging process performed on a set of Markov Chain Monte-Carlo

simulations of region partition maps constrained to be spatially piecewise uniform

(ie constant in the grey level value sense) for each estimated constant-value regions

For the estimation of these region partition maps the unsupervised Markovian

framework is adopted in which parameters are automatically estimated in least square

sense

Hirakawa et al [123] proposed an image denoising scheme using total least

squares (TLS) where an ideal image patch is modeled as a linear combination of

vectors cropped from the noisy image The model is fitted to the real image data by

allowing a small perturbation in the TLS sense

Shen et al [125] designed nonseparable Parseval frames from separable

(tensor) products of a piecewise linear spline tight frame These nonseparable

framelets are capable of detecting first and second order singularities in directions that

are integral multiples of 450 Using these framelets two image denoising algorithms

are proposed for suppression of AWGN

A new class of fractional-order anisotropic diffusion equations for image

denoising is proposed in [128] for noise removal These equations are Euler-Lagrange

equations of a cost functional which is an increasing function of the absolute value of

the fractional derivative of the image intensity function so the proposed equations can

be seen as generalization of second-order and fourth-order anisotropic diffusion

equations

Now-a-days wavelet transform is employed as a powerful tool for image

denoising [98-106 129-136] Image denoising using wavelet techniques is effective

because of its ability to capture most of the energy of a signal in a few significant

transform coefficients when natural image is corrupted with Gaussian noise Another

reason of using wavelet transform is due to development of efficient algorithms for

signal decomposition and reconstruction [59] for image processing applications such

as denoising and compression Many wavelet-domain techniques are already available

in the literature Out of various techniques soft-thresholding proposed by Donoho and

Johnstone [98] is most popular The use of universal threshold to denoise images in

wavelet domain is known as VisuShrink [99] In addition subband adaptive systems



having superior performance such as SureShrink [100101] BayesShrink [102]

NeighShrink [103] SmoothShrink [104] are available in the literature Bala et al

[129] proposed a multivariate thresholding technique for image denoising using

multiwavelets The proposed technique is based on the idea of restoring the spatial

dependence of the pixels of the noisy image that has undergone a multiwavelet

decomposition Coefficients with high correlation are regarded as elements of a vector

and are subject to a common thresholding operation In [130] translation-invariant

contourlet transform is used for image denoising

A number of recent approaches for denosing have taken advantage of joint

statistical relationships by adaptively estimating the variance of a coefficient from a

local neighborhood consisting of coefficients within a sub-band One such method

where statistical relationship of coefficients in a neighborhood is considered is locally

adaptive window maximum likelihood (LAWML) estimation [105] It is important to

construct a statistical model in order to accurately estimate the signal In [106] a

Hidden Markov Model is used in wavelet domain for denoising where the existence

of significant spatial dependencies in the transform coefficients are recognized and

these dependencies are described using data structures P Shui and Y Zhao [117]

proposed an image denoising algorithm using doubly local Wiener filtering with

block-adaptive windows in wavelet domain In [120] M Kazubek demonstrated that

denoising performance of the Wiener filtering can be increased by preprocessing

images with a thresholding operation in wavelet-domain

Tan et al [112] proposed a wavelet domain denoising algorithm by combining

the expectation maximization scheme and the properties of the Gaussian scale mixture

models The algorithm is iterative in nature and the number of iterations depends on

the noise variance For high variance Gaussian noise the method undergoes many

iterations and therefore the method is computational-intensive

J Ma and G Plonka [118] proposed diffusion-based curvelet shrinkage is

proposed for discontinuity-preserving denoising using a combination of a new tight

frame of curvelets with a nonlinear diffusion scheme In order to suppress the pseudo-

Gibbs and curvelet-like artifacts the conventional shrinkage results are further

processed by a projected total variation diffusion where only the insignificant curvelet



coefficients or high-frequency part of signal are changed by use of a constrained

projection

Portilla et al [124] developed a method for removing noise from digital

images based on a statistical model of the coefficients of an over-complete multiscale

oriented basis Neighborhoods of coefficients at adjacent positions and scales are

modeled as a product of two independent random variables a Gaussian vector and a

hidden positive scalar mulitiplier The latter modulates the local variance of the

coefficients in the neighborhood and is thus able to account for the empirically

observed correlation between the coefficientsrsquo amplitudes Under this model the

Baysian least squares estimate of each coefficient reduces to a weighted average of

the local linear estimates over all possible values of the hidden multiplier variable

Some fractal-wavelet image denoising schemes are explained in [126] Zhong

and Ning [127] proposed a very efficient algorithm for image denoising based on

wavelets and multifractals for singularity detection By modeling the intensity surface

of a noisy image as statistically self-similar multifractal process and taking advantage

of the multiresolution analysis with wavelet transform to exploit the local statistical

self-similarity at different scales the point-wise singularity strength value

characterizing the local singularity at each scale was calculated By thresholding the

singularity strength wavelet coefficients at each scale were classified into two

categories the edge-related and regular wavelet coefficients and the irregular wavelet

coefficients The irregular wavelet coefficients were denoised using an approximate

minimum mean-squared error (MMSE) estimation method while the edge-related and

regular wavelet coefficients were smoothed using the fuzzy weighted mean (FWM)

filter preserving the edges and details when reducing noise

Many color image denoising techniques [137-142] are available in the

literature for suppression of AWGN Lian et al [139] proposed an edge preserving

image denoising via optimal color space projection method SURE-LET multichannel

image denoising is proposed by F Luiser and T Blu [141] where the denoising

algorithm is parameterized as a linear expansion of thresholds (LET) and optimized

using Steinrsquos unbiased risk estimate (SURE) A non-redundant orthonormal wavelet

transform is first applied to the noisy data followed by the (subband-dependent)

vector-valued thresholding of individual multi-channel wavelet coefficients which are



finally brought back to the image domain by inverse wavelet transform Lian et al

[142] proposed a color image denoising technique in wavelet domain for suppression

of AWGN The proposed method is based on minimum cut algorithm where the inter-

scale and intra-scale correlations of wavelet coefficients are exploited to suppress the

additive noise Some blind techniques using independent component analysis (ICA)

[151152] for image denoising are available in the literature But none of the filters

available in literature is able to achieve perfect restoration Further there is a need to

reduce computational complexity of a filtering algorithm for its use in real-time

applications

Hence it may be concluded that there is enough scope to develop better

filtering schemes with very low computational complexity that may yield high noise

reduction as well as preservation of edges and fine details in an image

14 The Problem Statement

In the present research work efforts are made to develop many efficient

filtering schemes to suppress AWGN For real-time applications like television

photo-phone etc it is essential to reduce the noise power as much as possible and to

retain the fine details and the edges in the image as well Moreover it is very

important to have very low computational complexity so that the filtering operation is

performed in a short time for online and real-time applications

Thus the problem taken for this research work is ldquoDevelopment of Efficient

Image Filters to suppress AWGN for Online and Real-Time Applicationsrdquo Since

linear filters donrsquot perform well nonlinear filtering schemes are adopted for achieving

better performance The processing may be done in spatial-domain or in transform-

domain

Therefore the objective of this doctoral research work is to develop some

novel spatial-domain and transform-domain digital image filters for efficient

suppression of additive white Gaussian noise



15 Image Metrics

The quality of an image is examined by objective evaluation as well as

subjective evaluation For subjective evaluation the image has to be observed by a

human expert The human visual system (HVS) [109] is so complicated that it is not

yet modeled properly Therefore in addition to objective evaluation the image must

be observed by a human expert to judge its quality

There are various metrics used for objective evaluation of an image Some of

them are mean squared error (MSE) root mean squared error (RMSE) mean absolute

error (MAE) and peak signal to noise ratio (PSNR) [7107]

Let the original noise-free image noisy image and the filtered image be

represented by ( )f x y ( )g x y and ˆ ( )f x y respectively Here x and y represent

the discrete spatial coordinates of the digital images Let the images be of size MtimesN

pixels ie x=123hellipM and y=123hellipN Then MSE and RMSE are defined as

( )1 1

2ˆ ( ) ( )

M N

x y

f x y f x y

M NMSE = =

minus

times

sumsum= (111)

MSERMSE = (112)

The MAE is defined as

( )1 1

ˆ ( ) ( )

M N

x y

f x y f x y

M NMAE = =

minus

times

sumsum= (113)

The PSNR is defined in logarithmic scale in dB It is a ratio of peak signal

power to noise power Since the MSE represents the noise power and the peak signal

power is unity in case of normalized image signal the image metric PSNR is defined

as

)1(log10 10 MSEPSNR = dB (114)



For the color image processing the color peak signal to noise ratio (CPSNR)

[142] in decibel is used as performance measure The CPSNR is defined as

1

10

110 log

3c

c R G B

CPSNR MSE

minus

isin

= sdot

sum dB (115)

where MSEc is the mean squared error in a particular channel of the color space

Though these image metrics are extensively used for evaluating the quality of

a restored (filtered) image and thereby the capability and efficiency of a filtering

process none of them gives a true indication of noise in an image It is very important

to note that RMSE MAE and PSNR are all related to MSE In addition to these

parameters a new metric universal quality index (UQI) [108] is extensively used in

literature to evaluate the quality of an image now-a-days Further some parameters

eg method noise [88] and execution time [150] are also used in literature to evaluate

the filtering performance of a filter These parameters are discussed below

Universal Quality Index

The universal quality index (UQI) is modeled by considering three different

factors (i) loss of correlation (ii) luminance distortion and (iii) contrast distortion It

is defined by

where

( ) ( )ˆ ˆ

2 2 22

ˆ ˆ

ˆ 22

ˆ

ff f f

f ff f

f fUQI

f f

σ σ σ

σ σ σ σ= sdot sdot

++

1 1

1 1

1( )

1ˆ ˆ( )

M N

x y

M N

x y

f f x yM N

f f x yM N

= =

= =

=times

=times

sumsum

sumsum

( )

( )

22

1 1

22

ˆ

1 1

1( )

1

1 ˆ ˆ( )1

M N

f

x y

M N

fx y

f x y fM N

f x y fM N

σ

σ

= =

= =

= minustimes minus

= minustimes minus

sumsum

sumsum

( )( )ˆ

1 1

1 ˆ ˆ( ) ( )1

M N

f fx y

f x y f f x y fM N

σ= =

= minus minustimes minus

sumsum

(119)

(120)

(121)

(118)

(117)

(116)



The UQI defined in (116) consists of three components The first component

is the correlation coefficient between the original noise-free image f and the restored

image f that measures the degree of linear correlation between them and its

dynamic range is [-11] The second component with a range of [0 1] measures the

closeness between the average luminance of f and f It reaches the maximum value

of 1 if and only if f equals f The standard deviations of these two images fσ and

fσ are also regarded as estimates of their contrast-levels So the third component in

(116) is necessarily a measure of the similarity between the contrast-levels of the

images It ranges between 0 and 1 and the optimum value of 1 is achieved only when

fσ =f

σ

Hence combining the three parameters (i) correlation (ii) average luminance

similarity and (iii) contrast-level similarity the new image metric universal quality

index (UQI) becomes a very good performance measure

Method Noise

Since linear filters do not perform well nonlinear filters are predominantly

used for suppressing AWGN from an image But an image denoising filter degrades

even an original noise-free input image due to its inherent nonlinear characteristics In

many occasions it unnecessarily yields some noise at the output This is quite

undesirable

The method noise [8889] MN of a filter is defined as noise in the output

image when the input is noise-free It is described as an error voltage level in terms of

its mean absolute value The method noise is defined as

1 =1

M

( )x y

x y==

times

sumsumM N

M N

N

N (122)

where Mˆ( ) ( ) ( )x y f x y f x y= minusN (123)



( )ˆ ( ) ( )f x y T f x y= (124)

T() is the method (filtering operation)

Execution Time

Execution Time (TE) of a filter is defined as the time taken by a digital

computing platform to execute the filtering algorithm when no other software except

the operating system (OS) runs on it

Though TE depends essentially on the computing systemrsquos clock time-period

yet it is not necessarily dependant on the clock time alone Rather in addition to the

clock-period it depends on the memory-size the input data size and the memory-

access time etc

The execution time taken by a filter should be low for online and real-time

image processing applications Hence a filter with lower TE is better than a filter

having higher TE value when all other performance-measures are identical

Since the execution time is platform dependant some standard hardware

computing platforms SYSTEM-1 SYSTEM-2 and SYSTEM-3 presented in

Table-11 are taken for the simulation work Thus the TE parameter values for the

various existing and proposed filters are evaluated by running these filtering

algorithms on these platforms

Table-11 Details of hardware platforms (along with their operating system) used for simulating

the filters

Hardware platforms Processor Clock (GHz) RAM (GB) Operating System (OS)

SYSTEM-1 Pentium IV Core 2 Duo

Processor

24 2 Windows Vista 64 bit OS

SYSTEM-2 Pentium IV Duo Processor 28 1 Windows XP 32 bit OS

SYSTEM-3 Pentium IV Processor 17 1 Windows XP 32 bit OS



16 Chapter-wise Organization of the Thesis

The chapter-wise organization of the thesis is outlined


Preview



Literature Review

Problem Statement

Image Metrics

Chapter-wise Organization of Thesis

Conclusion

Chapter-2 Study of Image Denoising Filters

Preview

Order Statistics Filter

Wiener and Lee Filter

Anisotropic Diffusion (AD) and Total Variation (TV) Filters

Bilateral Filter

Non-local Means (NL-means) Filter

Wavelet Domain Filters

Simulation Results

Conclusion

Chapter-3 Development of Novel Spatial-Domain Image Filters

Preview

Development of Adaptive Window Wiener Filter

Development of Circular Spatial Filter

Simulation Results

Conclusion

Chapter-4 Development of Transform-Domain Filters

Preview

Development of Gaussian Shrinkage based DCT-domain Filter



Development of Total Variation based DWT-domain Filter

Development of Region Merging based DWT-domain Filter

Simulation Results

Conclusion

Chapter-5 Development of Some Color Image Denoising Filters

Preview

Multi-Channel Color Image Filtering

Multi-Channel Mean Filter

Multi-Channel LAWML Filter

Development of Multi-Channel Circular Spatial Filter

Development of Multi-Channel Region Merging based DWT-domain Filter

Simulation Results

Conclusion

Chapter-6 Conclusion Preview

Comparative Analysis

Conclusion

Scope for Future Work

17 Conclusion

In this chapter the fundamentals of digital image processing sources of noise

and types of noise in an image the existing filters and their merits and demerits and

the various image metrics are discussed It is obvious that AWGN is the most

important type of noise during acquisition and transmission processes Hence in

common applications like television photo-phone etc the digital images are

supposed to be corrupted with AWGN quite often Therefore it is decided to make

efforts to develop efficient filters to suppress additive noise The various metrics for

describing and quantifying the qualities of an image as well those of a filtering

process are discussed and analyzed here In addition details of various hardware

platforms on which the filtering algorithms are run are mentioned for further

reference in the subsequent chapters

Chapter 2

Study of Image

Denoising Filters


Development of Some Spatial-Domain and Transform-Domain Digital Image Filters 26

Preview

Image denoising is a common procedure in digital image processing aiming at

the suppression of additive white Gaussian noise (AWGN) that might have corrupted

an image during its acquisition or transmission This procedure is traditionally

performed in the spatial-domain or transform-domain by filtering In spatial-domain

filtering the filtering operation is performed on image pixels directly The main idea

behind the spatial-domain filtering is to convolve a mask with the whole image The

mask is a small sub-image of any arbitrary size (eg 3times3 5times5 7times7 etc) Other

common names for mask are window template and kernel An alternative way to

suppress additive noise is to perform filtering process in the transform-domain In

order to do this the image to be processed must be transformed into the frequency

domain using a 2-D image transform Various image transforms such as Discrete

Cosine Transform (DCT) [21517] Singular Value Decomposition (SVD) Transform

[2] Discrete Wavelet Transform (DWT) [10-1418-21] etc are used

In this chapter various existing spatial-domain and transform-domain image

denoising filters are studied and their filtering performances are compared They are

2



some well-known standard and benchmark filters available in literature Novel filters

designed and developed in this research work are compared against these filters in

subsequent chapters Therefore attempts are made here for detailed and critical

analysis of these existing filters

The organization of the chapter is given below

Order Statistics Filters



Bilateral Filter

Non-local Means (NL-Means) Filter


Simulation Results

Conclusion

21 Order Statistics Filters

Usually sliding window technique [126] is employed to perform pixel-by-pixel

operation in a filtering algorithm The local statistics obtained from the neighborhood

of the center pixel give a lot of information about its expected value If the

neighborhood data are ordered (sorted) then ordered statistical information is

obtained If this order statistics vector is applied to a finite impulse response (FIR)

filter then the overall scheme becomes an order statistics (OS) filter [156061]

For example if a 3times3 window is used for spatial sampling then 9 pixel data are

available at a time First of all the 2-D data is converted to a 1-D data ie a vector

Let this vector of 9 data be sorted Then if the mid value (5th

position pixel value in

the sorted vector of length = 9) is taken it becomes median filtering with the filter

weight vector [0 0 0 0 1 0 0 0 0] If all the order statistics are given equal weightage

then it becomes a moving average or mean filter (MF) Strictly speaking the MF is a

simple linear filter and it has nothing to do with the ordered statistics Since the MF

operation gives equal emphasis to each input data it is immaterial whether the input

vector is sorted or not Thus simply to have a generalization of OS filters the MF is



considered a member of this class Otherwise it is quite different from all other

members of this family of filters The median (MED) alpha-trimmed mean (ATM)

min max filters are some members of this interesting family

211 Mean and Median Filters

The moving average or mean filter (MF) is a simple linear filter [1-6] All the

input data are summed together and then the sum is divided with the number of data

It is very simple to implement in hardware and software The computational

complexity is very low It works fine for low power AWGN As the noise power

increases its filtering performance degrades If the noise power is high then a larger

window should be employed for spatial sampling to have better local statistical

information As the window size increases MF produces a reasonably high blurring

effect and thus thin edges and fine details in an image are lost

The median (MED) filter [36061] on the other hand is a nonlinear filter The

median is a very simple operation Once the sorting (ordering) operation is performed

on the input vector the job is done as the mid-value is taken as the output Of course

if the length of the input vector is even then the average of two mid-ordered statistical

data is taken as output Usually such a computation is not required in most of image

processing applications as the window length is normally an odd number Thus the

MED operation can be completed in a very short time That is a MED filter may be

used for online and real-time applications to suppress noise If an image is corrupted

with a very low variance AWGN then this filter can perform a good filtering

operation [42]

212 Alpha Trimmed Mean Filter

The alpha-trimmed mean (ATM) filter [1] is based on order statistics and

varies between a median and mean filter It is so named because rather than

averaging the entire data set a few data points are removed (trimmed) and the

remainders are averaged The points which are removed are most extreme values

both low and high with an equal number of points dropped at each end (symmetric



trimming) In practice the alpha-trimmed mean is computed by sorting the data low

to high and summing the central part of the ordered array The number of data values

which are dropped from the average is controlled by trimming parameter alpha

Let g(st) be a sub-image of noisy image g(xy) Suppose the 2

α lowest and the

2

α highest gray-level values of g(st) are deleted in the neighborhood Sxy Let gr(st)

represent the remaining mn αminus pixels A filter formed by averaging these remaining

pixels is called alpha trimmed mean filter which can be expressed as

( )

1ˆ( ) ( )xy

r

s t S

f x y g s tmn α isin

=minus

sum (21)

The alpha-trimmed mean also known as Rank-Ordered Mean (ROM) filter is

used when an image is corrupted with mixed noise (both Gaussian and salt amp pepper

noise) [42] Choice of parameterα is very critical and it determines the filtering

performance Hence the ATM filter is usually employed as an adaptive filter whose

α may be varied depending on the local signal statistics Therefore it is a

computation-intensive filter as compared to simple mean and median filter Another

problem of ATM is that the detailed behavior of the signal cannot be preserved when

the filter window is large

22 Wiener Filter and Lee Filter

The Wiener filter [962-64] and Lee filter [79-89] are spatial-domain filters

which are developed long back and are used for suppression of additive noise The

details of these two filters are explained below

221 Wiener Filter

Norbert Wiener proposed the concept of Wiener filtering in the year 1942

[16] There are two methods (i) Fourier-transform method (frequency-domain) and

(ii) mean-squared method (spatial-domain) for implementing Wiener filter The

former method is used only for complete restoration (denoising and deblurring)



whereas the later is used for denoising In Fourier transform method of Wiener

filtering normally it requires a priori knowledge of the power spectra of noise and the

original image But in mean-squared method no such a priori knowledge is required

Hence it is easier to use the mean-squared method for image denoising Wiener filter

is based on the least-squared principle ie the filter minimizes the mean-squared

error (MSE) between the actual output and the desired output

Image statistics vary too much from a region to another even within the same

image Thus both global statistics (mean variance etc of the whole image) and

local statistics (mean variance etc of a small region or sub-image) are important

Wiener filtering is based on both the global statistics and local statistics and is given

by

( )2

2 2ˆ ( ) ( )

f

f n

f x y g g x y gσ

σ σ= + minus

+ (22)

where g is the local mean 2

fσ is the local signal variance 2

nσ is the noise variance

and ˆ ( )f x y denotes the restored image

For (2a+1) times (2b+1) window of noisy image g(x y) the local mean g and local

variance 2

gσ are defined by

1( )

a b

s a t b

g g s tL = minus = minus

= sum sum (23)

where L is the total number of pixels in a window ie L = (2a+1) times (2b+1)

and

( )22 1

( )1

a b

g

s a t b

g s t gL

σ= minus = minus

= minusminussum sum (24)

The local signal variance 2

fσ used in (22) is calculated from 2

gσ with a priori

knowledge of noise variance 2

nσ simply by subtracting 2

nσ from 2

gσ with the

assumption that the signal and noise are not correlated with each other

From (22) it may be observed that the filter-output is equal to local mean if

the current pixel value equals local mean Otherwise it outputs a different value the



value being some what different from local mean If the input current value is more

(less) than the local mean then the filter outputs a positive (negative) differential

amount taking the noise variance and the signal variance into consideration Thus the

filter output varies from the local mean depending upon the local variance and hence

tries to catch the true original value as far as possible

In statistical theory Wiener filtering is a great land mark It estimates the

original data with minimum mean-squared error and hence the overall noise power in

the filtered output is minimal Thus it is accepted as a benchmark in 1-D and 2-D

signal processing

222 Lee Filter

The Lee filter [79-82] developed by Jong-Sen Lee is an adaptive filter which

changes its characteristics according to the local statistics in the neighborhood of the

current pixel The Lee filter is able to smooth away noise in flat regions but leaves

the fine details (such as lines and textures) unchanged It uses small window (3times3

5times5 7times7) Within each window the local mean and variances are estimated

The output of Lee filter at the center pixel of location (x y) is expressed as

[ ]ˆ ( ) ( ) ( )f x y k x y g x y g g= minus + (25)

where

22 2

2

2 2

1 ( )

0

n

g n

g

g n

k x y

σσ σ

σ

σ σ

minus gt

= le

(26)

The parameter k(x y) ranges between 0 (for flat regions) and 1 (for regions

with high signal activity)

The distinct characteristic of the filter is that in the areas of low signal activity

(flat regions) the estimated pixel approaches the local mean whereas in the areas of

high signal activity (edge areas) the estimated pixel favors the corrupted image pixel

thus retaining the edge information It is generally claimed that human vision is more

sensitive to noise in a flat area than in an edge area The major drawback of the filter

is that it leaves noise in the vicinity of edges and lines However it is still desirable to

reduce noise in the edge area without sacrificing the edge sharpness Some variants of



Lee filter available in the literature handle multiplicative noise and yield edge

sharpening [83-87]

23 Anisotropic Diffusion (AD) Filter and Total Variation (TV) Filter

Anisotropic Diffusion (AD) and Total Variation (TV) filters are used for

suppressing AWGN from images [6769] The methods are iterative in nature and

they need more iterations as noise variance increases

231 Anisotropic Diffusion (AD) Filter

It has been proven that it is necessary to extract a family of derived images of

multiple scales of resolution in order to be able to identify global objects through

blurring [6566] and that this may be viewed equivalently as the solution of the heat

conduction or diffusion equation given by

2tg C g= nabla (27)

where t

g is the first derivative of the image signal g in time t and 2nabla is the

Laplacian operator with respect to space variables respectively In (27) C is

considered as a constant independent of space location There is no fundamental

reason why this must be so Koenderink [66] considered it so because it simplifies the

analysis greatly Perona and Malik [67] developed a smoothing scheme based on

anisotropic diffusion filtering that overcomes the major drawbacks of conventional

spatial smoothing filters and improves the image quality significantly Perona and

Malik considered the anisotropic diffusion equation as

2

( )[ ( ) ( )]

( )

t

g x y tg div C x y t g x y t

t

C x y t g C g

part= = nabla

part

= nabla + nabla nabla

(28)

where div and nabla define the divergence and gradient operators with respect to space

variables respectively By letting C(x y t) be a constant (28) reduces to (27) the

isotropic diffusion equation



In [68] Perona and Malik considered the image gradient as an estimation of

edges and ( )C U g= nabla in which U() has to be a nonnegative monotonically

decreasing function with U(0) = 1 (in the interval of uniform region) and tends to zero

at infinity There are some possible choices for U() the obvious being a binary

valued function Some other functions [68] could be

2

2( ) exp

sU s

k

= minus

(29)

or

2

1( )

1

U ss

k

=

+

(210)

where k is the threshold level for removing noise Equation (28) can be discretized

using four nearest neighbors (north south east west) and the Laplacian operator [4]

as given by

[ ]1( ) ( ) ( ) ( ) ( ) ( )nn n

N N S S W W E Eg x y g x y C g x y C g x y C g x y C g x yλ+ = + nabla + nabla + nabla + nabla 211)

where 1( )ng x y

+ is the discrete value of g(xy) in the (n+1)th iteration set by n as g is

determined by t in continuous space It follows that

( )( )N N

C U g x y= nabla

( ) ( 1 ) ( )N

g x y g x y g x ynabla = minus minus (212a)

( )( )S SC U g x y= nabla

( ) ( 1 ) ( )Sg x y g x y g x ynabla = + minus (212b)

( )( )W WC U g x y= nabla

( ) ( 1) ( )W g x y g x y g x ynabla = minus minus (212c)

( )( )E E

C U g x y= nabla

( ) ( 1) ( )Eg x y g x y g x ynabla = + minus (212d)

and λ is a single parameter needed for stability [68]

The filtered image is then 1ˆ ( ) ( )nf x y g x y

+=



232 Total Variation (TV) Filter

Rudin et al proposed Total variation (TV) [69] which is a constrained

optimization type of numerical algorithm for removing noise from images The total

variation of the image is minimized subject to constraints involving the statistics of

the noise The constraints are imposed using Lagrange multipliers The solution is

obtained using the gradient-projection method This amounts to solving a time

dependent partial differential equation on a manifold determined by the constraints

As trarrinfin the solution converges to a steady state which is the denoised image

In total variation algorithm the gradients of noisy image g(xy) in four

directions (East West North and South) are calculated The gradients in all four

directions are calculated as follows

( )( ) ( ) ( 1 )N g x y g x y g x ynabla = minus minus (213a)

( )( ) ( 1 ) ( )Sg x y g x y g x ynabla = + minus (213b)

( )( ) ( ) ( 1)W g x y g x y g x ynabla = minus minus (213c)

( )( ) ( 1) ( )E g x y g x y g x ynabla = + minus (213d)

where nabla is the gradient operator

The noisy image undergoes several iterations to suppress AWGN The

resulted output image after (n+1) iterations is expressed as

(214)

( ) ( )( )

( ) ( )( )

( )

1

22

22

( ) ( )

( )

( ) ( ) ( )

( )

( ) ( ) ( )

( ) ( )

n n

n

SN

n n n

S E W

n

EW

n n n

E S N

n n

g x y g x y

g x yt

hg x y m g x y g x y

g x y

g x y m g x y g x y

t g x y g x yλ

+ =

nabla∆

+ nabla nabla + nabla nabla

nabla


minus ∆ minus



where

( )

( ) min mod( )

sgn sgnmin

2

m a b a b

a ba b

=

+ =

(215)

where

1 0sgn( )

1 0

xx

x

ge=

minus lt (216)

In (214) lsquoλrsquo is a controlling parameter lsquo t∆ rsquo is the discrete time-step and lsquohrsquo is a

constant

A restriction imposed for stability is given by

2

tc

h

∆le (217)

where lsquocrsquo is a constant


+=



24 Bilateral Filter

The Bilateral filter [70] a nonlinear filter proposed by Tomasi and Manduchi

is used to suppress additive noise from images Bilateral filtering smooths images

while preserving edges by means of a nonlinear combination of nearby image values

The method is noniterative local and simple It combines gray levels or colors based

on both their geometric closeness and their photometric similarity and prefers near

values to distant values

The Bilateral filter kernel w is a product of two sub-kernels (weighing

functions)

(i) photometric (gray-level) kernel wg and

(ii) geometric (distance) kernel wd

The gray-level distance (ie photometric distance) between any arbitrary pixel

of intensity value g(x1 y1) at location (x1 y1) with respect to its center pixel of

intensity value g(x y) at location (x y) is given by

122 2

1 1( ) ( )gd g x y g x y = minus (218)

The photometric or gray-level sub-kernel is expressed by

2

1exp

2

g

g

g

dw

σ

= minus

(219)

where lsquo gσ rsquo is the distribution function for gw

The spatial distance (ie geometric distance) between any arbitrary pixel at a

location (x1 y1) with respect to the center pixel at location (x y) is the Euclidean

distance given by

( ) ( )2 2

1 1sd x x y y= minus + minus (220)



The geometric or distance sub-kernel is defined by

2

1exp

2

sd

d

dw

σ

= minus

(221)

where lsquodσ rsquo is the standard deviation of the distribution function

dw

The kernel for bilateral filter is obtained by multiplying the two sub-kernels

gw and dw

b g dw w w= (222)

The estimated pixel ˆ ( )f x y resulted after sliding the filtering kernel

bw throughout the noisy image is

( ) ( )ˆ ( )

( )

a b

b

s a t b

a b

b

s a t b

w s t g x s y t

f x y

w s t

=minus =minus

=minus =minus

+ +

=sum sum

sum sum (223)

The filter has been used for many applications such as texture removal [71]

dynamic range compression [72] photograph enhancement [7374] It has also been

adapted to other domains such as mesh fairing [7576] volumetric denoising [77] and

exposure corrections of videos [78] The large success of bilateral filter is because of

various reasons such as its simple formulation and implementation The bilateral filter

is also non-iterative ie it achieves satisfying results with only a single pass



25 Non-local Means (NL-Means) Filter

NL-means filter [8889] introduced by Buades et al is based on the natural

redundancy of information in images It is due to the fact that every small window in

a natural image has many similar windows in the same image The property of this

filter is that the similarity of pixels has been more robust to noise by using a region

comparison rather than pixel comparison and also that matching patterns are not

restricted to be local That is the pixels far away from the pixel being filtered are not

penalized

Non-local Means Theory

The NL-Means algorithm assumes that the image contains an extensive

amount of self-similarity Efros and Leung originally developed the concept of self-

similarity for texture synthesis [90] An example of self-similarity is displayed in

Fig 21 It shows three pixels p q1 and q2 and their respective neighborhoods The

neighborhoods of pixels p and q1 are similar but that of p and q2 are dissimilar

Adjacent pixels tend to have similar neighborhoods but non-adjacent pixels will also

have similar neighborhoods when there are similar structures in the image [88] For

example in this figure most of the pixels in the same column as p will have similar

neighborhoods to prsquos neighborhood The self-similarity assumption can be exploited

to denoise an image Pixels with similar neighborhoods can be used to determine the

denoised value of a pixel



Non-local Means Method

Given an image g the filtered value at a point p located at (xy) using the

NL-Means method is calculated as a weighted average of all the pixels in the image

using the following formula

( ) [ ]1 1

1 1

( )

ˆ ( ) ( ) ( ) ( ) ( )x y

f x y NL g x y w x y x y g x yforall

= = sum (224)

[ ] [ ]1 1

1 1 1 1

( )

0 ( ) ( ) 1 ( ) ( ) 1x y

with w x y x y and w x y x yforall

le le =sum (225)

where (x1y1) represents any other image pixel location such as q1 and q2

p

q1

q2

Fig 21 Example of self-similarity in an image

Pixels p and q1 have similar neighborhoods but pixels p and q2

do not have similar neighborhoods Because of this pixel q1 will

have a stronger influence on the denoised value of p than q2



The weights [ ]1 1( )( )w x y x y are based on the similarity between the neighborhoods

of p and any arbitrary pixel q with a user defined radius Rsim The similarity of

[ ]1 1( )( )w x y x y is then calculated as

[ ][ ]1 1

1 1 2

( ) ( )1( ) ( ) exp

p

d x y x yw x y x y

Z h

= minus

(226)

[ ]

1 1

1 1

2( )

( ) ( )expp

x y

d x y x yZ

hforall

= minus

sum (227)

where Zp is the normalizing constant and h is an exponential decay control parameter

The parameter d is a Gaussian weighted Euclidian distance of all the pixels

of each neighborhood

[ ] ( )( ) ( )( )1 1

2

1 1 ( ) ( )

sim

x y x yR

d x y x y G g N g Nσ= minus (228)

N(xy) pixel located at (xy) with its neighborhood

( )1 1x yN any arbitrary pixel located at (x1y1) with its neighborhood

where Gσ is a normalized Gaussian weighting function with zero mean and standard

deviation of σ (usually set to 1) that penalizes pixels far from the center of the

neighborhood window by giving more weight to pixels near the center The center

pixel of the Gaussian weighting window is set to the same value as that of the pixels

at a distance 1 to avoid over-weighting effects

When the pixel to be filtered is compared with itself the self similarity will be very

high which will lead to over-weighting effect To avoid such situation

[ ]( ) ( )w x y x y is calculated as

[ ] ( ) ( )( ) ( ) ( )1 1 1 1( )( ) max w x y x y w x y x y x y x y= forall ne (229)



Non-local Means Parameters

The non-local means algorithm has three parameters The first parameter h is

the weight-decay control parameter which controls where the weights lay on the

decaying exponential curve If h is set too low not enough noise will be removed If

h is set too high the image will become blurred When an image contains white noise

with a standard deviation of σn h should be set between 10 σn and 15 σn [8889]

The second parameter Rsim is the radius of the neighborhoods used to find

the similarity between two pixels If Rsim is too large no similar neighborhoods will

be found but if it is too small too many similar neighborhoods will be found

Common values for Rsim are 3 and 4 to give neighborhoods of size 7times7 and 9times9

respectively [8889]

The third parameter Rwin is the radius of a search window Because of the

inefficiency of taking the weighted average of every pixel for every pixel it will be

reduced to a weighted average of all pixels in a window The window is centered at

the current pixel being computed Common values for Rwin are 7 and 9 to give

windows of size 15times15 and 19times19 respectively [8889]

Non-local means can be applied to other image applications such as non-local

movie denoising [91-93] MRI denoising [9495] image zooming [96] and

segmentation [97]



26 Wavelet-Domain Filters

Wavelet domain filters essentially employs Wavelet Transform (WT) and

hence are named so Fig 22 shows the block schematic of a wavelet-domain filter

Here the filtering operation is performed in the wavelet-domain A brief introduction

to wavelet transform is presented here

261 An Overview of Wavelet Transform

Wavelet transform [18-21] due to its localization property has become an

indispensable signal and image processing tool for a variety of applications including

compression and denoising [98-102] A wavelet is a mathematical function used to

decompose a given function or continuous-time signal into different frequency

components and study each component with a resolution that matches its scale A

wavelet transform is the representation of a function by wavelets The wavelets are

scaled and translated copies (known as daughter wavelets) of a finite length or fast

decaying oscillating waveform (known as mother wavelet) Wavelet transforms are

classified into continuous wavelet transform (CWT) and discrete wavelet transform

(DWT)

The continuous wavelet transform (CWT) [110-13] has received significant

attention for its ability to perform a time-scale analysis of signals On the other hand

the discrete wavelet transform (DWT) is an implementation of the wavelet transform

using a discrete set of wavelet scales and translations obeying some definite rules In

other words this transform decomposes the signals into mutually orthogonal set of

Forward

WT

Filtering Algorithm Inverse

WT

Input

Image

Output

Image

Fig 22 A Wavelet Domain Filter



wavelets The Haar [1] Daubechies[14] Symlets [20] and Coiflets [21] are compactly

supported orthogonal wavelets There are several ways of implementation of DWT

algorithm The oldest and most known one is the Mallat-algorithm or Mallat-tree

decomposition [19] In this algorithm the DWT is computed by successive low-pass

and high-pass filtering of discrete time-domain signal as shown in Fig 23 (a) In this

figure the signal is denoted by the sequence f(n) where n is an integer The low-pass

filter is denoted by G0 while the high-pass filter is denoted by H0 At each level the

high-pass filter produces detailed information d(n) while the low-pass filter

associated with scaling function produces coarse approximations a(n)

The original signal is then obtained by concatenating all the coefficients a(n)

and d(n) starting from the last level of decomposition as shown in Fig 23 (b)

The wavelet decomposition of an image is done as follows In the first level of

decomposition the image is decomposed into four subbands namely HH (high-high)

HL (high-low) LH (low-high) and LL (low-low) subbands The HH subband gives

the diagonal details of the image the HL subband gives the horizontal features while

the LH subband represents the vertical structures The LL subband is low resolution

residual consisting of low frequency components and it is further split at higher levels

of decomposition It is convenient to label the subbands of transform as shown in

Fig 24 In Fig 25 an example of second level of decomposition of Lena image

using Daubechiesrsquo tap-8 (Db-8) wavelet is shown



Fig23 Two-level wavelet Mallat-tree

(a) decomposition

(b) reconstruction

f(n)

d1(n) H0 darr2

G0 darr2

H0 darr2

G0 darr2

a1(n)

d2(n)

a2(n)

(a)

f(n)

d1(n)

H1

darr2 G1

darr2

a1(n)

d2(n)

a2(n)

H1

darr2 G1

darr2

(b)



LL2 HL2

HL1

LH2 HH2

LH1 HH1

Fig24 Subbands of the 2D Wavelet

Transform

Fig25 Two label decomposition of Lena

Image



262 DWT-Domain Filters

Recently a lot of methods have been reported that perform denoising in

DWT-domain [98-106] The transform coefficients within the subbands of a DWT

can be locally modeled as iid (independent identically distributed) random variables

with generalized Gaussian distribution Some of the denoising algorithms perform

thresholding of the wavelet coefficients which have been affected by additive white

Gaussian noise by retaining only large coefficients and setting the rest to zero These

methods are popularly known as shrinkage methods However their performance is

not quite effective as they are not spatially adaptive Some other methods evaluate the

denoised coefficients by an MMSE (Minimum Mean Square Error) estimator in

terms of the noised coefficients and the variances of signal and noise The signal

variance is locally estimated by a ML (Maximum Likelihood) estimator in small

regions for every subband where variance is assumed practically constant These

methods present effective results but their spatial adaptivity is not well suited near

object edges where the variance field is not smoothly varied Further these methods

introduce artifacts in the smooth regions of the output image Some efficient wavelet-

domain filters are discussed in subsequent sub-sections

263 VisuShrink

VisuShrink [99] is thresholding by applying universal threshold [98] proposed

by Dohono and Johnston This threshold is given by

2 logU nT Lσ= (230)

where 2

nσ is the noise variance of AWGN and L is the total number of pixels in an

image

It is proved in [99] that a large fraction of any L number of random data array with

zero mean and variance 2

nσ will be smaller than the universal threshold TU with high

probability the probability approaching 1 as L increases Thus with high probability

a pure noise signal is estimated as being identically zero Therefore for denoising

applications VisuShrink is found to yield a highly smoothed estimate This is because

the universal threshold is derived under the constraint that with high probability the



estimate should be at least as smooth as the signal So the TU tends to be high for large

values of L killing many signal coefficients along with the noise Thus the threshold

does not adapt well to discontinuities in the signal

264 SureShrink

SureShrink [100101] is an adaptive thresholding method where the wavelet

coefficients are treated in level-by-level fashion In each level when there is

information that the wavelet representation of that level is not sparse a threshold that

minimizes Steinrsquos unbiased risk estimate (SURE) is applied SureShrink is used for

suppression of additive noise in wavelet-domain where a threshold TSURE is employed

for denoising The threshold parameter TSURE is expressed as

( )arg min ( hSURE T hT SURE T Y= (231)

SURE(TY) is defined by

( )22 2

1

1( ) 2 min

L

h n n i h i h

i

SURE T Y i Y T Y TL

σ σ=

= minus times le minus

sum (232)

where 2

nσ is the noise variance of AWGN

L is the total number of coefficients in a particular subband

Yi is a wavelet coefficient in the particular subband

[ ]0h UT Tisin TU is Donohorsquos universal threshold

265 BayesShrink

In BayesShrink [102] an adaptive data-driven threshold is used for image

denoising The wavelet coefficients in a sub-band of a natural image can be

represented effectively by a generalized Gaussian distribution (GGD) Thus a

threshold is derived in a Bayesian framework as

2ˆ

ˆn

B

F

Tσ

σ= (233)



where 2ˆnσ is the estimated noise variance of AWGN by robust median estimator and

ˆF

σ is the estimated signal standard deviation in wavelet-domain

The robust median estimator is stated as

( )

1ˆ

06745

ij

n ij

Median YY subband HHσ = isin (234)

This estimator is used when there is no a priori knowledge about the noise variance

The estimated signal standard deviation is calculated as

( )2 2ˆ ˆ ˆmax ( )0F Y nσ σ σ= minus (235)

where 2ˆYσ is the variance of Y Since Y is modeled as zero-mean 2ˆ

Yσ can be found

empirically by

2 2

2 1

1ˆ

n

Y i j

i j

Yn

σ=

= sum (236)

In case 2 2ˆ ˆn Y

σ σge ˆF

σ will become 0 That is B

T becomesinfin Hence for this case

( )maxB ijT Y=

266 OracleShrink and OracleThresh

OracleShrink and OracleThresh [102] are two wavelet thresholding methods

used for image denoising These methods are implemented with the assumption that

the wavelet coefficients of original decomposed image are known The OracleShrink

and OracleThresh employ two different thresholds denoted as TOS and TOT

respectively Mathematically they are represented by

( )2

1

arg min ( )h

h

n

OS T ij ijT

i j

T Y Fξ=

= minussum (237)



( )2

1

arg min ( )h

h

n

OT T ij ijT

i j

T Y Fζ=

= minussum (238)

where with Fij are the wavelet coefficient of original decomposed image

and ( )hTξ i and ( )

hTζ i are soft-thresholding and hard-thresholding functions defined

as

( )( ) sgn( ) max 0T x x x Tξ = minus (239)

and

( ) T

x x x Tζ = gt1 (240)

which keeps the input if it is larger than the threshold T otherwise it is set to zero

267 NeighShrink

Chen et al proposed a wavelet-domain image thresholding scheme by

incorporating neighboring coefficients namely NeighShrink [103] The method

NeighShrink thresholds the wavelet coefficients according to the magnitude of the

squared sum of all the wavelet coefficients ie the local energy within the

neighborhood window The neighborhood window size may be 3times3 5times5 7times7 9times9

etc But the authors have already demonstrated through the results that the 3times3

window is the best among all window sizes []

The shrinkage function for NeighShrink of any arbitrary 3times3 window

centered at (ij) is expressed as

2

21 U

ij

ij

T

S+

Γ = minus

(241)

where UT is the universal threshold and 2

ijS is the squared sum of all wavelet

coefficients in the respective 3times3 window given by

1 12 2

1 1

j i

ij m n

n j m i

S Y+ +

= minus = minus

= sum sum (242)



Here + sign at the end of the formula means to keep the positive values while setting

it to zero when it is negative

The estimated center wavelet coefficient îj

F is then calculated from its noisy

counterpart ijY as

îj ij ijF Y= Γ (243)

268 SmoothShrink

Mastriani et al proposed SmoothShrink [104] wavelet-domain image

denoising method for images corrupted with speckle noise It employs a convolution

kernel based on a directional smoothing (DS) function applied on the wavelet

coefficients of the noisy decomposed image The size of the window may vary from

3times3 to 33times33 but the studies [104] show that the 3times3 window gives better result as

compared to others Though this approach is meant for speckle noise it is observed

that it works satisfactorily even for additive noise Therefore the method

SmoothShrink is stated here

SmoothShrink Algorithm

Step-1

The average of the wavelet coefficients in four directions (d1 d2 d3 d4) as shown in

Fig 24 is calculated

d1

d2

d3

d4

Fig 26 A 3times3 directional smoothing window showing four directions d1 d2 d3 d4



Step-2

The absolute difference between the center wavelet coefficient and each directional

average is calculated as

1 23 4nn d ijd Y Y n∆ = minus = (244)

where ndY = average of wavelet coefficients in n

th direction

Step-3

The directional average which gives minimum absolute difference is found out

( )arg mindn

nY

d= ∆K (245)

Step-4

The estimated center wavelet coefficient is therefore replaced with the minimum

directional average obtained in Step-3 ie

îjF =K (246)

The SmoothShrink algorithm is applied to all subbands of noisy decomposed image

except the LL subband

269 LAWML

Mihcak et al [105] proposed a simple spatially adaptive statistical model for

wavelet coefficients and applied it to image denoising The resulting method for

image denoising is called as locally adaptive window based denoising using maximum

likelihood (LAWML) The size of the window used in the method may be 3times3 5times5

7times7 etc In this method the variance of original decomposed image of a particular

window in a given sub-band is estimated using maximum likelihood (ML) estimator

The ML estimator can be mathematically expressed as

( )2

2 2

0( )

2 2

( )

ˆ ( ) arg max ( )

1max 0 ( )

j N k

n

j N k

k P Y j

Y jL

σσ σ

σ

geisin

isin

=

= minus

prod

sum (247)



where ( )2P σ is the Gaussian distribution with zero mean and variance 2 2

nσ σ+ L is

the number of coefficients in N(k) and 2


The estimated wavelet coefficient of original decomposed image is calculated by

using minimum mean squared error (MMSE) estimator [106]

Thus the estimated wavelet coefficient is calculated by the MMSE estimator given

by

2

2 2

ˆ ( )ˆ ( ) ( )ˆ ( ) n

kF k Y k

k

σ

σ σ= sdot

+ (248)

27 Simulation Results

The existing spatial-domain filters Mean Median Alpha-trimmed-mean

(ATM) Wiener Lee Anisotropic Diffusion (AD) Total Variation (TV) Bilateral

Non-local means and existing wavelet-domain filters VisuShrink SureShrink

BayesShrink OracleShrink NeighShrink SmoothShrink locally adaptive window

maximum likelihood (LAWML) are simulated on MATLAB 70 platform The test

images Lena Pepper Goldhill and Barbara of sizes 512times512 corrupted with AWGN

of standard deviation σn = 5 10 15 20 25 30 35 40 45 and 50 are used for

simulation purpose The peak-signal-to-noise ratio (PSNR) root-mean-squared error

(RMSE) universal quality index (UQI) and method noise and execution time are

taken as performance measures

The PSNR values of the different filters for various images are given in the

tables Table-21 to Table-24 The highest (best) PSNR value for a particular standard

deviation of Gaussian noise is highlighted to show the best performance

The RMSE values of different filters are given in the tables Table-25 to

Table-28 The smallest (best) RMSE value for a particular standard deviation of

Gaussian noise is highlighted for analysis



The UQI of various filters are given in the tables Table-29 to Table-212 The

value of UQI is always less than 1 The highest (best) value of UQI for a particular

standard deviation of Gaussian noise is identified and is highlighted for analysis

The method noise of the various filters is shown in Table-213 The filtering

performance is better if the method noise is very low since it talks of little distortion

when a non-noisy image is passed through a filter Therefore a least value of method

noise for a particular noise standard deviation is highlighted to show the best

performance

The execution time of the different filters is given in Table-214 The filter

having less execution time is usually required for online and real-time applications

The least value of execution time is highlighted

Fig 27 Fig28 and Fig 29 illustrate the resulting performance measures

(PSNR RMSE and UQI) of some high performing filters (Mean ATM BayesShrink

NeighShrink and LAWML) under different noise conditions for various test images

The best performance value for a particular standard deviation of AWGN irrespective

of window size of a filter is taken in the figures These figures based on Table-21 ndash

Table-212 are given for ease of analysis

For subjective evaluation the filtered output images of various filters are

shown in the figures Fig 210 to Fig 217 The images corrupted with AWGN of

standard deviation σn = 15 (moderate-noise) and σn = 40 (high-noise) are applied to

different filters and the resulted output images are shown in these figures



Table-21 Filtering performance of various filters in terms of PSNR (dB) operated on Lena

image under various noise conditions (σn varies from 5 to 50)

Peak-Signal-to-Noise Ratio PSNR (dB) Standard deviation of AWGN

SlNo Denoising Filters 5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094

5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382

6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496

7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322

8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586

9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613

10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186

11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469

12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534

13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393

14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412

15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268

16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534

17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595

18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368

19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573

20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519

21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636

22 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148

23 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621

24 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607

25 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815

26 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542

27 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497

28 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131

29 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458

30 LAWML [5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602

31 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638



Table-22 Filtering performance various filters in terms of PSNR (dB) operated on Pepper




Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102

5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419

6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562

7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312

8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632

9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687

10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185

11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460

12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526

13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361

14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376

15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271

16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547

17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609

18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348

19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592

20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552

21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651

22 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137

23 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454

24 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505

25 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835

26 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564

27 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451

28 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728

29 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447

30 LAWML [5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560

31 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575



Table-23 Filtering performance of various filters in terms of PSNR (dB) operated on Goldhill




Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102

5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343

6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420

7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162

11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368

12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407

13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340

14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378

15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258

16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451

17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469

18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325

19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451

20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400

21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668

22 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026

23 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462

24 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409

25 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921

26 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724

27 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411

28 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762

29 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361

30 LAWML [5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443

31 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443



Table-24 Filtering performance of various filters in terms of PSNR (dB) operated on Barbara




Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998

5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121

6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214

7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3657 3167 2865 2921 2750 2606 2489 2390 2297 2213

11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255

12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293

13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226

14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231

15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166

16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277

17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319

18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199

19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229

20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231

21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667

22 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989

23 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286

24 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271

25 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044

26 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708

27 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326

28 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739

29 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295

30 LAWML [5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371

31 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378



Table-25 Filtering performance of various filters in terms of RMSE operated on a Lena image

under various noise conditions (σn varies from 5 to 50)

Root-Mean-Squared Error (RMSE) Standard deviation of AWGN


Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287

5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642

6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438

7 ATM [3times3] 511 589 696 821 9639 1106 1267 1428 1593 1759

8 ATM [5times5] 828 844 869 910 9562 1004 1071 1134 1208 1298

9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257

10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057

11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484

12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377

13 AD 470 688 772 874 989 1109 1236 1369 1491 1621

14 TV 428 555 663 782 902 1032 1167 1298 1445 1586

15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871

16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377

17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285

18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667

19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318

20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402

21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876

22 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150

23 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247

24 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267

25 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155

26 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320

27 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438

28 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193

29 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505

30 LAWML [5times5] 299 474 621 747 863 955 1046 1127 1198 1275

31 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223



Table-26 Filtering performance of various filters in terms of RMSE operated on Pepper image




Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267

5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573

6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333

7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779

8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231

9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155

10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060

11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499

12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389

13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680

14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652

15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864

16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356

17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264

18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706

19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287

20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349

21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809

22 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177

23 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512

24 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425

25 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083

26 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212

27 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517

28 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487

29 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524

30 LAWML [5times5] 293 472 607 732 852 966 1070 1166 1263 1338

31 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315



Table-27 Filtering performance of various filters in terms of RMSE operated on Goldhill image




Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267

5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716

6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570

7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114

11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667

12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593

13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723

14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649

15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894

16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514

17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484

18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751

19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514

20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606

21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735

22 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474

23 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498

24 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592

25 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792

26 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503

27 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588

28 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353

29 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682

30 LAWML [5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531

31 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531



Table-28 Filtering performance of various filters in terms of RMSE operated on Barbara image




Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555

5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216

6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991

7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994

11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899

12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818

13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963

14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953

15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106

16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851

17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764

18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027

19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958

20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953

21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740

22 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582

23 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834

24 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866

25 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424

26 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568

27 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752

28 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443

29 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815

30 LAWML [5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663

31 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650



Table-29 Filtering performance of various filters in terms of UQI operated on a Lena image


Universal Quality Index (UQI) Standard deviation of AWGN


Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951

5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419

6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539

7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340

8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621

9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637

10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098

11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503

12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557

13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417

14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458

15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239

16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566

17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613

18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385

19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598

20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557

21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451

22 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178

23 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636

24 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621

25 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021

26 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953

27 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530

28 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661

29 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484

30 LAWML [5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622

31 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649



Table-210 Filtering performance of various filters in terms of UQI operated on Pepper image




Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163

5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578

6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687

7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460

8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732

9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760

10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261

11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588

12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638

13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488

14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525

15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392

16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665

17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702

18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476

19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689

20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662

21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908

22 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289

23 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568

24 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617

25 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400

26 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484

27 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579

28 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022

29 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575

30 LAWML [5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675

31 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689



Table-211 Filtering performance of various filters in terms of UQI operated on Goldhill image




Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345

5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610

6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669

7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569

8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732

9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734

10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385

11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602

12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628

13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578

14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636

15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501

16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670

17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680

18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565

19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662

20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620

21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339

22 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328

23 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673

24 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627

25 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926

26 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443

27 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638

28 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541

29 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592

30 LAWML [5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656

31 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658



Table-212 Filtering performance of various filters in terms of UQI operated on Barbara image




Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024

5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227

6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360

7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314

8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398

9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411

10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201

11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395

12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434

13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358

14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396

15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284

16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425

17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469

18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316

19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329

20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312

21 NL-Means 09957 09943 098 65

09716 09516 09285 09010 08737 08423 08127

22 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138

23 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424

24 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401

25 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005

26 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136

27 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491

28 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233

29 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433

30 LAWML [5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517

31 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521



Table-213 Method Noise MN of various filters operated on different test images

Sl No

Denoising Images

Filters

Lena Pepper Goldholl Barbara

1 Mean [3times3] 262 290 410 668

2 Mean [5times5] 443 408 642 946

3 Mean [7times7] 573 520 793 1035

4 Median [3times3] 132 153 252 438

5 Median [5times5] 270 239 443 693

6 Median [7times7] 395 311 499 744

7 ATM [3times3] 262 290 410 668

8 ATM [5times5] 443 408 642 946

9 ATM [7times7] 573 520 793 1035

10 Wiener [3times3] 186 204 318 387

11 Wiener [5times5] 367 351 540 637

12 Wiener [7times7] 464 387 576 668

13 AD 204 237 295 497

14 TV 211 234 334 573

15 Lee [3times3] 00118 109 00336 00583

16 Lee [5times5] 00530 114 01109 02057

17 Lee [7times7] 01315 201 01853 110

18 Bilateral [3times3] 288 308 423 680

19 Bilateral [5times5] 497 433 663 966

20 Bilateral [7times7] 601 545 826 1104

21 NL-Means 117 137 186 211

22 VisuShrink 318 423 471 637

23 SureShrink 517 673 770 1007

24 BayesShrink 00232 00273 00194 00190

25 OracleShrink 00285 00267 00242 00238

26 OracleThresh 00285 00267 00242 00238

27 NeighShrink 408times10-10

466times10-10

334times10-10

497times10-10

28 SmoothShrink 660 752 645 790

29 LAWML [3times3] 408times10-10

466times10-10

334times10-10

497times10-10


466times10-10

334times10-10

497times10-10


466times10-10

334times10-10

497times10-10



Table-214 Execution time (seconds) TE taken by various filters for Lena image

Execution time (seconds) in three different hardware platforms Sl No Denoisg Filters

SYSTEM-1 SYSTEM-2 SYSTEM-3

1 Mean [3times3] 318 701 1713

2 Mean [5times5] 323 712 1749

3 Mean [7times7] 327 720 1776

4 Median [3times3] 402 742 2445

5 Median [5times5] 409 747 2469

6 Median [7times7] 415 812 2490

7 ATM [3times3] 732 1677 3018

8 ATM [5times5] 809 1723 3056

9 ATM [7times7] 813 1784 3084

10 Wiener [3times3] 787 1559 2806

11 Wiener [5times5] 807 1598 2876

12 Wiener [7times7] 843 1670 3006

13 AD ------ ------- ------

14 TV ------ ------- ------

15 Lee [3times3] 874 1426 3509

16 Lee [5times5] 887 1446 3545

17 Lee [7times7] 968 1579 3779

18 Bilateral [3times3] 536 1100 3265

19 Bilateral [5times5] 583 1353 3520

20 Bilateral [7times7] 588 1359 3639

21 NL-Means 44667 99620 221838

22 VisuShrink 0540 119 392

23 SureShrink 060 134 442

24 BayesShrink 188 415 1369

25 OracleShrink 2 440 1452

26 OracleThresh 197 435 1435

27 NeighShrink 414 912 3009

28 SmoothShrink 108 239 788

29 LAWML [3times3] 367 809 2669

30 LAWML [5times5] 370 815 2689

31 LAWML [7times7] 374 823 2715



Fig 27 Performance comparison of various filters in terms of PSNR (dB) under

different noise levels of AWGN on the images

(a) Lena

(b) Pepper (c) Goldhill

(d) Barbara

σn

PS

NR

(d

B)

PSNR values for Lena Image

PS

NR

(d

B)

PSNR values for Pepper Image P

SN

R (

dB

)

PSNR values for Goldhill Image PSNR values for Barbara Image

PS

NR

(d

B)

(a) (b)

(c) (d)

σn

σn σn



Fig 28 Performance comparison of various filters in terms of RMSE under different noise levels of AWGN on the images

(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

RM

SE

RMSE values for Lena Image

RM

SE

RMSE values for Pepper Image

(a) (b)

RM

SE

RMSE values for Goldhill Image

RM

SE

(c) (d)

RMSE values for Barbara Image

σn σn

σn σn



Fig 29 Performance comparison of various filters in terms of UQI under


(a) Lena (b) Pepper

(c) Goldhill (d) Barbara

UQ

I UQI values for Lena Image

UQ

I

UQI values for Pepper Image U

QI

UQI values for Goldhill Image

UQ

I

UQI values for Barbara Image

(a) (b)

(c) (d)

σn σn

σn σn



(b)

(f)

(j)

(n)

(a)

(e)

(i)

(m)

(q)

(r)

(c)

(d)

(g)

(h)

(k)

(l)

(o)

(p)

(s)

Fig 210 Performance of Various Filters for Lena Image with AWGN σn = 15

(a) Original image (b) Noisy image

(c) ndash (s) Results of various filtering schemes

(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee (j) Bilateral

(k) NL-Means (l) VisuShrink (m) SureShrink (n) BayesShrink (o) OracleShrink

(p) OracleThresh (q) NeighShrink (r) SmoothShrink (s) LAWML



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)

Fig 211 Performance of Various Filters for Lena Image (Smooth Region) with

AWGN σn = 15








(a) (b) (c) (d) (e) (f) (g)

(h) (i) (j) (k) (l)

(m)

(l) (m) (n)

(o) (p) (q) (r) (s)

Fig 212 Performance of Various Filters for Lena Image (Complex Region) with AWGN σn = 15








(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m) (n) (o) (p)

(q) (r) (s)

Fig 213 Performance of Various Filters for Pepper Image with AWGN σn = 15 (a) Original image (b) Noisy image







(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)









(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)


AWGN σn = 40








(a)

(b) (c)

(d)

(f) (g)

(h)

(i)

(e)

(j) (k) (l) (m) (n)

(o) (p) (q) (r) (s)









(d)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)

Fig 217 Performance of Various Filters for Pepper Image with AWGN σn = 40








28 Conclusion

The performance of various spatial-domain filters Mean Median ATM

Wiener AD TV Lee Bilateral NL-Means and various wavelet-domain filters

VisuShrink SureShrink BayesShrink OracleShrink OracleThresh NeighShrink

SmoothShrink LAWML are studied under low moderate and high noise conditions

From Table-21 to Table-24 it is observed that the filters ATM NeighShrink

and LAWML perform better in terms of PSNR The wavelet-domain filter

NeighShrink performs better under low noise conditions Under moderate noise

conditions LAWML generally gives better performance The spatial-domain filter

ATM works well under high noise conditions

The RMSE values of different filters are shown in tables Table-25 to

Table-28 From the tables it is observed that the filters ATM NeighShrink and

LAWML give better performance as compared to others

From tables Table-29 to Table-212 it is observed that LAWML gives better

UQI values under low and moderate noise conditions When noise level is high the

spatial-domain filter ATM yields better performance in terms of UQI values

Table-213 shows the method noise of different spatial-domain and wavelet-

domain filters From the table it is seen that the method noise of LAWML is

minimum (quite negligible) Hence the LAWML filter is best among all the filters

compared here for yielding minimal noise when the input is undistorted

The execution time of different filters is shown in the Table-214 The wavelet-

domain filter VisuShrink takes least execution time as compared to other spatial-

domain and wavelet-domain filters However among the spatial-domain filters the

simplest mean filter takes quite less execution time as compared to other spatial-

domain filters



For proper judgment of performance of filters the subjective evaluation

should be taken into consideration The filtering performances of various filters on a

smooth region and a complex region of Lena image are shown in the figures

Fig 211 Fig 212 Fig 215 and Fig 216 From these figures it is observed that the

wavelet-domain filters yield artifacts in the smooth regions However the wavelet-

domain filters are effective in preserving the edges and other detailed information up

to some extent Further when the various wavelet-domain filters are compared then it

is observed that NeighShrink and LAWML filters yield very high visual quality

Hence they are expected to be good competitors for the novel filters proposed in this

research work

Chapter 3

Development of

Novel Spatial-Domain

Image Filters



Preview

Mean and Wiener filters suppress additive white Gaussian noise (AWGN)

from an image very effectively under low and moderate noise conditions But these

filters distort and blur the edges unnecessarily Lee filter and non-local means (NL-

Means) filter work well under very low noise condition The method noise [88] for

these filters is low as compared to other spatial-domain filters The computational

complexity of simple mean filter is low whereas that of NL-Means filter is very high

Mean Wiener Lee and NL-means filters are incapable of suppressing the Gaussian

noise quite efficiently under high noise conditions

Therefore some efficient spatial-domain filters should be designed with the

following ideal characteristics

i) Suppressing Gaussian noise very well under low moderate and high noise

conditions without distorting the edges and intricate details of an image

ii) Having low method noise and

iii) Having less computational complexity

3



In this chapter two novel spatial-domain image denoising schemes are

proposed The Adaptive Window Wiener filter (AWWF) [P1] developed here is a

very good scheme to suppress Gaussian noise under moderate noise conditions On

the other hand the second proposed filter the Circular Spatial filter (CSF) [P2] is

found to be quite efficient in suppressing the additive noise under moderate and high

noise conditions It also retains the edges and textures of an image very well




Simulation Results

Conclusion



31 Development of Adaptive Window Wiener Filter

An Adaptive Window Wiener Filter (AWWF) [P1] is developed for suppressing

Gaussian noise under low (the noise standard deviation σnle10) and moderate noise

(10ltσnle 30) conditions very efficiently But it does not perform well under high

noise (30ltσnle5 0) conditions This filter is a modified version of Wiener filter [962]

where the size of the window varies with the level of complexity of a particular region

in an image and the noise power as well A smooth or flat region (also called as

homogenous region) is said to be less complex as compared to an edge region The

region containing edges and textures are treated as highly complex regions The

window size is increased for a smoother region and also for an image with high noise

power

Since the edges in an image are specially taken care of in this algorithm the

proposed filter is found to be good in edge preservation The work begins by using a

mean filter on a noisy image to get the blurred version of the image Using the edge

extraction operator the edges of the resulted blurred image is found out The Wiener

filter of variable size is applied throughout the noisy image to suppress the noise The

window size is made larger in smooth regions and is kept smaller in the regions where

edges are located This scheme is adopted not to blur a complex or edge region too

much

The organization of this section is outlined below

The AWWF Theory

The AWWF Algorithm

Window Selection



311 The AWWF Theory

It is a fact that a noise-free sample can be estimated with better accuracy from

a large number of noisy samples Similarly in order to estimate a true pixel in a

particular region from a noisy 2-D image a large number of pixels in the

neighborhood surrounding the noisy pixel are required In other words a larger-sized

window surrounding the pixel to be filtered can be considered for better estimation

In a homogenous region the correlation amongst the pixels is high Hence a larger-

sized window can be taken if the pixel to be filtered belongs to a homogenous

region On the other hand a pixel that belongs to a non-homogenous region or the

region containing edges has got less number of correlated pixels in its neighborhood

In such a case smaller-sized window has to be taken for denoising a pixel belonging

to a non-homogenous region However a little bit of noise will still remain in the non-

homogenous or edge region even after filtration But human eye is not so sensitive to

noise in any edge region Hence a variable sized window may be a right choice for

efficient image denoising

In the proposed adaptive window Wiener filter the window is made adaptive

ie the size of the window varies from region to region In a flat or homogenous

region the size of the window taken is large enough The size of window is small in

the regions containing edges The problem here is to distinguish the edge and smooth

regions The edges and smooth regions are easily distinguished if the edge extraction

operators are used Many edge extraction operators such as Sobel Canny Roberts

Prewitt etc are proposed in the literature [22-27] But finding the true edges in a

noisy environment is not so easy The edge extraction operator works well on noise

free images So it is important to make the noisy image a little bit blurred before edge

extraction In the proposed filter the mean filter of window size 5times5 is used when the

noise level is low and moderate to get the blurred version of the noisy image whereas

a 7times7 window is taken for high-noise AWGN The Sobel operator is then used on the

resulted blurred image to find the edges

A small amount of noise still remains in different regions even after passing

the noisy image through the mean filter The Sobel operator is less sensitive to



isolated high intensity point variations since the local averaging over sets of three

pixels tends to reduce this In effect it is a ldquosmall barrdquo detector rather than a point

detector Secondly it gives an estimate of edge direction as well as edge magnitude at

a point which is more informative Also the Sobel operator is still relatively easy to

implement in hardware form most obviously by a pipeline approach

312 The AWWF Algorithm

The proposed algorithm is given below

Step-1

The noisy image is passed through a mean filter as shown in Fig 31 to get a blurred

version of the image

Step-2

Edge operator (Sobel operator) is applied on the blurred image obtained in Step-1 to

get the edge image The pixels belong to smooth region and edge region are identified

as lsquoprsquo and lsquoqrsquo respectively This operation is shown in Fig 32

Step-3

Adaptive window Wiener filter is applied on the noisy image The size of the window

is varied with the following concepts

A-i) If the center pixel is an edge pixel then the size of the window is small

A-ii) If the center pixel belongs to smooth region the size of the window is large

B-i) If the noise power is low (σnle10 ) then the size of the window is small

B-ii) If the noise power is moderate (10ltσnle30 ) then the size of the window is

medium

B-iii) If the noise power is high (30ltσnle50) then the size of the window is large

This adaptive filtering concept is depicted in Fig 33

Step-4

All the filtered pixels are united together to obtain the denoised (filtered) image as

shown in Fig 34

The exact window sizes taken for various conditions are presented in the next

sub-section



p1cup q1cup helliphellip = Filtered Image

Mean Filter Noisy Image Blurred Image

Fig 31 Blurred Image resulted from mean filter

Sobel operator

Fig 32 Edge Image using lsquoSobelrsquo operator

Blurred Image

Edge Image

p

q

lsquoprsquo belongs to smooth region

lsquoqrsquo belongs to edge region

Fig 34 Filtered image showing filtered pixels

Fig 33 Filtering operation of AWWF for the pixels lsquoprsquo (belonging to smooth region) and lsquoqrsquo (belonging to edge region)

The pixels lsquop1rsquo and lsquoq1rsquo are the filtered pixels for the corresponding pixels lsquoprsquo and lsquoqrsquo respectively

q

p

Wiener

Filtering

p1 OR q1



313 Window Selection

The selection of window is based on the level of noise present in the noisy

image If the noise level is unknown a robust median estimator [102] may be applied

to predict the level of noise

When the noise level is low (σnle10)

i) a 3times3 window is selected for filtering the noisy pixels belonging to

homogenous regions

ii) the pixel is unaltered if the noisy pixels belong to edges

When the noise level is moderate (10ltσnle 30)

i) a 5times5 window is chosen for filtration of noisy pixels of flat regions

ii) the window size is 3times3 if the noisy pixels to be filtered are identified as edge

pixels

When the noise level is high (30ltσnle50)

i) a 7times7 window is used for filtration of noisy pixels of flat regions

ii) if the noisy pixels to be filtered are identified as edge pixels the window size

used is 5times5

The proposed filter AWWF is implemented on MATLAB 70 platform and its

simulation results are presented in Section 33



32 Development of Circular Spatial Filter

A novel circular spatial filter (CSF) is proposed [P2] for suppressing additive

white Gaussian noise (AWGN) In this method a circular spatial-domain window

whose weights are derived from two independent functions (i) spatial distance and

(ii) gray level distance is employed for filtering The proposed filter is different from

Bilateral filter [70] and performs well under moderate and high noise conditions The

filter is also capable of retaining the edges and intricate details of the image


The circular spatial filtering method

The parameter and window selection

Simulation Results

Conclusion

321 The circular spatial filtering method

In circular spatial filter (CSF) the name circular refers to the shape of the

filtering kernel or window being circular In this method the filtering kernel consists

of distance kernel and gray level kernel The circular shaped kernel is moved

invariably throughout the image to remove the noise The proposed filter has got some

resemblance with Bilateral filter where the filtering kernel is a combination of

domain-filtering kernel and range-filtering kernel The weighting function used in

gray level kernel of circular spatial filter is similar to the weighting function used in

range-filtering kernel But the weighting function used in distance kernel of CSF and

domain-filtering kernel of Bilateral filter are different The weighting function used in

domain-filtering kernel is exponential whereas it is a simple nonlinear function in case

of distance kernel of the proposed method



3211 Distance kernel

In an image the spatial distance between any arbitrary pixel in a particular

window at location (x1y1) and the center pixel at location (xy) is calculated as

( ) ( )2 2


Now the distance kernel is defined by

max

1 sd

dw

d= minus (32)

where dmax is the maximum radial distance from center

The correlation between pixels goes on decreasing as the distance increases

Hence when wd becomes very small the correlation can be taken as zero When the

small values of distance kernel are replaced by zero we get a circular shaped filtering

kernel The circular shaped kernel is denoted asdcw

3212 Gray level kernel

The gray level distance between any arbitrary pixel g(x1y1) of a particular

window at location (x1y1) and the center pixel g(xy) at location (xy) is calculated as

( )1

2 2 2

1 1| ( ) |gd g x y g x y = minus (33)

The gray level distance dg can be used to find the gray level kernel which is defined

by

2

2exp

2

g

g

g

dw

σ

minus=

(34)

where lsquoσgrsquo is the standard deviation of the distribution function wg



The filtering kernel of CSF can be prepared from dcw and

gw as

dc gw w w= sdot (35)

The filtering kernel w is slided throughout the image corrupted with noise to get the

estimated output The estimated pixel can be expressed as

( )( ) ( )

ˆ

( )

a b

s a t b

a b

s a t b

w s t g x s y t

f x y

w s t

= minus = minus

= minus = minus

+ +

=

sum sum

sum sum (36)

In the filtering window the center coefficient is given the highest weight The

weight goes on decreasing as distance increases from center and it is zero when

correlation is insignificant A pictorial representation of circular spatial filtering mask

is shown in Figure 31 (a) A more general filtering mask ie a square mask is also

depicted in Figure 31 (b) to illustrate the difference It is evident from Figure 31 (a)

that there are necessarily some zeros in the circular spatial filter mask whereas it is

not so in the case of a general square window shown in Figure 31 (b)

Fig 35 (a) A typical Circular Spatial Filtering mask of size 7 times 7

(b) A square filtering mask of size 7 times 7

(a) (b)



322 The parameter and window selection

The circular spatial filter has one parameter lsquoσgrsquo which controls the weights in

the gray level kernel For efficient filtering operation the value σg should be

optimum The choice of σg is based on experimentation Two experiments are

performed to find the optimal value of σg

Experiment 1

An experiment is conducted to find the peak-signal-to-noise ratio (PSNR) for

various values of σg under different noise conditions In this experiment Lena and

Goldhill images are selected and their noisy versions are generated by adding

Gaussian noise of standard deviation σn = 30 40 and 50 The PSNR values obtained

are plotted against the values of σg which are shown in Fig 36 From the figure it is

observed that the PSNR values settle at σg = 1 and do not change much even if σg is

increased significantly

Experiment 2

The noisy versions of Lena and Goldhill are used to perform this experiment

Here the universal quality index (UQI) values for different values of σg under the

Gaussian noise of standard deviation σn = 30 40 and 50 are calculated The UQI

values are plotted for different values of σg and are shown in Fig 37 As σg increases

and approaches 1 the UQI value increases and approaches steady state value The

value of UQI remains constant with further increase of σg

From these two experiments it is learnt that the optimum value of σg should

be taken as 1

The selection of window in CSF is equally important as the selection of

parameter The noise levels of AWGN are taken into consideration for selection of

window If there is no a-priori knowledge of the noise level the robust median

estimator is used to find it For low moderate and high noise conditions 3times3 5times5 and

7times7 windows are selected respectively for effective suppression of Gaussian noise

The size of the window is kept constant and is never varied even though the image

statistics change from point to point for a particular noise level



Fig 36 PSNR vs σg under AWGN of σn = 30 40 and 50

(a) Lena image

(b) Goldhill image

0 1 2 3 4 515

20

25

30

σ = 30

σ = 40

σ = 50n

n

n

gσ

PS

NR

(d

B)

(a)

0 1 2 3 4 516

18

20

22

24

26

28

σ = 30

σ = 40

σ = 50

n

n

n

PS

NR

(d

B)

gσ

(b)



0 1 2 3 4 507

075

08

085

09

095

1

σ = 30

σ = 40

σ = 50

n

n

n

UQ

I

gσ

(a)

gσ

UQ

I

0 1 2 3 4 508

085

09

095

1

σ = 30

σ = 40

σ = 50

n

n

n

(b)

Fig 37 UQI vs σg under AWGN of σn = 30 40 and 50

(a) Lena image

(b) Goldhill image




Extensive computer simulation is carried out on MATLAB 70 platform to

access the performance of the proposed filters Adaptive Window Wiener Filter

(AWWF) and Circular Spatial Filter (CSF) and the standard existing filters Mean

filter Median filter Alpha Trimmed Mean (ATM) filter Wiener filter Anisotropic

Diffusion (AD) filter Total Variation (TV) filter Lee filter Bilateral filter Non-local

Means (NL-Means) filter and The test images Lena Pepper Goldhill and Barbara of

sizes 512times512 corrupted with AWGN of standard deviation σn = 5 10 15 20 25

30 35 40 45 and 50 are used for testing the filtering performance The peak-signal-

to-noise ratio (PSNR) root-mean-square error (RMSE) universal quality index

(UQI) method noise and execution time are taken as performance measures

The PSNR values of different filters are given in the tables Table-31 to

Table-34 When the noise level is high the proposed filter CSF exhibits very high

performance For moderate noise conditions its performance is close to that of

AWWF The largest PSNR value for a particular standard deviation of Gaussian noise

is highlighted to show the best performance in these tables



Gaussian noise is highlighted for analysis purpose

The UQI values of various filters are given in the tables Table-39 to Table

312 The largest (best) value of UQI for a particular standard deviation of Gaussian

noise is identified and is highlighted for analysis purpose

The method noise of various filters for different images is given in the

Table 313 It is observed that the Lee filter is the best performer whereas the

NL-Means filter is the second best in terms of method noise The proposed filter CSF



also gives very low method noise and its performance is comparable with that of the

NL-Means filter

The spatial-domain filters are simulated on three different computing systems

depicted in Table-11 in Section 15 The execution time taken for different filtering

schemes is shown in Table-314 As the AD and TV filters are iterative in nature their

simulation times are not included in the table The execution time of CSF is close to

the simplest mean filter Thus it is quite useful for real-time applications

The performance of proposed filters and some high performing filters in terms

of PSNR RMSE and UQI are illustrated in figures Fig 38 to Fig 310 for easy

analysis

For subjective evaluation the output images of different spatial-domain filters

are shown in the figures Fig 311 to Fig 318 The test images Lena and Pepper are

used for subjective evaluation A smooth region and a complex region of Lena image

are also demonstrated through various figures for critical analysis

Conclusions are drawn in the next section



Table-31 Filtering performance of various filters in terms of PSNR (dB) operated on Lena image under various noise conditions (σn varies from 5 to 50)



Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094

5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382

6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496

7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322

8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586

9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613

10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186

11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469

12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534

13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393

14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412

15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268

16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534

17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595

18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368

19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573

20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519

21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636

22 AWWF 3488 3336 3178 3056 2929 2813 2741 2688 2601 2585

23 CSF [3times3] 3719 3287 2971 2735 2551 2397 2269 2155 2060 1970

24 CSF [5times5] 3371 3280 3158 3031 2911 2796 2688 2598 2507 2432

25 CSF [7times7] 3015 2987 2962 2932 2896 2847 2801 2749 2699 2646



Table-32 Filtering performance various filters in terms of PSNR (dB) operated on Pepper image under various noise conditions (σn varies from 5 to 50)



Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102

5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419

6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562

7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312

8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632

9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687

10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185

11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460

12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526

13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361

14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376

15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271

16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547

17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609

18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348

19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592

20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552

21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651

22 AWWF 3516 3396 3258 3101 3011 2891 2821 2743 2710 2638

23 CSF [3times3] 3680 3275 2968 2739 2552 2400 2271 2159 2063 1973

24 CSF [5times5] 3499 3381 3235 3084 2949 2819 2705 2607 2514 2434

25 CSF [7times7] 3217 3126 3091 3044 2991 2925 2861 2792 2730 2696



Table-33 Filtering performance of various filters in terms of PSNR (dB) operated on Goldhill image under various noise conditions (σn varies from 5 to 50)



Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102

5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343

6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420

7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162

11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368

12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407

13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340

14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378

15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258

16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451

17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469

18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325

19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451

20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400

21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668

22 AWWF 3434 3234 3087 2918 2815 2720 2638 2539 2510 2446

23 CSF [3times3] 3615 3250 2960 2738 2559 2411 2282 2171 2079 1992

24 CSF [5times5] 3189 3127 3041 2940 2838 2741 2641 2552 2464 2389

25 CSF [7times7] 2914 2854 2836 2809 2776 2730 2692 2644 2590 2534



Table-34 Filtering performance of various filters in terms of PSNR (dB) operated on Barbara image under various noise conditions (σn varies from 5 to 50)



Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998

5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121

6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214

7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3657 3167 2865 2821 2750 2606 2489 2390 2297 2213

11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255

12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293

13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226

14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231

15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166

16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277

17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319

18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199

19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229

20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231

21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667

22 AWWF 3319 3169 3028 2954 2798 2671 2585 2475 2360 2273

23 CSF [3times3] 3188 3013 2922 2851 2698 2666 2551 2445 2249 2169

24 CSF [5times5] 2865 2820 2792 2756 2714 2671 2618 2557 2504 2455

25 CSF [7times7] 2796 2744 2739 2729 2716 2701 2683 2662 2633 2607



Table-35 Filtering performance of various filters in terms of RMSE operated on a Lena image under various noise conditions (σn varies from 5 to 50)



Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287

5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642

6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438

7 ATM [3times3] 511 589 696 821 963 1106 1267 1428 1593 1759

8 ATM [5times5] 828 844 869 910 956 1004 1071 1134 1208 1298

9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257

10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057

11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484

12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377

13 AD 470 688 772 874 989 1109 1236 1369 1491 1621

14 TV 428 555 663 782 902 1032 1167 1298 1445 1586

15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871

16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377

17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285

18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667

19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318

20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402

21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876

22 AWWF 459 545 655 754 874 999 1086 1152 1275 1295

23 CSF [3times3] 352 578 831 1094 1351 1614 1869 2131 2379 2639

24 CSF [5times5] 526 583 670 777 892 1017 1152 1280 1420 1550

25 CSF [7times7] 792 818 841 869 907 961 1012 1076 1139 1211



Table-36 Filtering performance of various filters in terms of RMSE operated on Pepper image under various noise conditions (σn varies from 5 to 50)



Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267

5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573

6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333

7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779

8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231

9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155

10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060

11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499

12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389

13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680

14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652

15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864

16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356

17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264

18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706

19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287

20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349

21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809

22 AWWF 445 510 596 716 795 912 989 1083 1124 1221

23 CSF [3times3] 368 586 836 1088 1349 1606 1864 2121 2371 2629

24 CSF [5times5] 453 517 614 731 854 991 1132 1267 1410 1545

25 CSF [7times7] 628 696 724 765 813 877 9460 1022 1099 1142







Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267

5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716

6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570

7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114

11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667

12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593

13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723

14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649

15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894

16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514

17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484

18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751

19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514

20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606

21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735

22 AWWF 489 614 729 884 997 1111 1221 1369 1415 1524

23 CSF [3times3] 397 604 844 1088 1338 1588 1841 2093 2328 2573

24 CSF [5times5] 648 696 767 861 971 1086 1218 1349 1494 1629

25 CSF [7times7] 890 953 971 1004 1042 1099 1147 1213 1290 1377







Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555

5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216

6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991

7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994

11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899

12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818

13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963

14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953

15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106

16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851

17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764

18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027

19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958

20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953

21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740

22 AWWF 558 663 780 849 1017 1175 1298 1473 1683 1861

23 CSF [3times3] 649 793 879 956 1139 1183 1351 1527 1912 2098

24 CSF [5times5] 941 991 1022 1065 1119 1175 1249 1341 1425 1509

25 CSF [7times7] 1019 1081 1088 1101 1116 1137 1160 1188 1229 1267







Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951

5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419

6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539

7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340

8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621

9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637

10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098

11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503

12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557

13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417

14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458

15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239

16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566

17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613

18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385

19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598

20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557

21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451

22 AWWF 09953 09934 09898 09865 09820 09765 09721 09690 09620 09568

23 CSF [3times3] 09973 09949 09849 09742 09611 09452 09272 09067 08854 08614

24 CSF [5times5] 09938 09924 09900 09866 09822 09771 09710 09640 09555 09469

25 CSF [7times7] 09912 09848 09839 09828 09813 09789 09765 09735 09700 09659







Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163

5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578

6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687

7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460

8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732

9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760

10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261

11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588

12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638

13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488

14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525

15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392

16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665

17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702

18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476

19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689

20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662

21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908

22 AWWF 09974 09960 09941 09912 09888 09852 09791 09745 09700 09656

23 CSF [3times3] 09976 09962 09879 09796 09689 09561 09412 09246 09068 08862

24 CSF [5times5] 09964 09952 09949 09915 09871 09828 09778 09716 09652 09571

25 CSF [7times7] 09925 09913 09906 09895 09889 09861 09838 09810 09785 09766







Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345

5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610

6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669

7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569

8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732

9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734

10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385

11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602

12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628

13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578

14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636

15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501

16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670

17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680

18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565

19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662

20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620

21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339

22 AWWF 09961 09950 09938 09895 09872 09840 09786 09750 09733 09713

23 CSF [3times3] 09979 09961 09940 09843 09762 09666 09550 09418 09282 09126

24 CSF [5times5] 09944 09935 09920 09899 09873 09847 09797 09749 09693 09630

25 CSF [7times7] 09886 09877 09871 09862 09850 09832 09815 09792 09762 09751







Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024

5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227

6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360

7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314

8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398

9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411

10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201

11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395

12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434

13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358

14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396

15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284

16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425

17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469

18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316

19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329

20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312

21 NL-Means 09957 09943 09865 09716 09516 09285 09010 08737 08423 08127

22 AWWF 09943 09918 09893 09836 09748 09690 09614 09568 09492 09453

23 CSF [3times3] 09964 09945 09895 09773 09721 09666 09536 09485 09313 09261

24 CSF [5times5] 09913 09896 09866 09838 09793 09779 09692 09576 09517 09458

25 CSF [7times7] 09834 09818 09799 09783 09779 09752 09717 09659 09600 09534




Sl No

Denoising Images

Filters


1 Mean [3times3] 262 290 410 668

2 Mean [5times5] 443 408 642 946

3 Mean [7times7] 573 520 793 1035

4 Median [3times3] 132 153 252 438

5 Median [5times5] 270 239 443 693

6 Median [7times7] 395 311 499 744

7 ATM [3times3] 262 290 410 668

8 ATM [5times5] 443 408 642 946

9 ATM [7times7] 573 520 793 1035

10 Wiener [3times3] 186 204 318 387

11 Wiener [5times5] 367 351 540 637

12 Wiener [7times7] 464 387 576 668

13 AD 204 237 295 497

14 TV 211 234 334 573

15 Lee [3times3] 00118 109 00336 00583

16 Lee [5times5] 00530 114 01109 02057

17 Lee [7times7] 01315 201 01853 110

18 Bilateral [3times3] 288 308 423 680

19 Bilateral [5times5] 497 433 663 966

20 Bilateral [7times7] 601 545 826 1104

21 NL-Means 117 137 186 211

22 AWWF 183 206 321 387

23 CSF [3times3] 122 142 183 318

24 CSF [5times5] 272 257 402 675

25 CSF [7times7] 4437 390 619 907




Execution time (seconds) in three different hardware

platforms Sl No Denoisg Filters


1 Mean [3times3] 318 701 1713

2 Mean [5times5] 323 712 1749

3 Mean [7times7] 327 720 1776

4 Median [3times3] 402 742 2445

5 Median [5times5] 409 747 2469

6 Median [7times7] 415 812 2490

7 ATM [3times3] 732 1677 3018

8 ATM [5times5] 809 1723 3056

9 ATM [7times7] 813 1784 3084

10 Wiener [3times3] 787 1559 2806

11 Wiener [5times5] 807 1598 2876

12 Wiener [7times7] 843 1670 3006

13 AD ------ ------- ------

14 TV ------ ------- ------

15 Lee [3times3] 874 1426 3509

16 Lee [5times5] 887 1446 3545

17 Lee [7times7] 968 1579 3779

18 Bilateral [3times3] 536 1100 3265

19 Bilateral [5times5] 583 1353 3520

20 Bilateral [7times7] 588 1359 3639

21 NL-Means 44667 99620 221838

22 AWWF 1181 2417 4546

23 CSF [3times3] 338 706 1866

24 CSF [5times5] 343 717 1898

25 CSF [7times7] 352 729 1930





(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

PS

NR

(d

B)

PSNR values for Lena Image PSNR values for Pepper Image

PS

NR

(d

B)

(a) (b)

σn σn

PSNR values for Goldhill Image

PS

NR

(d

B)

PSNR values for Barbara Image P

SN

R (

dB

)

(c) (d)

σn σn



Fig 39 Performance comparison of various filters in terms of RMSE under


(a) Lena (b) Pepper


RM

SE


RM

SE


(a) (b)

σn σn


RM

SE


RM

SE

(c) (d)

σn σn



Fig 310 Performance comparison of various filters in terms of UQI under different noise levels of AWGN on the images

(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

UQI values for Lena Image

UQ

I

UQI values for Pepper Image

UQ

I

(a) (b)

σn σn

UQ

I

UQ

I

UQI values for Barbara Image UQI values for Goldhill Image

(c) (d)

σn σn



(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)



(c) ndash (m) Results of various filtering schemes


(k) NL-Means (l) AWWF (m) CSF



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

Fig 312 Performance of Various Filters for Lena Image (Smooth Region)

with AWGN σn = 15



(c) Mean (d) Median (e) ATM (f) Wiener (g) AD (h) TV (i) Lee

(j) Bilateral (k) NL-Means (l) AWWF (m) CSF



(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k) (l) (m)

Fig 313 Performance of Various Filters for Lena Image (Complex Region) with

AWGN σn = 15







(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

(m)


AWGN σn = 40







(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k)

(l) (m)













(d)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(l)

(m)



34 Conclusion

It is observed that the proposed filters AWWF and CSF are very efficient in

suppressing AWGN from images

It is seen that AWWF outperforms the other existing spatial-domain filters in

suppressing additive noise under moderate noise (10lt σnle30) conditions The PSNR

and UQI values are relatively high as compared to other filters under moderate noise

conditions The NL-means filter shows better performance under low noise (σnle10)

condition

Hence it may be concluded that the AWWF is best spatial-domain filter in

suppressing additive noise under moderate noise conditions It preserves the edges

and fine details very well as observed in Fig 313 compared to other filters The

filter does not perform well under high noise conditions as observed in Fig 317 and

tables Table 31- Table 312

On the other hand the proposed circular spatial filter (CSF) is an excellent

filter for suppressing high power additive noise Its performance is observed to be

much better as compared to other spatial-domain filters under high noise conditions

This is quite evident from the observation tables for PSNR RMSE and UQI

Moreover the visual quality of its output under high noise conditions is very good as

observed in Fig 315 The filter CSF is also seen to preserve fine details and edges and

is seen not to yield unnecessarily high blurring effect in smooth regions under high

noise conditions This is evident from Fig 316

Thus it is observed that the proposed filter AWWF is very good in

suppressing moderate power AWGN whereas the CSF is found to be a very efficient

filter under nigh noise conditions

Comparing the method noise of various spatial-domain filters it is found from

Table 313 that the existing Lee filter is best among all Nevertheless the proposed

filter CSF with a window of 3times3 is also observed to be a good competitor for the test

image Pepper



The execution time TE taken by a filter is an important measure to find its

computational complexity It is observed from Table 314 that the proposed filter

CSF is second only to the simplest mean filter Hence its computational complexity is

found to be very low whereas the other proposed filter AWWF is observed to possess

moderate computational complexity

The proposed filter CSF may be used in many real-time applications due to its

following advantages [P2]

i) The circular spatial filter has got relatively low computational

complexity as compared to other efficient spatial-domain filters and it

is very close to the simplest mean filter

ii) It suppresses AWGN very effectively from homogenous and

monotonically increasing and decreasing regions as compared to

others

iii) The filter retains the detailed information very well as compared to

other spatial-domain filters

iv) As the method noise is quite less which is very close to NL-Means

filter the filter causes little distortion to the original image

Thus the proposed filtering schemes are observed to be very good

spatial-domain image denoising filters

Chapter 4

Development of

Transform-Domain

Filters



Preview

Image transforms play an important role in digital image processing Various

image transforms such as Discrete Cosine Transform (DCT) [1517] Singular Value

Decomposition (SVD) Transform [2] Discrete Wavelet Transform (DWT) [18-21]

etc are employed for various applications like image denoising image compression

object recognition etc

The two-dimensional DCT is a very efficient transform for achieving a sparse

representation of image blocks For natural images its decorrelating performance is

close to the optimum Karhunen-Loegraveve (KL) transform [2] Thus the DCT has been

successfully used as the key element in many denoising applications However in the

presence of singularities or edges such near-optimality fails Because of the lack of

sparsity edges can not be restored effectively and ringing artifacts arising from Gibbs

phenomenon become visible

The Discrete Wavelet Transform (DWT) is another powerful tool for image

denoising Image denoising using wavelet techniques is effective because of its ability

to capture most of the energy of a signal in a few significant transform coefficients

4



when image is corrupted with Gaussian noise One method that has received

considerable attention in recent years is wavelet thresholding or shrinkage an idea of

killing coefficients of low magnitude relative to some threshold The various

thresholding or shrinkage techniques proposed in the literature are VisuShrink [9899]

SureShrink [100101] BayesShrink [102] NeighShrink [103] SmoothShrink [104]

OracleShrink [102] OracleThresh [102 ] etc The windowing techniques such as

locally adaptive window maximum likelihood (LAWML) estimation [105] are also

available in the literature where the statistical relationship of coefficients in a

neighborhood is considered The wavelet domain methods are suitable in retaining the

detailed structures but they introduce mat-like structures in the smooth regions of the

filtered image

In this chapter three transform-domain image denoising filters (i) Gaussian

Shrinkage based DCT-domain (GS-DCT) Filter [P3] (ii) Total Variation based DWT-

domain (TV-DWT) Filter [P4] (iii) Region Merging based DWT-domain (RM-DWT)

Filter [P5] are developed The performances of the developed filters are compared

with existing transform-domain filter in terms of objective and subjective evaluations

to demonstrate the effectiveness of the developed filters

The organization of this chapter is outlined below




Simulation Results

Conclusion



41 Development of Gaussian Shrinkage based DCT-domain

Filter

The proposed filter Gaussian Shrinkage based DCT-domain (GS-DCT) filter

[P3] presents a simple image denoising scheme by using an adaptive Gaussian

smoothing based thresholding in the discrete cosine transform (DCT) domain The

edge pixel density on the current sliding window decides the threshold level in the

DCT domain for removing the high frequency components eg noise Since the hard

threshold approach is discontinuous in nature and it tends to yield artifacts (like Gibbs


DCT coefficients is proposed

The section is organized as follows

bull The Proposed Scheme

bull Mask Selection

bull Parameters Selection

411 The Proposed Scheme

In the proposed method soft thresholding technique is applied in DCT domain

for suppression of additive white Gaussian noise (AWGN) The soft thresholding

decision is based on the image complexity in the windowed data Here the percentage

of edge pixel (PEP) is considered to determine the image complexity The block

diagram of the proposed method is shown in Figure 41 Seven threshold values are

predefined which are selected adaptively depending on the percentage of edge pixels

in the current window The PEP can be defined as follows

100Number of edge pixels

PEPTotal number of pixels in the current window

= times (41)

Thresholding is nothing but considering certain number of DCT coefficients and

making others zero In other words the DCT coefficient matrix is multiplied point-by-



point by another matrix of same size of suitable values at desired row and column to

get the modified DCT coefficient matrix This matrix is termed as mask The values

of mask are obtained from a Gaussian function defined in equation (42)

2

2

( ) exp2

exp

2

exp2

kxf x A

xA

k

xA

c

σ

σ

= minus

minus =

minus =

(42)

where x = spatial-distance

σ = standard deviation of the Gaussian function

k = a constant

c =σ2k = controlling parameter

Thus a mask contains varying weights for the DCT coefficients These

weights are tapered from low frequency to high frequency components so that noise

gets less scope to reproduce itself Choosing a mask is very important The shaded

portions represented in the Fig41 in the mask represent the non-zero Gaussian values

and rests are zeros



Fig 41 Block Diagram of the Proposed Filter

INPUT NOISY

IMAGE

7times7

window

DCT

Edge Detection

Percentage of

Edge Pixels Adaptive Threshold

Selection

7times7 DCT Coefficient matrix

FILTERED IMAGE

Masking matrices

IDCT

Point by point matrix

multiplication Mask-1 Mask-2 Mask-3 Mask-4 Mask-5 Mask-6 Mask-7



412 Mask Selection

The selection of an appropriate mask depends on the PEP value If in a

window the percentage of edge pixels (PEP) is low then the image segment most

probably contains a flat or almost a flat or monotonic region that may be encoded in

DCT domain with less number of coefficients On the other hand if the PEP is high

then the selected image segment must be encoded with more number of DCT

coefficients in order to preserve the edges and fine details of the image Based on this

heuristic a mask selection criterion is proposed here

1 5

2 5 8

3 8 12

4 12 18

5 18 24

6 24 30

7 30

Mask if PEP

Mask if PEP

Mask if PEP

Mask Mask if PEP

Mask if PEP

Mask if PEP

Mask if PEP

le lt le lt le

= lt le lt le

lt le

lt

(43)

The mask provides the Gaussian weights to the DCT coefficients of the image

block The DC coefficient which is located at the upper left corner holds most of the

image energy and represents the average value This DC coefficient should be

retained as it is and hence it should be provided with unity weight Other DCT

coefficients are necessarily given weights less than unity The weights are varied in

accordance with (42)



413 Parameters Selection

The appropriate value of the parameter lsquoArsquo and the parameter lsquocrsquo has to be

chosen for efficient suppression of Gaussian noise

The selection of parameter lsquoArsquo

In (42) for x = 0 f (0) = A

The DC coefficient of DCT block should be provided with a weight of 1 ie f(0) = 1

Hence A = 1

So the parameter A in (42) is set to 1

The selection of parameter lsquocrsquo

The filtering performance of the proposed method in terms of peak-signal-to-

noise ratio (PSNR) is tested on the noisy images Lena Pepper and Goldhill for

different values of lsquocrsquo The noisy version of the test images are generated by

corrupting the images with Gaussian noise of standard deviation σn = 20 and 30 The

values of c are varied from 001 to 01 It is observed that the PSNR increases upto

c = 004 Between the values of c = 004 and 007 the PSNR almost remains constant

Then the PSNR detoriates slightly beyond 007 The PSNR values obtained are

plotted against the values of c which are shown in Fig 42

It is observed that high values of PSNR are obtained while the parameter lsquocrsquo

lies within 004 to 007 for various images under different noise conditions Therefore

an optimal value of 005 is chosen for the parameter lsquocrsquo in (42) for efficient

suppression of additive noise

The developed filter GS-DCT is tested and its simulation results are presented

in Section 44



002 004 006 008 0127

28

29

30

31

Lena

Pepper

Goldhill

Pea

k S

ign

al

to N

ois

e R

ati

o (

dB

)

parameter c

(a)

Fig 42 PSNR vs different values of c for noisy images Lena

Pepper and Goldhill under AWGN of

(a) σn = 20

(b) σn = 30

002 004 006 008 0125

26

27

28

29

Lena

Pepper

Goldhill

Pea

k S

ign

al

to N

ois

e R

ati

o (

dB

)

(b)

parameter c



42 Development of Total Variation based DWT-domain Filter

The proposed filter introduces a Total Variation (TV) based wavelet domain

scheme for image denoising The TV algorithm [69] is employed in spatial-domain

and is found to be effective in suppressing Gaussian noise from a homogenous region

(small variation in image pixel values) of an image corrupted with a low power noise

(standard deviation σnle10) However the method undergoes several iterations for

suppressing the noise when the level of noise is high Hence to estimate the number

of iteration for suppressing noise is a major disadvantage in TV based denoising

Another disadvantage of TV based denoising is to find the tuning parameter lsquoλrsquo The

value of lsquoλrsquo increases with increase of noise

In wavelet domain methods [98-106] the noisy image is decomposed to

around five levels for efficient denoising This leads to increase in computational

complexity extra hardware and extra cost

To take the advantages of TV algorithm for observing image variations in

different directions as well as to take the advantages of wavelet-domain processing for

analyzing an image at different levels of resolution it is proposed to develop a filter

based on TV-algorithm in DWT-domain Here the noisy image is decomposed to

single level and TV algorithm undergoes only single iteration The tuning parameter

lsquoλrsquo in TV algorithm used in the proposed filter varies from 02 to 08


The Proposed Method

The Proposed Algorithm

The Choice of Tuning Parameter



421 The Proposed Method

In the proposed method the total variation algorithm is applied on a noisy

image decomposed in wavelet domain for suppression of additive white Gaussian

noise (AWGN) After the decomposition process four different subbands low-low

(LL) low-high (LH) high-low (HL) and high-high (HH) are obtained The LL

subband is a coarse (low resolution) version of the image and the HL LH and HH

subbands contain details with vertical horizontal and diagonal orientations

respectively The total number of coefficients in the four subbands is equal to the total

number of pixels in the image The Daubechiesrsquo tap-8 wavelet (Db8) [14] is used in

the proposed method for the purpose of decomposition The edge detection algorithm

is applied on the LL subband of a single decomposed noisy image to find horizontal

vertical and diagonal edges Many edge detection algorithms such as Sobel Canny

Roberts Prewitt etc are proposed in the literature [22-27] In the proposed algorithm

the Sobel operator is used for finding the edges (horizontal vertical and diagonal) of

the LL subband Using the pixel positions of the resulting horizontal edges the

corresponding wavelet coefficients in HL subband are retained thresholding others to

zero Adopting the same procedure the vertical and diagonal details of LH and HH

subands are retained The method TV is applied to LL subband for one iteration only

Applying inverse wavelet transform on modified wavelet coefficients the denoised

image is obtained This output contains some noise The residual noise is quite low as

compared to the input noise level This noise can further be suppressed using the TV

algorithm with single iteration in the spatial-domain

The advantage of Sobel operator

The Sobel operator has the advantage of providing both a differencing and a

smoothing effect [1] Because derivatives enhance noise the smoothing effect is

particularly an attractive feature of Sobel operator The operator also gives an

estimate of edge direction as well as edge magnitude at a point which is more

informative It is relatively easy to implement the operator in hardware most

obviously by a pipeline approach



422 The Proposed Algorithm


Step ndash 1

The noisy image is decomposed to one level using Daubechiesrsquo tap-8 (Db8) wavelet

This gives rise to four subbands (LL HL LH and HH)

Step ndash 2

The Sobel operator is used to find the horizontal vertical and diagonal edges of the

LL subband obtained in Step-1

Step ndash 3

Using the pixel positions of the resulting horizontal vertical and diagonal edges the

corresponding wavelet coefficients of HL LH and HH subbands are retained

thresholding others to zero This gives rise to the modified wavelet coefficients of the

subbands HL LH and HH ieHL LH andHH respectively

Step ndash 4

Total variation (TV) algorithm with single iteration is applied on the LL subband (low

resolution version of the image) to suppress the Gaussian noise Here the modified

wavelet coefficients corresponding to LL subband ieLL is obtained

Step ndash 5

The inverse wavelet transform is applied on the modified wavelet coefficients

(LL HL LH and HH ) to get the image with a small residual noise f

Step ndash 6

The TV filter with single iteration is applied on the image f obtained in Step-5 to get

the filtered image f



423 The Choice of Tuning Parameter

The tuning parameter λ of the TV algorithm used in the proposed method is

important for efficient denoising The choice of λ is completely based on

experimentation An experiment is conducted on the various noisy test images at

different noise levels for various values of λ to obtain optimal PSNR The experiment

does not converge to a single value of λ The value is different for different images as

well as for different noise levels However the value of PSNR does not differ much

for slight variations of λ From the experiment it is found that the value of λ is varied

from 02 to 08 The observation details are given in the Table-41

Table-41 Optimal value of λ for TV algorithm used in the proposed filter at different

noise levels of AWGN for obtaining optimal PSNR

Noise level of AWGN

Sl No

Value of λ at different steps

of proposed algorithm

Low

(σnle10)

Moderate

(10lt σnle30)

High

(30lt σnle50)

1 Optimal value of λ in DWT-

domain (for Step-4) 02 04 05

2 Optimal value of λ in

spatial-domain (for Step-6) 03 055 08

The proposed TV-DWT image filtering scheme is implemented on

MATLAB 70 platform and its simulation results are presented in Section 44



43 Development of Region Merging based DWT-domain Filter

The proposed region merging based DWT-domain (RM-DWT) filter

introduces an image denoising scheme with region merging approach in wavelet-

domain In the proposed method the wavelet transform is applied on the noisy image

to yield the wavelet coefficients in different subbands A region including the

denoising point in the particular subband is partitioned in order to get distinct sub-

regions The signal-variance in a sub-region is estimated by using maximum

likelihood (ML) estimation [105] It distinguishes a sub-region with some reasonably

high ac signal power from a sub-region containing negligible ac signal power The

sub-regions containing some appreciable ac signal power are merged together to get a

large homogenous region However if the sub-region including denoising point has

negligible ac signal power then this sub-region can be merged with other likelihood

sub-regions with negligible ac signal power to get a homogenous region Now in a

large homogenous region in wavelet domain the signal variance is estimated with



minimum mean squared error (MMSE) estimator [105]


The Proposed Scheme





In order to find the filtered image it is necessary to estimate the wavelet

coefficients of the original (noise-free) image decomposed in wavelet domain The

minimum mean squared error (MMSE) estimator plays an efficient role in estimating

coefficients of original (noise-free) decomposed image from the wavelet coefficients

of noisy decomposed image The minimum mean squared error estimator is defined

as

2

2 2

ˆˆ

ˆk

k k

k n

w yσ

σ σ=

+ (44)

where ˆk

w and k

y are the estimated and known wavelet coefficients in a kth

region of a

particular subband

In (44) 2ˆkσ and 2

nσ are the estimated signal variance and noise variance respectively

It is then important to estimate the signal variance in a region However this

can be estimated from maximum likelihood (ML) principle which is defined as

( )

( )

2

2 2

0(k)

2 2

(k)

arg max P Y(j) |

1max 0 Y j

k

j

n

jM

σσ σ

σ

geisin

isin

=

= minus

prod

sum

N

N

(45)

where Y(j) is the wavelet coefficients in a sub-region N(k) and M is the total number

of coefficients in the particular sub-region

In the proposed scheme the noisy image undergoes five levels of

decomposition in wavelet domain to yield wavelet coefficients in different subbands

The Daubechiesrsquo tap-8 (Db8) [14] wavelet is used for the purpose of decomposition

After a decomposition process four different subbands low-low (LL) low-high

(LH) high-low (HL) and high-high (HH) are found In a particular subband a square

shaped 9times9 region is divided into distinct 3times3 sub-regions So in a large region nine

distinct sub-regions are obtained In each distinct sub-region the signal variance is

estimated using ML estimator Depending upon the ac power level the sub-regions



are merged to form a larger sub-region for better estimation of signal component

Then the MMSE algorithm is applied to this large sub-region to estimate the wavelet

coefficients of original image

The RM-DWT algorithm is presented below


The proposed algorithm RM-DWT is presented in the form of a flow-chart

shown in Fig 43

Input

DWT

Get a sub-image by

windowing (Sliding window of size 9times9)

Split into 3times3 sub-regions

Find signal variance using

ML Estimation

Merge similar regions

Estimate wavelet coefficients of original image using MMSE

(applied on large homogenous region)

IDWT

ˆ ( )f x y

Y

Y

( ) ( ) ( )g x y f x y x yη= +

Noisy Image

Output

Fig 43 Flow Chart of the RM-DWT algorithm



The proposed filter RM-DWT is implemented on MATLAB 70 platform and

its simulation results are presented in Section 44


The proposed transform-domain filters Gaussian Shrinkage based DCT-

domain (GS-DCT) filter Total Variation based DWT-domain (TV-DWT) filter and

Region Merging based DWT-domain (RM-DWT) filter are simulated in MATLAB

70 platform The test images Lena Pepper Goldhill and Barbara of sizes 512times512

corrupted with AWGN of standard deviation σn = 5 10 15 20 25 30 35 40 45 and

50 are used for simulation purpose The performances of the proposed transform-

domain filters are compared with those of existing wavelet-domain filters VisuShrink

SureShrink BayesShrink OracleShrink OracleThresh NeighShrink SmoothShrink

and Locally adaptive window maximum likelihood (LAWML) The peak-signal-to-

noise ratio (PSNR) root-mean-squared error (RMSE) universal quality index (UQI)

method noise (MN ) and execution-time (TE) are taken as performance measures

The PSNR values of the different transform-domain filters for various images

are given in the tables Table-42 to Table-45 The largest PSNR value for a

particular standard deviation of Gaussian noise is highlighted to show the best

performance The PSNR values under different noise conditions are graphically

represented in Fig 44 Only high performing filters are included in the figure


Table-49 The smallest RMSE value for a particular standard deviation of Gaussian

noise is highlighted The RMSE values vs Standard deviation of AWGN for various

images are shown in Fig 45 The proposed filters are compared with only some high

performing filters

The UQI of various filters are given in the tables Table-410 to Table-413

The value of UQI is always less than 1 The greatest value of UQI for a particular

standard deviation of Gaussian noise is identified and is highlighted The UQI values



of proposed filters and some existing high performing filters under different noise

conditions for various images are plotted in Fig 46

The method noise of the proposed transform-domain filters are compared with

existing transform-domain filters and the values are tabulated in Table-414 The

filtering performance is better if the method noise is very low since it talks of little

distortion when a non-noisy image is passed through a filter Therefore a least value

of method noise for a particular noise standard deviation is highlighted to show the

best performer

The filters are simulated on three different computing systems SYSTEM-1

SYSTEM-2 and SYSTEM-3 presented in Table-11 in Section-15 The execution

time of the different filters is given in Table-415 The filter having less execution

time is usually required for online and real-time applications The least value of

execution time is highlighted

For subjective evaluation the filtered output images are shown in figures

Fig 47 to Fig 414 The test images Lena and Pepper are used for subjective

evaluation A smooth region and a complex region of Lena image are taken for

critical analysis The performance of various filters for smooth regions is shown in

Fig 413 whereas that for complex regions is shown in Fig 414

Conclusions are drawn in Section 45



Table-42 Filtering performance of mean filter and various transform-domain filters in terms

of PSNR (dB) operated on Lena image under various noise conditions (σn varies from 5 to 50)

Peak-Signal-to-Noise Ratio PSNR (dB)

Standard deviation of AWGN Sl

No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148

5 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621

6 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607

7 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815

8 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542

9 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497

10 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131

11 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458

12 LAWML[5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602

13 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638

14 GS-DCT 3376 3313 3188 3098 3001 2911 2746 2706 2689 2611

15 TV-DWT 3465 3376 3229 3056 296 2844 2736 2667 2558 2477

16 RM-DWT 3910 3472 3236 3069 2948 2858 2781 2723 2655 2602



Table-43 Filtering performance of mean filter and various transform-domain filters in

terms of PSNR (dB) operated on Pepper image under various noise conditions (σn varies from 5 to 50)



No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137

5 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454

6 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505

7 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835

8 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564

9 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451

10 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728

11 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447

12 LAWML[5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560

13 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575

14 GS-DCT 3379 3310 3259 3100 2976 2855 2766 2621 2610 2562

15 TV-DWT 3278 3183 3075 297 2865 2772 2675 2593 2507 2438

16 RM-DWT 3918 3481 3189 3083 2971 2852 2748 2687 2523 2454




terms of PSNR (dB) operated on Goldhill image under various noise conditions (σn varies from 5 to 50)



No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026

5 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462

6 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409

7 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921

8 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724

9 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411

10 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762

11 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361

12 LAWML[5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443

13 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443

14 GS-DCT 3325 3161 3089 2956 2821 2716 2623 2518 2474 2401

15 TV-DWT 2782 2693 2645 2594 254 2488 2434 2379 2327 2277

16 RM-DWT 3812 3331 3076 2922 2800 2719 2635 2555 2497 2442




of PSNR (dB) operated on Barbara image under various noise conditions (σn varies from 5 to 50)



No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989

5 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286

6 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271

7 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044

8 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708

9 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326

10 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739

11 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295

12 LAWML[5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371

13 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378

14 GS-DCT 3376 3195 3085 2995 2808 2649 2544 2439 2416 2321

15 TV-DWT 2712 2693 2645 2594 254 2488 2434 2379 2327 2277

16 RM-DWT 3793 3310 3012 2834 2689 2588 2496 2431 2372 2325




terms of RMSE operated on Lena image under various noise conditions (σn varies from 5 to 50)

Root-Mean-Squared Error (RMSE)


No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150

5 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247

6 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267

7 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155

8 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320

9 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438

10 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193

11 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505

12 LAWML[5times5] 299 475 621 747 863 955 1046 1127 1198 1275

13 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223

14 GS-DCT 558 562 649 720 805 893 1080 1131 1153 1261

15 TV-DWT 472 523 619 756 844 965 1092 1183 1341 1472

16 RM-DWT 282 468 614 744 856 949 1037 1109 1199 1275




terms of RMSE operated on Pepper image under various noise conditions (σn varies from 5 to 50)



No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177

5 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512

6 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425

7 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083

8 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212

9 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517

10 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487

11 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524

12 LAWML[5times5] 293 472 607 732 852 966 1070 1166 1263 1338

13 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315

14 GS-DCT 521 564 598 718 828 952 1055 1247 1263 1335

15 TV-DWT 585 653 739 834 941 1048 1172 1288 1422 1540

16 RM-DWT 280 463 648 732 833 956 1077 1156 1396 1512




terms of RMSE operated on Goldhill image under various noise conditions (σn varies from 5 to 50)



No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 174

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474

5 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498

6 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592

7 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792

8 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503

9 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588

10 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353

11 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682

12 LAWML[5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531

13 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531

14 GS-DCT 554 669 727 848 990 1118 1244 1404 1477 1607

15 TV-DWT 1036 1148 1213 1286 1369 1453 1547 1648 175 1853

16 RM-DWT 316 550 738 882 1015 1114 1227 1346 1438 1533




of RMSE operated on Barbara image under various noise conditions (σn varies from 5 to 50)



No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582

5 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834

6 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866

7 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424

8 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568

9 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752

10 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443

11 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815

12 LAWML[5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663

13 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650

14 GS-DCT 523 644 731 811 1005 1207 1363 1538 1579 1762

15 TV-DWT 1123 1148 1213 1286 1369 1453 1547 1648 1751 1853

16 RM-DWT 323 564 795 976 1153 1295 1440 1552 1661 1754




of UQI operated on Lena image under various noise conditions (σn varies from 5 to 50)

Universal Quality Index (UQI)


No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178

5 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636

6 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621

7 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021

8 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953

9 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530

10 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661

11 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484

12 LAWML[5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622

13 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649

14 GS-DCT 09944 09937 09911 09896 09856 09813 09740 09720 09626 09578

15 TV-DWT 09968 09938 09925 09877 09843 09788 09724 09652 09570 09481

16 RM-DWT 09985 09954 09917 09878 09844 09808 09766 09692 09654 09596




of UQI operated on Pepper image under various noise conditions (σn varies from 5 to 50)



No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289

5 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568

6 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617

7 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400

8 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484

9 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579

10 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022

11 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575

12 LAWML[5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675

13 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689

14 GS-DCT 09971 09960 09954 09921 09883 09822 09754 09721 09689 09635

15 TV-DWT 09953 09932 09908 09878 09839 09797 09741 09684 09613 09544

16 RM-DWT 09991 09971 09885 09868 09853 09833 09798 09752 09708 09639




of UQI operated on Goldhill image under various noise conditions (σn varies from 5 to 50)



No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328

5 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673

6 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627

7 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926

8 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443

9 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638

10 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541

11 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592

12 LAWML[5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656

13 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658

14 GS-DCT 09958 09949 09939 09913 09881 09845 09789 09756 09703 09648

15 TV-DWT 09976 09954 09935 09902 09873 09841 09779 09768 09718 09654

16 RM-DWT 09992 09961 09926 09889 09859 09788 09759 09698 09659 09599




of UQI operated on Barbara image under various noise conditions (σn varies from 5 to 50)



No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138

5 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424

6 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401

7 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005

8 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136

9 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491

10 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233

11 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433

12 LAWML[5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517

13 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521

14 GS-DCT 09945 09933 09913 09867 09823 09764 09701 09645 09532 09512

15 TV-DWT 09801 09783 09755 09724 09685 09643 09593 09537 09478 09413

16 RM-DWT 09989 09951 09898 09859 09807 09759 09700 09647 09573 09511



Table-414 Method Noise MN of mean filter and various transform-domain

filters operated on different test images

Sl No Images Denoising

Filters

Lena Pepper Goldhill Barbara

1 Mean [3times3]

262 290 410 668

2 Mean [5times5]

443 408 642 946

3 Mean [7times7]

573 520 793 1035

4 VisuShrink

318 423 471 637

5 SureShrink

517 673 770 1007

6 BayesShrink

00232 00273 00194 00190

7 OracleShrink

00285 00267 00242 00238

8 OracleThresh

00285 00267 00242 00238

9 NeighShrink

408times10-10

466times10-10

334times10-10

497times10-10

10 SmoothShrink

660 752 64515 790

11 LAWML [3times3]

408times10-10

466times10-10

334times10-10

497times10-10

12 LAWML[5times5]

408times10-10

466times10-10

334times10-10

497times10-10

13 LAWML [7times7]

408times10-10

466times10-10

334times10-10

497times10-10

14 GS-DCT

05737 072675 067065 07930

15 TV-DWT

201 226 341 479

16 RM-DWT

408times10-10

466times10-10

334times10-10

497times10-10



Table-415 Execution time (seconds) TE taken by mean filter and various transform-domain filters for Lena image


platforms Sl No Denoising Filters

SYSTEM-1

SYSTEM-2

SYSTEM-3

1 Mean [3times3] 318 701 2313

2 Mean [5times5] 323 712 2349

3 Mean [7times7] 327 720 2376

4 VisuShrink 0540 119 392







11 LAWML [3times3] 367 809 2669

12 LAWML[5times5] 370 815 2689

13 LAWML [7times7] 374 823 2715

14 GS-DCT 1381 3038 7025

15 TV-DWT 04261 09375 309

16 RM-DWT 515 1134 3742




PS

NR

(d

B)

PSNR values for Pepper Image

PS

NR

(d

B)

PS

NR

(d

B)


PS

NR

(d

B)

PSNR values for Barbara Image

(a) (b)

(c) (d)

Fig 44 Performance comparison of various filters in terms of PSNR (dB) under different noise levels of AWGN on the images

(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

σn

σn σn

σn




RM

SE

RM

SE


RM

SE

RMSE values for Goldhill Image RMSE values for Barbara Image

RM

SE

(a) (b)

(c) (d)

Fig 45 Performance comparison of various filters in terms of RMSE values under different noise levels of AWGN on the images

(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

σn σn

σn σn



UQ

I

UQI values for Lena Image UQI values for Pepper Image

UQ

I

UQ

I


UQ

I


(a) (b)

(c) (d)

Fig 46 Performance comparison of various filters in terms of UQI values under


(a) Lena (b) Pepper


σn σn

σn σn



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)



(c) ndash (n) Results of various filtering schemes

(c) Mean (d) VisuShrink (e) SureShrink (f) BayesShrink (g) OracleShrink

(h) OracleThresh (i) NeighShrink (j) SmoothShrink (k) LAWML (l) GS-DCT

(m) TV-DWT (n) RM-DWT

(l)

(m)

(n)



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

Fig 48 Performance of Various Filters for Lena Image (Smooth Region) with AWGN

σn = 15






(l)

(m)

(n)



(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)







(h) (i) (j)

(m) (k)

(l)

(m) (n)



(a) (b) (c)

(d)

(e) (f) (g) (h)

(i) (j) (k)







(l)

(m) (n)



(a) (b) (c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

Fig 411 Performance of Various Filters for Lena Image with AWGN σn = 40 (a) Original image (b) Noisy image





(l)

(m) (n)



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

Fig 412 Performance of Various Filters for Lena Image (Smooth Region) with AWGN σn = 40






(l)

(m) (n)



(a)

(b) (c)

(d) (e)

(g) (h) (i) (j)

(k)







(f)

(m) (n) (l)









(a) (b) (c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m) (n)



45 Conclusion

Three transform-domain filters GS-DCT TV-DWT and RM-DWT are

proposed for suppression of AWGN from images These filters are found to perform

well as compared to other existing filters

From tables Table-42 to Table-45 it is observed that the developed filters

RM-DWT and GS-DCT have higher PSNR values as compared to other filters at low

and moderate noise conditions respectively Under such noise conditions the filters

have smaller RMSE values which can be seen from tables Table-46 to Table-49

These filters also give superior performance in terms of UQI values which can be

observed from tables Table-410 to Table-413 From Table-414 it can be seen that

this two developed filters yield relatively less method noise

It is observed from these tables that the other proposed filter TV-DWT shows

moderate performance in terms of PSNR RMSE and UQI But its execution-time is

minimal as depicted in Table-415 Further it yields reasonably low method noise as

shown in Table-414 Thus the TV-DWT is a very good candidate for real-time

applications

From subjective evaluations it can be seen that the wavelet-domain filters

introduce artifacts in the smooth regions of the filtered image However they are

effective up to some extent in preserving the complex regions at the time of filtering

These are evident from Fig 412 and Fig 413 The proposed filter RM-DWT is

found to be the best in filtering smooth and complex regions with quite little distortion

and giving the best visual quality among all filters compared here

Chapter 5

Development of

Some Color Image

Denoising Filters



Preview

Most of the denoising techniques available in literature are developed and

tested only for gray images [62-106] Recently a few color image denoising filters are

reported in the literature [8137-142] Hence there is sufficient scope for developing

very good color image filters Efforts are made in this research work to develop

novel color image filters both in spatial-domain and in transform-domain

Since the circular spatial filter (CSF) and region merging based DWT-domain

(RM-DWT) filter are found in the preceding two chapters to be very efficient in

suppressing AWGN from gray images necessary modifications are made to develop

their multi-channel versions to cater to the need of color image processing

In this chapter two multi-channel filters Multi-channel Circular Spatial Filter

(MCSF) and Multi-channel Region Merging based DWT-domain (MRM-DWT) Filter

are developed for suppression of additive noise from color images The developed

filters MCSF and MRM-DWT are based on three-channel-processing (eg RGB-

5



processing YCbCr-processing etc) and hence are necessarily 3-Channel CSF and 3-

Channel RM-DWT respectively

The filtering performance is compared with Multi-channel versions of existing

filters (i) mean filter (simplest and oldest filter) [1] and (ii) locally adaptive window

maximum likelihood (LAWML) filter [105] (best performer among the existing

wavelet-domain filters examined in Chaper-2)

The organization of this chapter is given below





Development of Multi-Channel Region Merging based DWT-domain

Filter

Simulation Results

Conclusion



51 Multi-Channel Color Image Filtering

Multi-channel filters can be employed for denoising color images where each

color component of noisy image is applied to an independent channel processor The

denoising can be performed either in the basic RGB-color space or in any other color

space C such as YCbCr CMY CIE Lab etc [18] The block diagram of a multi-

channel filter is shown in Fig 51 A Type-I filter (RGB-color image filter) is

illustrated in Fig 51 (a) while a Type-II filter (any other color-space) is shown in

Fig 51 (b) A combination of a pre-processing transformation (RGB-to-other color

space) at the front end and a corresponding inverse transformation for post-processing

distinguishes a Type-II filter from Type-I filter



(a)

Filter R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

Input

Color Image

(RGB)

Output

Color Image

(RGB)

Filter

Filter

Fig 51 Block Diagram of a Multi-Channel Filter

(a) Type-I Filter (RGB-Color Space)

(b) Type-II Filter (Color Space C other than RGB)

Filter R-Channel

G-Channel

RG

B ndash

C

T

ran

sfo

rma

tio

n

C ndash

RG

B

T

ran

sfo

rma

tio

n

B-Channel

(b)

R-Channel

G-Channel

B-Channel Filter

Filter

Input

Color Image

(RGB)

Output Color Image

(RGB)



Helbert et al [137] Lian et al [139] Kim et al [140] and Luisier et al [141]

have shown that the RGB and YCbCr color spaces are found to be quite effective

color representation spaces for image (2-D) and video (3-D) denoising applications

Since the performance of denoising filters degrades in other color spaces more

concentrated efforts are made in this research work to develop color image denoising

filters only in RGB and YCbCr color spaces Nevertheless two other standard color

spaces CMY and CIE Lab are also employed initially to study their performance

An RGB to YCbCr-color space conversion [6] is given by

029900000 058700000 014400000

016873000 033126400 050000000

050000000 041866800 008131200

Y R

Cb G

Cr B

= minus minus minus minus

(51)

where Y is the luminance component of the color image and the Cb and Cr are the

blue-chrominance and red-chrominance of color image in YCbCr-color space

The conversion of RGB to CMY-color space is performed using the following

expression [1]

1

1

1

C R

M G

Y B

= minus

(52)

The RGB to CIE Lab-color space conversion is given by [153154]

1

3

1 1

3 3

1 1

3 3

116 16

500

200

n n

n n

YL

Yn

X Ya

X Y

Y Zb

Y Z

= minus

= minus

= minus

(53)



where the tristimulus values Xn Yn Zn are those of nominally white object color

stimulus and the values X Y and Z are defined by

0412 0358 0180

0213 0715 0072

0019 0119 0950

X R G B

Y R G B

Z R G B

= + +

= + +

= + +

(54)

Table 51 illustrates the performance of the denoising filters in four color

spaces RGB YCbCr CMY and CIE Lab It is observed that all filters exhibit their

best performance in YCbCr-color space Further it may be concluded that RGB is

the second-best color representation Hence CSF and RM-DWT filters are developed

for the basic color space RGB and the best color space YCbCr The performance of

various filters in terms of CPSNR (dB) is demonstrated as a bar plot in Fig 52 The

best CPSNR value for a particular standard deviation of AWGN irrespective of

window size of a filter is considered for the bar plot

Thus it is observed from Table-51 and Fig 52 that YCbCr-color space is the

most effective color representation space for image denoising applications Hence

only YCbCr-color space is considered for Type-II filter design hereafter

A brief introduction to the multi-channel versions of existing filters MF and

LAWML are given in Section 52 and Section 53 respectively The developed multi-

channel CSF (MCSF) is presented in the Section 54 Section 55 describes the

developed multi-channel RM-DWT (MRM-DWT) filter



Table-51 Filtering performance of color image denoising filters in different color spaces in terms of

CPSNR (dB) [Test Image Lena]

RGB color space

YCbCr color space

CMY color space

CIE LAB color space

Standard deviation of AWGN




Sl

No

Denoising

Filters

10

25

40

10

25

40

10

25

40

10

25

40

1 M-MF [3times3] 3350 2868 2572 3745 3326 3003 3311 2849 2555 3240 2789 2499

2 M-MF [5times5] 3029 2888 2701 3437 3322 3159 2990 2869 2684 2919 2809 2628

3 M-MF [7times7] 2820 2771 2660 3242 3195 3110 2781 2753 2643 2710 2692 2587

4 M-LAWML [3times3] 3425 2925 2583 3897 3416 3159 3386 2916 2566 3315 2846 2510

5 M-LAWML [5times5] 3455 3011 2712 3857 3341 3008 3416 2993 2695 3345 2932 2639

6 M-LAWML [7times7] 3496 3048 2755 3824 3266 2793 3457 3028 2738 3386 2969 2682

7 MCSF [3times3] 3357 2654 2245 3764 3044 2659 3318 2631 2228 3247 2575 2172

8 MCSF [5times5] 3330 3049 2686 3751 3417 3080 3291 3030 2669 3220 2970 2613

9 MCSF [7times7] 3101 2998 2835 3458 3357 3204 3062 2979 2818 2991 2919 2762

10 MRM-DWT 3502 3011 2765 3987 3388 3149 3463 2992 2748 3392 2932 2692



Fig 52 Bar plot showing the filtering performance in terms of CPSNR (dB)

in different color spaces of various filters on Lena image corrupted

with AWGN of the standard deviation

(a) σn=10 (low noise)

(b) σn=25 (moderate noise)

(c) σn=40 (high noise)

YC

bC

r

RG

B

CM

Y

CIE

La

b

CP

SN

R (

dB

)

(a)

CM

Y

RG

B

YC

bC

r

CIE

La

b

CP

SN

R (

dB

)

(b)

YC

bC

r

RG

B

CIE

La

b

CM

Y

CP

SN

R (

dB

) (c)



52 Multi-Channel Mean Filter

The mean filter is the simplest filter used for suppressing AWGN from gray

images For denoising color images the mean filter can be modified to multi-channel

mean filter (M-MF) by employing the lsquomeanrsquo operation in three independent channels

of color space (eg RGB YCbCr CMY CIE Lab etc) separately Its multi-channel

versions Type-I M-MF (RGB-color space) and Type-II M-MF (YCbCr-color

space) are developed here in accordance with Fig 51 (a) and Fig 51 (b)

respectively for color image denoising These two filters are represented in block

schematic in Fig 53

The performance of these filters is examined by extensive simulation work

presented in Section-56



Fig 53 Block Diagram of a Multi-Channel Mean Filter


(b) Type-II Filter (Color Space YCbCr)

Input

Color Image

(RGB)

Mean

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

Mean

Filter

Mean

Filter

(a)

Mean

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

Mean

Filter

Mean

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)



53 Multi-Channel LAWML Filter

The locally adaptive window maximum likelihood (LAWML) filter [105] is a

wavelet-domain filter that performs well for suppressing additive noise The filtering

performance of LAWML has already been examined and found to be very promising

for gray images Therefore its multi-channel versions Type-I M-LAWML (RGB-

color space) and Type-II M-LAWML (YCbCr color space) are developed here in

accordance with Fig 51 (a) and Fig 51 (b) respectively for color image denoising

These two filters are represented in block schematic in Fig 54





Input

Color Image

(RGB)

LAWML

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

LAWML

Filter

LAWML

Filter

(a)

LAWML

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

LAWML

Filter

LAWML

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)

Fig 54 Block Diagram of a Multi-Channel LAWML Filter





54 Development of Multi-Channel Circular Spatial Filter

The Circular Spatial Filter (CSF) is a spatial-domain filter that performs very

well for suppressing AWGN from gray images The filtering operation for

suppressing AWGN is explained in Chaper-3 The CSF is found to be quite efficient

in suppressing AWGN under moderate and high noise conditions yielding less

distortion to the filtered image The filtering performance of CSF has already been

examined and found to be very promising for gray images Therefore its multi-

channel versions Type-I MCSF (RGB-color space) and Type-II MCSF (YCbCr-

color space) are developed here [P6] in accordance with Fig 51 (a) and Fig 51 (b)


schematic in Fig 55





Input

Color Image

(RGB)

CSF

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

CSF

Filter

CSF

Filter

(a)

CSF

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

CSF

Filter

CSF

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)

Fig 55 Block Diagram of a Multi-Channel CSF Filter






DWT-domain Filter

The noise suppression capability of the Region Merging based DWT-domain

(RM-DWT) filter has been examined for the gray image in Chapter-4 It has been

observed that it performs very well for low noise conditions For denoising color

images its multi-channel versions Type-I MRM-DWT (RGB-color space) and

Type-II MRM-DWT filters are developed here in accordance with Fig 51 (a) and

Fig 51 (b) respectively These two filters are represented in block schematic in

Fig 56





Input

Color Image

(RGB)

RM-DWT

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

RM-DWT

Filter

RM-DWT

Filter

(a)

RM-DWT

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

RM-DWT

Filter

RM-DWT

Filter

Input

Color Image

(RGB)

Output Color Image

(RGB)

Fig 56 Block Diagram of a Multi-Channel RM-DWT Filter






Extensive simulation is carried out to study the performance of the multi-

channel filters M-MF M-LAWML MCSF and MRM-DWT The performance of

these filters is studied in RGB- and YCbCr-color spaces The performance measures

color-peak-signal-to-noise ratio (CPSNR) root-mean-squared error (RMSE) and

universal quality index (UQI) method noise (MN ) and execution time (TE) are

evaluated and presented in tables Table-52 to Table-518

The simulation work is performed on color test images Lena (512times512times3

pixels) and Pepper (512times512times3 pixels) corrupted with AWGN of standard deviation

σn = 5 10 15 20 25 30 35 40 45 and 50 The noise level of additive noise is

categorized as low (noise standard deviation σnle10) moderate (10ltσnle30) and high

(30ltσnle50)

The CPSNR values of multi-channel filters for RGB-color space are given in

Table-52 and Table-53 and for YCbCr-color space are given in Table-58 and Table-

59 The largest CPSNR value for a particular standard deviation of Gaussian noise is

highlighted to show the best performance

The RMSE values of multi-channel filters for RGB-color space are given in

the tables Table-54 to Table-55 For YCbCr-color space the RMSE values of multi-

channel filters are given in the tables Table-510 to Table-511 The smallest RMSE

value (best performance) for a particular standard deviation of Gaussian noise is

highlighted

The UQI values of various multi-channel filters for RGB-color space are given

in the tables Table 56 to Table 57 For YCbCr-color space the performances of

different multi-channel filters in terms of UQI values are given in Table-512 to

Table-513 The maximum value of UQI for a particular standard deviation of

Gaussian noise is identified and is highlighted as the best performance

The method noise of various multi-channel filters for the images Lena and

Pepper is presented in the table Table 514 to Table 515





time taken for different filtering schemes is given in the Table-516 and Table-517

Fig 57 illustrates the resulting CPSNR of different multi-channel filters in

RGB- and YCbCr-color spaces for Lena image that is corrupted with different levels

of AWGN The best performance measure for a particular standard deviation of

AWGN irrespective of window size of a filter is shown in the figures The execution

time (TE) of various filters is shown as bar plot in Fig 58 The TE of a filter with

larger window size (for worst-case analysis) is taken in the bar plot

For subjective evaluation the filtered output images of various multi-channel

filters are shown in the figures Fig 59 to Fig 520 The images corrupted with

AWGN of standard deviation σn = 15 (moderate-noise) and σn = 40 (high-noise) are

applied to different filters and the resulted output images are shown

It has been observed from Table-51 that the filters perform very well in

YCbCr-color space It needs further investigations whether the Type-II versions

(YCbCr-color space) exhibit good filtering characteristics in flat and smooth regions

as well as complex regions of an image To examine the distortion and artifacts the

different multi-channel filters in YCbCr-color space are applied on a smooth region

and a complex region of color Lena image corrupted with AWGN of σn = 15 and σn =

40 and the filtering performances are shown in the figures Fig 517 to Fig 520 to

demonstrate the effectiveness of the filters

In Fig 521 the magnified (zoomed) versions of output-images of the filters

M-LAWML MCSF and MRM-DWT of complex regions that are already

demonstrated in Fig 520 are shown In Fig 521 six regions (containing textures

and fine details) are chosen which are identified with green circles for critical

analysis




Table-52 Filtering performance of Type-I color image denoising filters in RGB-color space in

terms of CPSNR (dB) operated on Lena image under various noise conditions (σn varies

from 5 to 50)

CPSNR (dB)


No Denoising Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 3470 3350 3227 3078 2868 2778 2686 2572 2495 2458

2 M-MF[5times5] 3051 3029 2977 2902 2888 2855 2783 2701 2659 2599

3 M-MF[7times7] 2829 2820 2789 2776 2761 2714 2689 2660 2645 2591

4 M-LAWML [3times3] 3501 3425 3263 3078 2925 2777 2662 2583 2513 2476

5 M-LAWML[5times5] 3513 3455 3336 3161 3011 2893 2769 2712 2682 2623

6 M-LAWML [7times7] 3537 3496 3344 3179 3048 2905 2867 2755 2698 2658

7 MCSF [3times3] 3488 3357 3077 2845 2654 2477 2355 2245 2189 2083

8 MCSF [5times5] 3402 3388 3375 3179 3049 2876 2774 2686 2595 2541

9 MCSF [7times7] 3331 3101 3085 3039 2998 2952 2942 2835 2789 2733

10 MRM-DWT 3587 3502 3373 3175 3046 2908 2876 2765 2698 2661


terms of CPSNR (dB) operated on Pepper image under various noise conditions (σn varies

from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 3346 3176 3087 2942 2831 2725 2629 2538 2458 2388

2 M-MF[5times5] 3271 3097 3065 3009 2956 2894 2835 2776 2713 2673

3 M-MF[7times7] 3162 2914 2916 2859 2834 2812 2773 2737 2734 2682

4 M-LAWML [3times3] 3538 3501 3254 3076 2934 2811 2714 2638 2574 2520

5 M-LAWML[5times5] 3579 3543 3325 3163 3031 2922 2833 2758 2689 2639

6 M-LAWML [7times7] 3593 3545 3327 3170 3049 2939 2849 2777 2703 2657

7 MCSF [3times3] 3443 3346 3039 281 2623 2471 2342 223 2134 2044

8 MCSF [5times5] 3462 3464 3327 3174 3032 2902 2788 269 2597 2517

9 MCSF [7times7] 3432 3313 3278 3131 3078 3012 2948 2879 2817 2783

10 MRM-DWT 3596 3548 3318 3167 3053 2941 2856 2781 2712 2656



Table-54 Filtering performance of Type-I color image denoising filters in RGB-color space

in terms of RMSE operated on Lena image under various noise conditions (σn varies from 5

to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 469 538 620 737 938 1041 1157 1319 1442 1505

2 M-MF[5times5] 760 779 828 902 917 952 1035 1137 1194 1279

3 M-MF[7times7] 981 992 1028 1067 1049 1120 1153 1192 1213 1291

4 M-LAWML [3times3] 452 494 595 737 879 1042 1190 1303 1412 1474

5 M-LAWML[5times5] 446 477 547 669 796 912 1052 1123 1162 1244

6 M-LAWML [7times7] 434 455 542 656 763 899 939 1069 1141 1195

7 MCSF [3times3] 459 534 737 963 1201 1472 1694 1923 2051 2317

8 MCSF [5times5] 507 551 523 656 762 930 1046 1157 1285 1367

9 MCSF [7times7] 550 717 720 765 808 852 862 975 1028 1096

10 MRM-DWT 412 452 660 692 796 896 930 1056 1141 1191

Table-55 Filtering performance of Type-I color image denoising filters in RGB color space

in terms of RMSE operated on Pepper image under various noise conditions (σn varies

from 5 to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 541 658 729 862 979 1106 1236 1372 1505 1631

2 M-MF[5times5] 590 721 748 798 848 911 978 1043 1122 1175

3 M-MF[7times7] 669 890 888 948 9762 1001 1047 10915 1095 1162

4 M-LAWML [3times3] 434 452 601 738 870 1002 1120 12233 1316 1401

5 M-LAWML[5times5] 414 431 554 668 778 882 977 10655 1153 1221

6 M-LAWML [7times7] 407 430 553 663 762 865 959 10424 1135 1196

7 MCSF [3times3] 484 541 770 1003 1244 1482 1722 19568 2185 2424

8 MCSF [5times5] 473 472 553 659 777 902 1029 11522 1282 1406

9 MCSF [7times7] 490 631 656 693 737 795 856 92692 995 1035

10 MRM-DWT 406 429 559 665 758 863 951 10376 1123 1198




terms of UQI operated on Lena image under various noise conditions (σn varies from 5 to 50)

UQI



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 09954 09936 09906 09863 09811 09746 09677 09593 09502 09392

2 M-MF[5times5] 09871 09853 09842 09826 09806 09784 09751 09715 09682 09628

3 M-MF[7times7] 09768 09755 09749 09741 09733 09717 09699 09675 09652 09617

4 M-LAWML [3times3] 09966 09959 09916 09864 09811 09754 0969 09627 09561 09498

5 M-LAWML[5times5] 09978 09965 09932 09892 09852 09812 09772 09727 09685 09637

6 M-LAWML [7times7] 09977 09966 09932 09898 09861 09827 09788 09747 09709 09665

7 MCSF [3times3] 09972 09963 09863 09756 09625 09466 09286 09081 08868 08628

8 MCSF [5times5] 09945 09939 09934 09899 09861 09828 09725 09655 09572 09484

9 MCSF [7times7] 09912 09903 09855 09844 09829 09805 09789 09751 09716 09675

10 MRM-DWT 09982 09973 09915 09881 09837 09786 09788 09747 09708 09663


terms of UQI operated on Pepper image under various noise conditions (σn varies from 5 to 50)

UQI



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 09917 09901 09873 09836 09788 09731 09663 09587 09506 09410

2 M-MF[5times5] 09886 09878 09867 09849 09827 09800 09770 09731 09688 09639

3 M-MF[7times7] 09820 09815 09807 09794 09780 09760 09738 09708 09678 09641

4 M-LAWML [3times3] 09980 09950 09912 09867 09816 09758 09702 09639 09576 09505

5 M-LAWML[5times5] 09978 09906 09897 09883 09864 09842 09816 09782 09747 0971

6 M-LAWML [7times7] 09991 09983 09957 09929 09898 09861 09822 09783 09735 09697

7 MCSF [3times3] 09987 09983 099 09817 0971 09582 09433 09267 09089 08883

8 MCSF [5times5] 09979 09971 09968 09934 09898 09847 09797 09735 09671 0959

9 MCSF [7times7] 09921 09913 09906 09895 09889 09862 09838 09810 09785 09766

10 MRM-DWT 09993 09986 09961 09929 09890 09861 09821 09776 09731 09695



Table-58 Filtering performance of Type-II color image denoising filters in YCbCr-color space

in terms of CPSNR (dB) operated on Lena image under various noise conditions (σn varies

from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 3863 3745 3602 3460 3326 3209 3099 3003 2917 2838

2 M-MF[5times5] 3456 3437 3407 3366 3322 3267 3216 3159 3100 3046

3 M-MF[7times7] 3249 3242 3230 3217 3195 3172 3143 3110 3076 3040

4 M-LAWML [3times3] 4173 3897 3683 3537 3416 3323 3236 3159 3088 3019

5 M-LAWML[5times5] 4145 3857 3608 3456 3341 3224 3099 3008 2938 2840

6 M-LAWML [7times7] 4129 3824 3555 3385 3266 3107 2963 2793 2782 2694

7 MCSF [3times3] 4078 3864 3455 3224 3044 2895 2767 2659 2567 2484

8 MCSF [5times5] 3976 3781 3774 3617 3417 3276 3174 3080 2991 2913

9 MCSF [7times7] 3786 3458 3432 3398 3357 3343 3260 3204 3150 3095

10 MRM-DWT 4372 3987 3652 3508 3388 3308 3224 3149 3076 3016


in terms of CPSNR (dB) operated on Pepper image under various noise conditions (σn

varies from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 3656 3581 3475 3364 3253 3152 3052 2967 2884 2812

2 M-MF[5times5] 3520 3494 3454 3403 3346 3286 3222 3156 3094 3030

3 M-MF[7times7] 3324 3312 3294 3271 3241 3206 3170 3126 3083 3032

4 M-LAWML [3times3] 4121 3811 3611 3453 3333 3224 3131 3047 2960 2881

5 M-LAWML[5times5] 4105 3781 3575 3390 3261 3127 3028 2929 2835 2760

6 M-LAWML [7times7] 4087 3747 3505 3354 3195 3047 2926 2812 2724 2595

7 MCSF [3times3] 4018 3743 3446 3220 3042 2893 2772 2665 2572 2491

8 MCSF [5times5] 3945 3821 3696 3540 3418 3282 3174 3077 2985 2904

9 MCSF [7times7] 3832 3565 3524 3474 3414 3355 3290 3221 3156 3087

10 MRM-DWT 4212 3895 3676 3535 3402 3314 3212 3130 3050 2974



Table-510 Filtering performance of Type-II color image denoising filters in YCbCr-color

space in terms of RMSE operated on Lena image under various noise conditions (σn varies

from 5 to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 298 342 403 474 554 633 719 803 887 971

2 M-MF[5times5] 477 487 504 529 556 592 622 671 718 764

3 M-MF[7times7] 605 610 618 628 644 661 683 710 738 770

4 M-LAWML [3times3] 208 287 367 434 499 555 614 671 728 788

5 M-LAWML[5times5] 215 300 400 477 544 623 719 798 866 969

6 M-LAWML [7times7] 219 312 425 517 593 712 841 1023 1036 1146

7 MCSF [3times3] 232 334 477 623 766 912 1054 1194 1327 1460

8 MCSF [5times5] 262 327 330 391 498 586 659 735 814 891

9 MCSF [7times7] 326 475 490 509 534 543 597 637 678 722

10 MRM-DWT 166 258 389 449 515 565 617 681 738 793


space in terms of RMSE operated on Pepper image under various noise conditions (σn


RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 378 413 466 530 602 676 759 837 921 1001

2 M-MF[5times5] 443 456 478 507 541 580 624 673 723 779

3 M-MF[7times7] 555 563 574 590 611 636 663 697 732 777

4 M-LAWML [3times3] 221 316 399 478 549 623 693 763 844 924

5 M-LAWML[5times5] 225 328 415 514 597 696 780 875 975 1063

6 M-LAWML [7times7] 230 341 450 536 644 763 878 1001 1108 1285

7 MCSF [3times3] 249 342 482 625 768 912 1048 1185 1319 1448

8 MCSF [5times5] 271 313 361 433 498 582 659 737 820 900

9 MCSF [7times7] 309 420 441 467 500 535 577 625 673 729

10 MRM-DWT 199 287 370 435 507 561 631 694 761 830




in terms of UQI operated on Lena image under various noise conditions (σn varies from 5 to 50)

UQI


No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 09926 09903 09865 09813 09747 09671 09579 09475

09366 09245

2 M-MF[5times5] 09807 09799 09784 09764 09739 09704 09667 09623 09570 09515

3 M-MF[7times7] 09686 09681 09673 09663 09646 09627 09601 09572 09540 09504

4

M-LAWML

[3times3] 09977 09945 09910 09870 09834 09796 09751 09705 09656 09598

5

M-

LAWML[5times5] 09975 09939 09894 09848 09803 09739 09659 09577 09506 09384

6

M-LAWML [7times7] 09974 09935 09880 09820 09764 09665 09533 09280 09288 09131

7 MCSF [3times3] 09943 09908 09815 09687 09533 09354 09149 08928 08701 08457

8 MCSF [5times5] 09924 09920 09918 09871 09837 09717 09641 09559 09462 09361

9 MCSF [7times7] 09912 09901 09896 09861 09819 09798 09776 09727 09668 09613

10 MRM-DWT 09982 09953 09873 09832 09789 09788 09744 09699 09644 09596

Table-513 Filtering performance of Type-II color image denoising filters in YCbCr color space in


UQI



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 09917 09901 09873 09836 09787 09731 09661 09588 09501 09411

2 M-MF[5times5] 09886 09879 09866 09849 09827 09802 09769 09731 09689 09640

3 M-MF[7times7] 09820 09815 09806 09795 09780 09760 09739 09710 09680 09641

4 M-LAWML [3times3] 09956 09932 09904 09872 09837 09806 09752 09703 09641 09571

5 M-LAWML[5times5] 09955 09929 09908 09855 09812 09750 09689 09613 09524 09423

6 M-LAWML [7times7] 09954 09925 09884 09843 09783 09704 09607 09501 09385 09177

7 MCSF [3times3] 09960 09931 09865 09774 09661 09528 09380 09213 09035 08850

8 MCSF [5times5] 09950 09943 09922 09888 09849 09801 09744 09681 09605 09526

9 MCSF [7times7] 09903 09897 09886 09872 09853 09831 09804 09769 09732 09686

10 MRM-DWT 09976 09950 09920 09889 09852 09812 09762 09711 09653 09585



Table-514 Method Noise MN of various Type-I multi-channel filters in RGB-color

space operated on different test images

Sl

No

Images

Denoising Filters Lena Pepper

1 M-MF [3times3] 265 308

2 M-MF[5times5] 446 425

3 M-MF[7times7] 573 563

4 M-LAWML [3times3] 379times10-10

456times10-10

5 M-LAWML[5times5] 379times10-10

456times10-10


456times10-10

7 MCSF [3times3] 124 150

8 MCSF [5times5] 275 270

9 MCSF [7times7] 438 400

10 MRM-DWT 379times10-10

456times10-10

Table-515 Method Noise MN of various Type-II multi-channel filters in

YCbCr-color space operated on different test images

Sl

No

Images


1 M-MF [3times3] 265 308

2 M-MF[5times5] 446 425

3 M-MF[7times7] 573 563


456times10-10


456times10-10


456times10-10

7 MCSF [3times3] 124 150

8 MCSF [5times5] 275 270

9 MCSF [7times7] 438 400


456times10-10



Table-516 Execution Time (seconds) TE taken by various Type-I multi-channel filters in

RGB-color space for Lena image


Filters


1 M-MF [3times3] 855 1539 4309

2 M-MF[5times5] 8966 1614 4519

3 M-MF[7times7] 945 1701 4762

4 M-LAWML [3times3] 1188 2139 5989

5 M-LAWML[5times5] 1198 2157 6039

6 M-LAWML [7times7] 1245 2242 6277

7 MCSF [3times3] 8711 1568 4390

8 MCSF [5times5] 928 1672 4681

9 MCSF [7times7] 1001 1803 5048

10 MRM-DWT 1307 2353 6588

Table-517 Execution Time (seconds) TE taken by various Type-II multi-channel filters in YCbCr-color space for Lena image

Sl No Images

Denoising

Filters


1 M-MF [3times3] 1042 1564 4848

2 M-MF[5times5] 1104 1656 5133

3 M-MF[7times7] 1150 1726 5350

4 M-LAWML [3times3] 1624 2436 7551

5 M-LAWML[5times5] 1688 2532 7849

6 M-LAWML [7times7] 1792 2688 8332

7 MCSF [3times3] 1067 1601 4963

8 MCSF [5times5] 1148 1722 5338

9 MCSF [7times7] 1210 1816 5629

10 MRM-DWT 1984 2976 9225



Fig 58 Bar plot showing the execution time (seconds) of various multi-channel

filters in YCbCr-color space on three different hardware platforms


Ex

ecu

tio

n T

ime

in s

econ

ds

Fig 57 Performance comparison of various multi-channel filters in terms of CPSNR [dB]

for the various standard deviation of AWGN operated on Lena image

(e) in RGB-color space

(f) in YCbCr-color space

CP

SN

R [

dB

]

Standard deviation of AWGN (σn) Standard deviation of AWGN (σn)

CP

SN

R [

dB

] (a) (b)

CPSNR values in RGB-color space CPSNR values in YCbCr-color space



(a) (b) (c)

(d) (e) (f)

Fig 59 Performance of Various Filters in RGB-Color Space

for Color Lena Image with AWGN of σn = 15

(a) Original image

(b) Noisy image

(c) Type-I M-MF ndash output image

(d) Type-I M-LAWML ndash output image

(e) Type-I MCSF ndash output image

(f) Type-I MRM-DWT ndash output image



(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)

Fig 511 Performance of Various Filters in RGB-Color Space for Color Pepper Image with AWGN of σn = 15

(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)


for Color Pepper Image with AWGN of σn = 40

(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)

Fig 513 Performance of Various Filters in YCbCr-Color Space


(a) Original image

(b) Noisy image

(c) Type-II M-MF ndash output image

(d) Type-II M-LAWML ndash output image

(e) Type-II MCSF ndash output image

(f) Type-II MRM-DWT ndash output image



(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image (c) Type-II M-MF ndash output image

(d) Type-II M-LAWML ndash output image (e) Type-II MCSF ndash output image




(a) (b) (c)

(d) (e) (f)




(c) Type-II M-MF ndash output image (d) Type-II M-LAWML ndash output image

(e) Type-II MCSF ndash output image (f) Type-II MRM-DWT ndash output image



(a) (b) (c)

(d) (e) (f)



(a) Original image






(a)

(b)

(c)

(d)

(e)

(f)

Fig 517 Performance of Various Filters in YCbCr-Color Space for Color Lena Image (Smooth Region) with AWGN of σn = 15

(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)


for Color Lena Image (Complex Region) with AWGN of σn = 15

(a) Original image

(b) Noisy image





(a)

(b)

(c)

(d)

(e)

(f)


for Color Lena Image (Smooth Region) with AWGN of σn = 40

(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image






Fig 521 Zoomed versions of Fig 520 (a) (d) (e) (f) showing six various regions

containing texture and fine details in complex regions of color Lena image

(a) Original image

(b) Type-II M-LAWML ndash output image

(c) Type-II MCSF ndash output image

(d) Type-II MRM-DWT ndash output image

(c)

2

1

3

4

5

6

(a)

2

1

3

4

5

6

(d)

2

1

3

4

5

6

(b)

2

1

3

4

5

6



57 Conclusion

The performance of multi-channel filters Multi-Channel Mean Filter (M-MF)

Multi-Channel LAWML (M-LAWML) Filter Multi-Channel Circular Spatial Filter

(MCSF) and Multi-Channel Region Merging based DWT-domain (MRM-DWT)

Filter are studied in RGB- and YCbCr-color spaces It is observed that the filtering

performance is better in YCbCr-color space for all filters

From Table-52 and Table-53 (for RGB-color space) and Table-58 and

Table-59 (for YCbCr-color space) it is observed that the CPSNR values are higher

for MCSF under moderate and high noise conditions When the noise level is low the

MRM-DWT performs better than other multi-channel filters


Table-511 (for YCbCr-color space) it is observed that the RMSE values are smaller


RMSE values are smaller for MRM-DWT

The UQI values of various multi-channel filters are given in the Table 56 and

Table-57 (for RGB-color space) and in Table-512 and Table-513 (for YCbCr-color

space) From the tables it is observed that the MRM-DWT filter is found to be

effective in terms of UQI under low noise conditions Under moderate and high noise

conditions the UQI values are higher for MCSF

Considering the performance measures CPSNR RMSE and UQI it can be

concluded that the MRM-DWT is efficient in noise suppression under low noise

conditions whereas the MCSF filter suppresses additive noise quite effectively under

moderate and high noise conditions effectively

The filtering performance in terms of method noise is shown in Table-514

(RGB-color space) and Table-515 (YCbCr-color space) From these tables it is

observed that the method noise is low in case of MRM-DWT and M-LAWML So

these filters yield less distortion to the original noise-free image while filtering



operation is done These tables also illustrate that the performance MCSF in terms of

method noise is moderate

The execution time (TE) of various filters is shown in Table-516 (RGB-color

space) and Table-517 (YCbCr-color space) From these tables it is seen that the

execution time of MCSF is smaller than other multi-channel filters (except M-MF)

and is close to the simplest M-MF

The subjective evaluation should also be taken into consideration to judge the

filtering performance The filtering performances of various multi-channel filters on a


Fig 517 to Fig 520 From these figures it is observed that the wavelet-domain

multi-channel filter M-LAWML yield a lot of artifacts in the smooth region The

other wavelet-domain filter MRM-DWT also yields artifacts but it is less than

M-LAWML filter The MCSF does not introduce artifacts in the smooth region In

Fig 521 some textures and detailed structures are identified in a complex region

From the figure it is seen that the developed filter MCSF retains the detailed

information and texture effectively as compared to other multi-channel filters This is

quite obvious when the regions 5 and 6 are examined in details Only the proposed

filter MCSF is found to be capable of preserving the details in these regions On the

other hand the other two high-performing filters M-LAWML and MRM-DWT yield

high blurring in these regions

Hence it is concluded that the proposed filter MCSF [P6] is found to be a

high performing filter for suppression of AWGN from color images

Chapter 6

Conclusion

Chapter-6 Conclusion


Preview

In this thesis various spatial-domain and transform-domain filters for

suppression of additive white Gaussian noise (AWGN) available in literature are

studied and their performances are analyzed Considering the limitations of the

existing filters efforts have been made to develop two spatial-domain filters (i)

adaptive window Wiener filter (AWWF) [P1] and (ii) circular spatial filter (CSF) [P2]

and three transform-domain filters (i) Gaussian shrinkage based DCT-domain

filter (GS-DCT) [P3] (ii) Total variation based DWT-domain (TV-DWT) filter [P4]

and Region Merging based DWT-domain (RM-DWT) filter [P5] The performances of

the proposed filters are compared with existing spatial-domain and transform-domain

filters The objective evaluation metrics peak-signal-to-noise ratio (PSNR) root-

mean-squared error (RMSE) universal quality index (UQI) method noise (MN ) and

execution time (TE) are considered for comparing their filtering performances

In this research work two multi-channel filters multi-channel circular spatial

filter (MCSF) and multi-channel region merging based DWT-domain (RM-DWT)

filter are developed for suppression of additive noise from color images The

6



developed filters are based on three-channel processing (eg RGB-processing

YCbCr-processing etc) and hence are necessarily 3-channel CSF and 3-channel RM-

DWT respectively The objective evaluation metrics color-peak-signal-to-noise ratio

(CPSNR) root-mean-squared error (RMSE) universal quality index (UQI) method

noise ( MN ) and execution time (TE) are considered for comparing filter performances

All the developed filters are compared against some well-known filters

available in literature



Conclusion


61 Comparative Analysis

The filtering performances of developed filters for gray and color images are

analyzed here

611 Comparative Analysis of Developed Filters for Denoising Gray

Images

The proposed spatial-domain filters and transform-domain filters are simulated

on test images Lena Pepper Goldhill and Barbara of sizes 512times512 pixels each


50 The noise level of AWGN is categorized as low (noise standard deviation



σnle10) moderate (10ltσnle30) and high (30ltσnle50) The proposed filters are

compared with the existing spatial-domain filters mean filter median filter alpha-

trimmed mean (ATM) filter Wiener filter anisotropic diffusion (AD) filter total

variation (TV) filter Lee filter Bilateral filter and non-local means (NL-Means) filter

and existing wavelet-domain filters VisuShrink SureShrink BayesShrink

OracleShrink OracleThresh NeighShrink SmoothShrink and locally adaptive

window maximum likelihood (LAWML) To check the filtering performance of the

proposed filters as well as the existing filters the performance-measures PSNR

RMSE UQI MN and TE are evaluated for all cases To give a concise presentation of

all simulation results so as to have a precise comparative study the performance-

measures of the proposed filters as well as some high-performing existing filters are

shown in Table-61 and Table-62 only for three cases of noise level σn = 10 σn = 20

and σn = 40 just to give an insight to low moderate and high noise power conditions

respectively Here Lena is taken as test image

Table-61 shows the performance of the various filters in terms of PSNR

RMSE and UQI whereas Table-62 shows method noise and execution time of

different filters The execution time is evaluated for Pentium IV Duo Processor

(Clock 28 GHz RAM 1 GB Windows XP 32 bit OS) ie the hardware platform

SYSTEM-2 presented in Table-11 Section-15 Since the TV filter is iterative in

nature its execution time is necessarily very high and hence is not considered

Therefore it is not included in Table-62



Table-61 Filtering performance of various filters in terms of PSNR (dB) RMSE and UQI

operated on Lena image under various noise conditions ( σn = 10 20 and 40)

Noise standard deviation σn

σn = 10

σn = 20

σn = 40

Denoising Filters PSNR RMSE UQI PSNR RMSE UQI PSNR RMSE UQI

Mean 3270 589 09922 2978 826 09849 2696 1142 09700

ATM 3271 589 09922 2983 821 09851 2703 1134 09710

Wiener 3401 507 09943 3019 787 09861 2655 1198 09671

TV 3322 555 09931 3025 782 09864 2585 1298 09633

Lee 3347 540 09936 2974 828 09847 2677 1167 09688

Bilateral 3258 596 09921 2977 826 09849 2671 1175 09686

BayesShrink 3364 527 09938 3020 787 09863 2711 1124 09711

NeighShrink 3445 481 09949 3011 795 09861 2608 1264 09642

Ex

isti

ng

Fil

ters

LAWML 3459 474 09950 3086 729 09882 2732 1086 09721

AWWF 3336 545 09934 3056 754 09865 2688 1152 09690

CSF 3287 578 09949 3031 777 09866 2749 1076 09735

GS-DCT 3310 563 09902 3098 719 09896 2710 1124 09720

TV-DWT 3376 522 09936 3056 754 09855 2667 1180 09652 Pro

po

sed

Fil

ters

RM-DWT 3472 466 09954 3022 785 09815 2734 1083 09725



Table-62 Filtering performance various filters in terms of Method Noise MN and

Execution Time TE on Lena image ( σn = 0 and σn = 40 for first and second column

respectively)

Denoising Filters Method Noise Execution Time (sec)

Mean 262 720

ATM 262 1784

Wiener 186 1614

TV 211 -------

Lee 00118 1508

Bilateral 288 1347

BayeShrink 00232 415

NeighShrink 408times10-10 912

Ex

isti

ng

F

ilte

rs

LAWML 408times10-10

809

AWWF 183 2417

CSF 122 729

GS-DCT 05737 3038

TV-DWT 2014 09375

Pro

po

sed

Fil

ters

RM-DWT 408times10-10 1134



It is observed that at low noise conditions the proposed filter RM-DWT

outperforms all other filters Its PSNR is 3472 dB whereas the existing filter

LAWML gives a PSNR of 3459 dB for σn = 10

Under moderate noise conditions the proposed filter GS-DCT gives superior

performance The PSNR value of the filter at σn = 20 is 3098 dB The PSNR of

LAWML is very close to GS-DCT with a value of 3086 dB at σn = 20

Under high noise conditions the proposed filter CSF gives best performance

among all filters considered here for comparison It yields a PSNR of 2749 dB and a

UQI of 09735 at σn = 40 that are best among all other filters considered here

The method noise of RM-DWT LAWML and NeighShrink filters are same

and found to be 408times10-10 ie quite negligible and hence are best suited for very low

noise conditions

From Table-62 it is observed that the developed filter TV-DWT takes

minimum execution time which is found to be 09375 sec However the developed

filter CSF takes execution time of 729 sec which is close to the execution time of

the simplest mean filter



612 Comparative Analysis of Developed Filters for Denoising Color

Images

The simulation work is performed on color test image Lena (512times512times3


σn = 5 10 15 20 25 30 35 40 45 and 50 The filtering performances of multi-

channel filters are examined on various color spaces (eg RGB YCbCr CMY and

CIE Lab) The filtering performance is compared with multi-channel versions of

existing filters (i) mean filter [1] (simplest and oldest filter) and (ii) locally adaptive

window maximum likelihood (LAWML) filter [105] (best performer among the

existing wavelet-domain filters examined in Chapter-2) The performance of various

filters in YCbCr-color space in terms of CPSNR RMSE and UQI is given in

Table-63 Here color Lena image corrupted with AWGN of σn = 10 (low noise) σn =

20 (moderate noise) and σn = 40 (high noise) is taken to test the filter performance

Table-64 shows the method noise and execution time of various filters in YCbCr-

color space operated on Lena image



Table-63 Filtering performance of various filters in terms of CPSNR (dB) RMSE and UQI

operated on Lena image under various noise conditions ( σn = 10 20 and 40) in YCbCr-color

space

Noise standard deviation

σn = 10 σn = 20 σn = 40

Denoising

Filters

CPSNR

RMSE

UQI

CPSNR

RMSE

UQI

CPSNR

RMSE

UQI

M-MF [3times3] 3745 342 09903 3460 474 09813 3003 803 09475

M-MF [5times5] 3437 487 09799 3366 529 09764 3159 671 09623

M-MF [7times7] 3242 610 09681 3217 628 09663 3110 710 09572

M-LAWML[3times3] 3897 287 09945 3537 434 09870 3159 671 09705

M-LAWML[5times5] 3857 300 09939 3456 477 09848 3008 798 09577

Ex

isti

ng

F

ilte

rs

M-LAWML[7times7] 3824 312 09935 3385 517 09820 2793 1023 09280

MCSF [3times3] 3864 334 09908 3224 623 09687 2659 1194 08928

MCSF [5times5] 3781 327 09920 3617 391 09871 3080 735 09559

MCSF [7times7] 3458 475 09901 3398 509 09861 3204 637 09727

Pro

po

sed

Fil

ters

MRM-DWT 3987 258 09953 3508 449 09832 3149 681 09699



Table-64 Filtering performance various filters in terms of Method

Noise MN and Execution Time TE on Lena image in YCbCr-color space

Denoising Filters

Method Noise

Execution Time

M-MF [3times3] 265 1564

M-MF [5times5] 446 1656

M-MF [7times7] 573 1726

M-LAWML[3times3] 379times10

-10

2436


-10 2532

Ex

isti

ng

F

ilte

rs


-10 2688

MCSF [3times3] 12495 1601

MCSF [5times5] 2754 1722

MCSF [7times7] 4386 1816

Pro

po

sed

Fil

ters

MRM-DWT 379times10

-10 2976

From Table-63 it is observed that the proposed filter MRM-DWT performs

better under low noise conditions whereas MCSF gives better performance under

moderate and high noise conditions From Table-64 it is seen that the wavelet-

domain filters MRM-DWT and M-LAWML have lower method noise as compared

to other methods The execution time is lowest in case of simplest M-MF The

proposed MCSF has got execution time of 1601 sec which is close to that of M-MF



62 Conclusion

The developed image denoising filters AWWF [P1] CSF [P2] GS-DCT

[P3] TV-DWT [P4] RM-DWT [P5] and MCSF [P6] are examined with extensive

simulation and the results are presented in the tables Table-61 to Table-64

From the results presented in Table-61 it is observed that

(i) The RM-DWT filter performs very efficiently for low-noise power

(ii) The GS-DCT filter performs very efficiently for moderate-noise power

(iii) The CSF filter performs very efficiently for high-noise power

for gray images This conclusion is derived on the concept of yielding high values of

PSNR UQI and low RMSE so that the filtered output contains very low noise power

On the other hand if method noise and execution time parameters are considered

then some other filters should be regarded as best performers Thus for the online and

real-time applications that need low MN and TE values it is observed that

(i) The RM-DWT is the best filter yielding minimum method noise

(ii) The TV-DWT is the best filter having minimum execution time

(iii) The CSF is an excellent filter having moderate values of both MN and TE

These observations are quite evident from Table-62 If an overall comparison is

drawn amongst all filters against all the performance measures ie to consider the

noise suppression capability (PSNR RMSE UQI) as well as the system-nonlinearity

(method noise) and the system-complexity (execution time) then for gray images it

is quite obvious that

(i) The proposed filter Circular Spatial Filter (CSF) [P2] is the best

performing filter under moderate and high noise conditions

(ii) The proposed filter RM-DWT [P5] is the best filter under low noise

conditions



It is observed from Table-63 that

(i) The MRM-DWT performs well under low noise conditions

(ii) The MCSF performs well under moderate and high noise conditions

for suppressing additive noise for color images

The results presented in Table-64 show that the multi-channel version of the

existing scheme LAWML ie M-LAWML yields minimal method noise and is thus

seen to be a very good candidate for color image denoising applications under very

low noise conditions Of course it does not have high significance since the noise

power level in practical situation is seldom so low

Finally it may be concluded that the proposed filter CSF [P2] and its

multi-channel version MCSF [P6] are the best performers considering all

performance measures

63 Scope for Future Work

Some new directions of research in the field of image denoising are not yet

fully explored There is sufficient scope to develop very effective filters in the

directions mentioned below

(a) Fuzzy logic and neural network may be employed for optimizing the tuning

parameters needed in the different filters

(b) The widow size of different filters can be made adaptive for efficient

denosing The shape of the window can also be varied and made adaptive to

develop very effective filters

(c) Some other transforms such as DHT curvelet and slantlet can be used for

image denoising

(d) Very few filters are developed based on blind techniques Independent

component analysis can be a very good candidate for blind denoising


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[8] R Lukac and KN Plataniotis Color Image Processing Methods and

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[9] JS Lim Two-Dimensional Signal and Image Processing Englewood Cliffs

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[12] JC Goswami and AK Chan Fundamentals of Wavelets Theory Algorithms

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[13] Y Meyer R D Ryan Wavelets Algorithms amp Applications Society for

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[18] S Mallat ldquoA Theory for Multiresolution Signal Decomposition The Wavelet

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[19] M Vetterli C Herley ldquoWavelets and Filter Banks Theory and Designrdquo

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[21] T Cooklev A Nishihara ldquoBiorthogonal coifletsrdquo IEEE Transactions on

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[23] L S Davis ldquoA survey on edge detection techniquesrdquo Computer Graphics and

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[24] F Russo ldquoColor edge detection in presence of Gaussian noise using nonlinear

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[25] P Bao L Zhang X Wu ldquoCanny edge detection enhancement by scale

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[29] P S Windyga ldquoFast impulsive noise removalrdquo IEEE Trans on image

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[32] H-L Eng and K-K Ma ldquo Noise adaptive soft switching median filterrdquo IEEE

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[33] T Chen and HR Wu ldquoAdaptive impulse detection using center-weighted

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[34] KN Plataniotis S Vinayagamoorthy D Androutsos AN Venetsanopoulos

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[35] S Schulte S Morillas V Gregori E E Kerre ldquoA new fuzzy color correlated

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[36] H Zhou KZ Mao ldquoAn impulsive noise color image filter using learning-

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[37] Y Li GR Arce J Bacca ldquoWeighted median filters for multichannel

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[38] Z Ma D Feng HR Wu ldquoA neighborhood evaluated adaptive vector filter

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[42] S Meher Development of Some Novel Nonlinear and Adaptive Digital Image

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[44] R Li YJ Zhang ldquoA hybrid filter for the cancellation of mixed Gaussian

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[45] R Manthalkar PK Biswas BN Chatterji ldquoRotation invariant texture

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[46] M Damian E Cernadas A Formella M Delgado P Sa-Otero ldquoAutomatic

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patterns with an application to facial expressionsrdquo IEEE Transactions on

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[50] Z Wang J Yong ldquoTexture analysis and classification with linear regression

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[51] X Xie M Mirmehdi ldquoTEXEMS Texture exemplars for defect detection on

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[53] A Diplaros T Gevers I Patras ldquoCombining color and shape information for

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[54] S Naik CA Murthy ldquoDistinct multicolored region descriptors for object

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[55] T Seree L Wolf S Bileschi M Riesenhuber T Poggio ldquoRobust object

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[56] IB Ayed A Mitiche ldquoA region merging prior for variational level set image

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[57] A Safou P Maragos ldquoGeneralized flooding and multicue PDE-based image

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[63] G Angelopoulos and I Pitas ldquoMultichannel Wiener filters in color image

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[64] L Shao R M Lewitt JS Karp and G Muehllehner ldquoCombination of

Wiener filtering and singular value decomposition filtering for volume

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[65] A P Wikin ldquoScale-space filteringrdquo Proc Int Joint Conf Artif Intell IJCAI

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[71] BM Oh M Chen J Dorsey F Durand ldquoImage-based modeling and photo

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[73] E Eisemann F Durand ldquoFlash photography enhancement via intrinsic

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[74] G Petschnigg M Agrawala H Hoppe R Szeliski M Cohen K Toyama

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on Graphics vol 23 no 3 pp 664-672 2004

[75] TR Jones F Durand M Desbrun ldquoNon-iterative feature-preserving mesh

smoothingrdquo ACM Transactions on Graphics vol 22 no 3 pp 943-949

2003

[76] S Fleishman I Drori D Cohen-Or ldquoBilateral mesh denoisingrdquo ACM

Transactions on Graphics vol 22 no 3 pp 950-953 2003

[77] WCK Wong ACS Chung SCH Yu ldquoTrilateral filtering for biomedical

imagesrdquo Proceedings of IEEE international symposium on biomedical

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[78] EP Bennett L McMillan ldquoVideo enhancement using per-pixel virtual

exposuresrdquo ACM Transactions on Graphics vol 24 no 3 pp 845-852 2005

[79] JS Lee ldquoDigital image enhancement and noise filtering by use of local

statisticsrdquo IEEE Transactions on Pattern Analysis and Machine Intelligence

vol 2 no 3 pp 165-168 1980

[80] JS Lee ldquoRefined filtering of image noise using local statisticsrdquo Computer

Graphics and Image Processing vol 15 no 4 pp 380-389 1981

[81] JS Lee ldquoSpeckle suppression and analysis for synthetic aperture radar

imagesrdquo Optical Engineering vol 25 no 5 pp 636-643 1986

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interpolation and the enhanced lee filter and its application to the SAR imagersquos

denoisingrdquo Proceedings of world congress on intelligent control and

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[84] J Zhu R Chen Y Hong ldquoA novel adaptive filtering algorithm for SAR

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[85] L Klaine B Vozel K Chehdi ldquoAn integro-differential method for adaptive

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[86] B Waske M Barun G Menz ldquoA segment-based speckle filter using

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[87] A Baraldi F Parmiggiani ldquoAn alternative form of the Lee filter for speckle

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[88] A Buades B Coll and J Morel ldquoA non-local algorithm for image

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pattern recognition pp 60-65 2005

[89] A Buades B Coll and J Morel ldquoOn image denoising methodsrdquo Technical

Report 2004-15 CMLA 2004

[90] A Efros and T Leung ldquoTexture synthesis by non parametric samplingrdquo Proc

international conference computer vision pp 1033-1038 1999

[91] A Buades B Coll J Morel ldquoNon-local movie and image denoisingrdquo

International Journal of Computer Vision 76 no 2 pp 123-139 2008

[92] A Baudes B Coll JM Morel ldquoDenoising image sequences does not require

motion estimationrdquo Proceedings IEEE international conference on advanced

video and image based surveillance pp 70-74 2005

REFERENCES


[93] M Mahmoudi G Sapiro ldquoFast image and video denoising via non local

means of similar neighborhoodrdquo IEEE Signal Processing Letters vol 12 no

12 pp 839-842 2005

[94] MV Jose CC Jose JL Juan GM Gracian MB Luis R Montserrat

ldquoMRI denoising using non-local meansrdquo Medical Image Analysis vol 12 no

4 pp 514-523 2008

[95] P Coupe P Yger C Barillot ldquoFast non-local means denoising for 3D MR

imagesrdquo Proc of medical image computing and computer assisted

intervention LNCS 2879 9no2 pp 33-40 2006

[96] M Ebrahimi ER Vrscay ldquoSolving the inverse problem of image zooming

using self examplesrdquo Image Analysis and Recognition LNCS 4633 Springer

pp 117-130 2007

[97] G Gilboa S Osher ldquoNon local linear image regularization and supervised

segmentationrdquo SIAM Journal on Multiscale Modeling and Simulation vol 6

no 2 pp 597-630 2007

[98] DL Donoho IM Johnstone ldquoDe-noising by soft-thresholdingrdquo IEEE

Transactions on Information Theory vol 41 no 3 pp 613ndash27 1995

[99] DL Donoho IM Johnstone ldquoIdeal spatial adaptation via wavelet

shrinkagerdquo Biometrika vol 81 no 3 pp 425-55 1994

[100] DL Donoho IM Johnstone ldquoAdapting to unknown smoothness via wavelet

shrinkagerdquo Journal of the American Statistical Association vol 90(432) pp

1200-1224 1995

[101] F Luisier T Blu M Unser ldquoA new SURE approach to image denosing

interscale orthonormal wavelet thresholdingrdquo IEEE Transactions on Image

Processing vol 16 (3) pp 593-606 2007

[102] S Chang B Yu M Vetterli ldquoAdaptive wavelet thresholding for image

denoising and compressionrdquo IEEE Transactions on Image Processing vol 9

no 9 pp 1532-1546 2000

[103] GY Chen TD Bui A Krzyzak ldquoImage denoising using neighboring

wavelet coefficientsrdquo proceedings of IEEE international conference on

acoustics speech and signal processing rsquo04 pp 917-920 2004

REFERENCES


[104] M Mastriani and AE Giraldez ldquoSmoothing of coefficients in wavelet domain

for speckle reduction in synthetic aperture radar imagesrdquo Journal of Graphics

Vision and Image Processing vol 7(special issue) pp 1-8 2007

[105] MK Mihcak I Kozintsev K Ramchandran P Moulin ldquoLow-complexity

image denoising based on statistical modeling of wavelet coefficientsrdquo IEEE

Signal Processing Letters vol 6 no 12 pp300-303 1999

[106] M Crouse R Nowak R Baraniuk ldquoWavelet based statistical signal

processing using hidden Markov modelsrdquo IEEE Transactions on Signal

Processing vol 46(4) pp886-902 1998

[107] M Marta S Grgic M Grgic ldquoPicture quality measures in image compression

systemsrdquo Proceedings EUROCON rsquo03 p 233-7 2003

[108] Z Wang AC Bovik ldquoA universal image quality indexrdquo IEEE Signal

Processing Letters vol 9 no 3 pp81-84 2002

[109] PGJ Barten Contrast sensitivity of human eye and its effects on image

quality SPIE Washington 1999

[110] T Rabie ldquoRobust estimation approach for blind denoisingrdquo IEEE

Transactions on Image Processing vol 14 no 11 pp 1755-1765 2005

[111] F Russo ldquoAutomatic enhancement of noisy images using objective evaluation

of image qualityrdquo IEEE Transactions on Instrumentation and Measurement

vol 54 no 4 pp 1600-1606 2005

[112] S Tan L Jio ldquoA unified iterative denoising algorithm based on natural image

statistical models derivation and examplesrdquo Optics Express vol 16 (2) pp

1056-1068 2008

[113] D V Ville M Nachtegael DV Weken EE Kerre W Philips I Lemahieu

ldquoNoise reduction by fuzzy image filteringrdquo IEEE Transactions on Fuzzy

Systems vol11 no 4 pp 429-436 2003

[114] C Kervrann J Boulanger ldquoOptimal spatial adaptation for patch-based image

denoisingrdquo IEEE Transactions on Image Processing vol 15 no 10 pp 2866-

2878 2006

[115] DD Muresan TW Parks ldquoAdaptive principal components and image

denoisingrdquo Proc IEEE international conference on image processing ICIP

2003 vol 1 pp I-101-I-104 2003

REFERENCES


[116] Z Hou TS Koh ldquoImage denoising using robust regressionrdquo IEEE Signal


[117] P Shui Y Zhao ldquoImage denoising algorithm using doubly local Wiener

filtering with block-adaptive windows in wavelet domainrdquo Signal Processing

vol 87 no 7 pp 1721-1734 2007

[118] J Ma G Plonka ldquoCombined curvelet shrinkage and nonlinear anisotropic

diffusionrdquo IEEE Transactions on Image Processing vol 16 no 9 pp 2198-

2205 2007

[119] H Takeda S Farsiu P Milanfar ldquoKernel regression for image processing

and reconstructionrdquo IEEE Transactions on Image Processing vol 16 no 2

pp349-365 2007

[120] M Kazubek ldquoWavelet domain image denoising by thresholding and Wiener

filteringrdquo IEEE Signal Processing Letters vol10 no 11 pp 324-326 2003

[121] K Dabov A Foi V Katkovnik ldquoImage denoising by sparse 3-D transform-

domain collaborative filteringrdquo IEEE Transactions on Image Processing vol

16 no 8 pp 2080-2095 2007

[122] M Mignotte ldquoImage denoising by averaging of piecewise constant

simulations of image partitionsrdquo IEEE Transactions on Image Processing vol

16 no 2 pp 523-533 2007

[123] K Hirakawa TW Parks ldquoImage denoising using total least squaresrdquo IEEE


[124] J Portilla V Strela MJ Wainwright EP Simoncelli ldquoImage denoising

using scale mixtures of Gaussian in the wavelet domainrdquo IEEE Transactions

on Image Processing vol12 no11 2003

[125] L Shen M Papadakis IA Kakadiaris I Konstantinidis D Kouri D

Hoffman ldquoImage denoising using a tight framerdquo IEEE Transactions on Image

Processing vol 15 no 5 pp 1254-1263 2006

[126] M Ghazel GH Freeman ER Vrscay ldquoFractal-wavelet image denoising

revisitedrdquo IEEE Transactions on Image Processing vol 15 no 9 pp 2669-

2675 2006

REFERENCES


[127] J Zhong R Ning ldquoImage denoising based on wavelets and multifractals for

singularity detectionrdquo IEEE Transactions on Image Processing vol14 no10

pp 1435-1447 2005

[128] J Bai X Feng ldquoFractional-order anisotropic diffusion for image denoisingrdquo

IEEE Transactions on Image Processing vol 16 no 9 2007

[129] E Bala A Ertuumlzuumln ldquoA multivariate thresholding techniques for image

denoisng using multiwaveletsrdquo EURASIP Journal an Applied Signal

Processsing vol 8 pp 1205-1211 2005

[130] R Eslami H Radha ldquoTranslation-invariant contourlet transform and its

applications to image denoisingrdquo IEEE Transactions on Image Processing

vol 15 no 11 pp 3362-3374 2006

[131] P Scheunders S Backer ldquoWavelet denosing of multicomponent images using

Gaussian scale mixtures models and a noise-free images as priorsrdquo IEEE


[132] SM Rahman M Omair MN Swamy ldquoBayesian wavelet-based image

denoising using the Gauss-Hermite expansionrdquo IEEE Transactions on Image

Processing vol17 no 10 pp 1755-1771 2008

[133] V Katkovnik V Spokoiny ldquoSpatially adaptive estimation via fitted local

likelihood techniquesrdquo IEEE Transactions on Signal Processing vol 56 no

3 pp 873-886 2008

[134] MH Bhuiyan MO Ahmad MS Swamy ldquoWavelet-based image denoising

with the normal inverse Gaussian prior and linear MMSE estimatorrdquo IET

Image Processing vol 2 no 4 pp 203-217 2008

[135] Y Hel-Or D Shaked ldquoA discriminative approach for wavelet denoisingrdquo

IEEE Transactions on Image Processing vol 17 no 4 pp 443-457 2008

[136] JA Guerrero-Colon L Mancera J Portilla ldquoImage restoration using space-

variant Gaussian scale mixtures in overcomplete pyramidsrdquo IEEE


[137] D Helbert P Carre E Andres ldquo3-D discrete analytical ridgelet transformrdquo


REFERENCES


[138] J Mairal M Elad G Sapiro ldquoSparse representation for color image

restorationrdquo IEEE Transactions on Image Processing vol 17 no 1 pp 53-

69 2008

[139] N Lian V Zagorodnov Y Tan ldquoEdge-preserving image denoising via

optimal color space projectionrdquo IEEE Transactions on Image Processing vol

15 no 9 pp 2575-2587 2006

[140] S Kim ldquoPDE-based image restoration A hybrid model and color image


1170 2006

[141] F Luisier T Blu ldquoSURE-LET multichannel image denoising interscale

orthonormal wavelet thresholdingrdquo IEEE Transactions on Image Processing

vol 17 no 4 pp 482-492 2006

[142] N Lian V Zagorodnov Y Tan ldquoColor image denoising using wavelets and

minimum cut analysisrdquo IEEE Signal Processing Letters vol 12 no 11 pp

741-744 2005

[143] RVL Hartley ldquoA more symmetrical Fourier analysis applied to transmission

problemsrdquo Proc IRE vol 30 no 3 pp 144-150 1942

[144] RN Bracewell ldquoDiscrete Hartley transform rdquo Journal of Opt Soc America

vol 73 no 12 pp 1832-1835 1983

[145] HS Hou ldquoThe fast Hartley transform algorithmrdquo IEEE Transactions on

Computers vol C-36 no 2 1987

[146] H Takeda S Farsiu P Milanfar ldquoDeblurring using regularized locally

adaptive kernel regressionrdquo IEEE Transactions on Image Processing vol 17

no 4 pp 550-563 2008

[147] M Jiang G Wang MW Skinner JT Rubinson MW Vannier ldquoBlind

deblurring of spiral CT imagesrdquo IEEE Transactions on Medical Imaging vol

22 no 7 pp 837-845 2003

[148] Z Wenyi A Pope ldquoImage restoration under significant additive noiserdquo IEEE

Signal Processing Letters vol 14 no 6 pp 401-404 2007

[149] M Haseyama M Takezawa K Kondo H Kitajima ldquoAn image restoration

method using IFSrdquo Proc IEEE international conference on image processing

vol 3 pp 774-777 2000

REFERENCES


[150] CR Jung J Schacanski ldquoAdaptive image denoising in scale-space using the

wavelet transformrdquo Proc of XIV Brazilian symposium on computer graphics

and image processing pp 172-178 2001

[151] Q Zhang H Yin NM Allinson ldquoA simplified ICA based denoising

methodrdquo Proc IEEE International Conference on Neural Networks vol 5

pp 479-482 2000

[152] Y Yu J Yang ldquoA new method of image feature extraction and denoising

based on independent component analysisrdquo Proc IEEE international

conference on robotics and biometrics pp 380-385 2006

[153] CIE home page httpmemberseunetatcie

[154] M Tkalcic JF Tasic ldquoColor spaces perceptual historical and applicational

background rdquo Proc IEEE EUROCORN 2003 vol 1 pp 304-308 2003


CONTRIBUTION BY THE CANDIDATE

(Explicitly Mentioned in Thesis)

[P1] N Bhoi S Meher ldquoEdge preserving adaptive window Wiener filter for

image denoisingrdquo submitted to International Journal of Computers

Communications amp Control (IJCCC)

[P2] NBhoi S Meher ldquoCircular spatial filtering under high noise variance

conditionsrdquo Computers amp Graphics Elsevier vol 32 no 5 pp 568-580

2008

[P3] N Bhoi S Meher ldquoA qualitative white noise removal scheme relying on

adaptive Gaussian filter in DCT domainrdquo revised and submitted to Journal

of Graphics Vision and Image Processing (GVIP) International congress

for global science and technology (ICGST)

[P4] NBhoi S Meher ldquoTotal variation based wavelet domain filter for image

denoisingrdquo IEEE International Conference on Emerging Trends in

Engineering amp Technology ICETET-2008 pp 20- 25 2008

[P5] NBhoi S Meher ldquoWavelet based image denoising with region merging

approachrdquo Proc National Conference on Signal Processing and

Automation NCSPA 2007

[P6] S Meher N Bhoi ldquoColor image denoising with multi-channel circular

spatial filteringrdquo accepted for presentation in International Conference

ICCESrsquo09 April 2009 Thailand



(Not Explicitly Mentioned in Thesis)

[P7] MR Meher SMeher N Bhoi ldquoA novel method of impulsive noise

detection and removal using DCT Proceedings of National Conference on

Soft Computing for Engineering Applications SCT-2006 NIT Rourkela

[P8] NBhoi SMeher ldquoEffect of DCT and local filters of B-Spline wavelets on

image denoisingrdquo Proc National Conference on Digital Information

Management NCDIMrsquo07 Mumbai

[P9] NBhoi SMeher ldquoA novel hybrid filter for suppression of mixed noiserdquo

Proc National Conference on Trends in Computing-2007 NCTC-07

Punjab

[P10] NBhoi SMeher ldquoImage denoising using maximum likelihood estimate in

wavelet domainrdquo Proc National Conference on Embedded Computing

Control amp Communication 2007 NECECube 07 Pune

[P11] NBhoi S Meher ldquoImage denoisig using singular value decompositionrdquo

Proc in National Conference on Computational Intelligence Control and

Computer Vision in Robotics amp Automation CICCRA-2008 NIT

Rourkela

[P12] NBhoi S Meher ldquoGaussian noise removal using anisotropic diffusionrdquo

Proc in National Conference on Nascent Technologies in the Engineering

NCNTE-2008 Mumbai

hellip dedicated to my loving parents

CERTFICATE












Engineering



Dr Sukadev Meher

Asst Professor





i

PREFACE

























Nilamani Bhoi


ii

ACKNOWLEDGEMENT












period






throughout



Nilamani Bhoi


iii






Communication Engg




PO-Kalamati







PUBLICATION





CONTENTS Page No

Certificate

Preface i

Acknowledgement ii


Contents iv

Abstract

vi



xii




15 Image Metrics 19



Preview




Filters

32





28 Conclusion 79

CONTENTS


v


Preview




34 Conclusion 122


Preview


127



Filter

137


45 Conclusion 167


Preview






DWT-domain Filter

183


57 Conclusion 209

6 Conclusion 211

Preview


62 Conclusion 221


References 223



Abstract



(AWGN)










possible





noise in an image












Abstract


vii













execution time




developed














Abstract


viii


of the image




























Abstract


ix




























suppressing AWGN



Abbreviations




4 SN Speckle Noise




8 LL Low-Low

9 LH Low-High

10 HL High-Low

11 HH High-High





16 MED Median








xi



24 HVS

Human Visual System


25 MF Mean Filter








Maximum Likelihood

DEVELOPED FILTERS










Symbols








7 TE Execution Time

8 MN Method Noise

9 2

nσ Noise Variance















xiii

22 ( )hT







28 C Color Space

Chapter 1

Introduction



Preview












Literature Review

Problem Statement

Image Metrics


Conclusion

1




















































( ) ( ) ( )f x y K i x y r x y= (11)


0 ( ) 1r x ylt lt (13)











(b)

(a)

(c)

(d)

Imaging

System

Sampler and

Quantizer

Digital Storage

System

Digital

Computer

Online

Buffer

Display

Device



Object

Transmitter

Recorder








used























etc











































noise are presented
















22

1 Vtn sdotlt











form










noise












( ) ( )AWGN G











f is same or very



represented by SPN



represented as

SPN

with probability 1

( ) 0 2

1 2

f(xy) p d

f x y p d

p d

= minus

= = =

(16)



of density d RVIN


RVIN



f(xy) p df x y

x y p dη

= minus=

=

(17)












( ) ( )tSttnSN

)( η= (18)

( ) ( ) ( ) ( ) SN



digital image SN



















( ) ( ) ( )g x y f x y x yη= + (110)














































































































sense















equations















































projection









































applications















domain






15 Image Metrics













( )1 1

2ˆ ( ) ( )

M N

x y

f x y f x y

M NMSE = =

minus

times

sumsum= (111)

MSERMSE = (112)


( )1 1

ˆ ( ) ( )

M N

x y

f x y f x y

M NMAE = =

minus

times

sumsum= (113)




as






1

10

110 log

3c

c R G B

CPSNR MSE

minus

isin

= sdot

sum dB (115)













is defined by

where

( ) ( )ˆ ˆ

2 2 22

ˆ ˆ

ˆ 22

ˆ

ff f f

f ff f

f fUQI

f f

σ σ σ


++

1 1

1 1

1( )

1ˆ ˆ( )

M N

x y

M N

x y

f f x yM N

f f x yM N

= =

= =

=times

=times

sumsum

sumsum

( )

( )

22

1 1

22

ˆ

1 1

1( )

1

1 ˆ ˆ( )1

M N

f

x y

M N

fx y

f x y fM N

f x y fM N

σ

σ

= =

= =

= minustimes minus

= minustimes minus

sumsum

sumsum

( )( )ˆ

1 1

1 ˆ ˆ( ) ( )1

M N

f fx y

f x y f f x y fM N

σ= =


sumsum

(119)

(120)

(121)

(118)

(117)

(116)












fσ =f

σ




Method Noise





undesirable




1 =1

M

( )x y

x y==

times

sumsumM N

M N

N

N (122)




( )ˆ ( ) ( )f x y T f x y= (124)


Execution Time







access time etc










the filters



Processor









Preview



Literature Review

Problem Statement

Image Metrics


Conclusion


Preview




Bilateral Filter



Simulation Results

Conclusion


Preview



Simulation Results

Conclusion


Preview






Simulation Results

Conclusion


Preview






Simulation Results

Conclusion



Conclusion


17 Conclusion












Chapter 2

Study of Image

Denoising Filters



Preview
















2











Bilateral Filter



Simulation Results

Conclusion









































operation [42]













α lowest and the

2




( )

1ˆ( ) ( )xy

r

s t S


=minus

sum (21)













221 Wiener Filter

















by

( )2

2 2ˆ ( ) ( )

f

f n

f x y g g x y gσ

σ σ= + minus

+ (22)






variance 2

gσ are defined by

1( )

a b

s a t b


= sum sum (23)


and

( )22 1

( )1

a b

g

s a t b

g s t gL

σ= minus = minus




gσ with a priori



nσ from 2

gσ with the














signal processing

222 Lee Filter








where

22 2

2

2 2

1 ( )

0

n

g n

g

g n

k x y

σσ σ

σ

σ σ

minus gt

= le

(26)













sharpening [83-87]










2tg C g= nabla (27)

where t









2

( )[ ( ) ( )]

( )

t


t

C x y t g C g

part= = nabla

part


(28)











2

2( ) exp

sU s

k

= minus

(29)

or

2

1( )

1

U ss

k

=

+

(210)



as given by

[ ]1( ) ( ) ( ) ( ) ( ) ( )nn n


where 1( )ng x y



( )( )N N

C U g x y= nabla

( ) ( 1 ) ( )N






( )( )E E

C U g x y= nabla




+=





















(214)

( ) ( )( )

( ) ( )( )

( )

1

22

22

( ) ( )

( )

( ) ( ) ( )

( )

( ) ( ) ( )

( ) ( )

n n

n

SN

n n n

S E W

n

EW

n n n

E S N

n n

g x y g x y

g x yt


g x y

g x y m g x y g x y

t g x y g x yλ

+ =

nabla∆


nabla


minus ∆ minus



where

( )

( ) min mod( )

sgn sgnmin

2

m a b a b

a ba b

=

+ =

(215)

where

1 0sgn( )

1 0

xx

x

ge=

minus lt (216)


constant


2

tc

h

∆le (217)



+=



24 Bilateral Filter








functions)






122 2

1 1( ) ( )gd g x y g x y = minus (218)


2

1exp

2

g

g

g

dw

σ

= minus

(219)




distance given by

( ) ( )2 2





2

1exp

2

sd

d

dw

σ

= minus

(221)


dw


gw and dw

b g dw w w= (222)



( ) ( )ˆ ( )

( )

a b

b

s a t b

a b

b

s a t b

w s t g x s y t

f x y

w s t

=minus =minus

=minus =minus

+ +

=sum sum

sum sum (223)
















penalized



















( ) [ ]1 1

1 1

( )

ˆ ( ) ( ) ( ) ( ) ( )x y


= = sum (224)

[ ] [ ]1 1

1 1 1 1

( )

0 ( ) ( ) 1 ( ) ( ) 1x y


le le =sum (225)


p

q1

q2










[ ][ ]1 1

1 1 2

( ) ( )1( ) ( ) exp

p

d x y x yw x y x y

Z h

= minus

(226)

[ ]

1 1

1 1

2( )

( ) ( )expp

x y

d x y x yZ

hforall

= minus

sum (227)




[ ] ( )( ) ( )( )1 1

2

1 1 ( ) ( )

sim

x y x yR

























respectively [8889]








segmentation [97]


















(DWT)






Forward

WT


WT

Input

Image

Output

Image



























(a) decomposition

(b) reconstruction

f(n)

d1(n) H0 darr2

G0 darr2

H0 darr2

G0 darr2

a1(n)

d2(n)

a2(n)

(a)

f(n)

d1(n)

H1

darr2 G1

darr2

a1(n)

d2(n)

a2(n)

H1

darr2 G1

darr2

(b)



LL2 HL2

HL1

LH2 HH2

LH1 HH1


Transform


Image




















263 VisuShrink




where 2


image













264 SureShrink









( )22 2

1

1( ) 2 min

L

h n n i h i h

i

SURE T Y i Y T Y TL

σ σ=


sum (232)

where 2





265 BayesShrink





2ˆ

ˆn

B

F

Tσ

σ= (233)




ˆF



( )

1ˆ

06745

ij

n ij






Yσ can be found

empirically by

2 2

2 1

1ˆ

n

Y i j

i j

Yn

σ=

= sum (236)

In case 2 2ˆ ˆn Y

σ σge ˆF



( )maxB ijT Y=







( )2

1

arg min ( )h

h

n

OS T ij ijT

i j

T Y Fξ=

= minussum (237)



( )2

1

arg min ( )h

h

n

OT T ij ijT

i j

T Y Fζ=

= minussum (238)




as


and

( ) T

x x x Tζ = gt1 (240)


267 NeighShrink










2

21 U

ij

ij

T

S+

Γ = minus

(241)




1 12 2

1 1

j i

ij m n

n j m i

S Y+ +

= minus = minus

= sum sum (242)







counterpart ijY as


268 SmoothShrink










Step-1



d1

d2

d3

d4




Step-2



1 23 4nn d ijd Y Y n∆ = minus = (244)


th direction

Step-3


( )arg mindn

nY

d= ∆K (245)

Step-4



îjF =K (246)



269 LAWML








( )2

2 2

0( )

2 2

( )

ˆ ( ) arg max ( )

1max 0 ( )

j N k

n

j N k

k P Y j

Y jL

σσ σ

σ

geisin

isin

=

= minus

prod

sum (247)




nσ σ+ L is






by

2

2 2

ˆ ( )ˆ ( ) ( )ˆ ( ) n

kF k Y k

k

σ

σ σ= sdot

+ (248)



























performance




















Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094

5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382

6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496

7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322

8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586

9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613

10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186

11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469

12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534

13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393

14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412

15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268

16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534

17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595

18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368

19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573

20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519

21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636

22 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148

23 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621

24 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607

25 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815

26 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542

27 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497

28 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131

29 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458

30 LAWML [5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602

31 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638







Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102

5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419

6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562

7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312

8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632

9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687

10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185

11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460

12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526

13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361

14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376

15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271

16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547

17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609

18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348

19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592

20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552

21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651

22 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137

23 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454

24 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505

25 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835

26 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564

27 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451

28 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728

29 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447

30 LAWML [5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560

31 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575







Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102

5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343

6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420

7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162

11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368

12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407

13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340

14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378

15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258

16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451

17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469

18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325

19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451

20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400

21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668

22 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026

23 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462

24 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409

25 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921

26 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724

27 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411

28 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762

29 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361

30 LAWML [5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443

31 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443







Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998

5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121

6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214

7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3657 3167 2865 2921 2750 2606 2489 2390 2297 2213

11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255

12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293

13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226

14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231

15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166

16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277

17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319

18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199

19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229

20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231

21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667

22 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989

23 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286

24 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271

25 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044

26 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708

27 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326

28 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739

29 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295

30 LAWML [5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371

31 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378







Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287

5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642

6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438

7 ATM [3times3] 511 589 696 821 9639 1106 1267 1428 1593 1759

8 ATM [5times5] 828 844 869 910 9562 1004 1071 1134 1208 1298

9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257

10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057

11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484

12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377

13 AD 470 688 772 874 989 1109 1236 1369 1491 1621

14 TV 428 555 663 782 902 1032 1167 1298 1445 1586

15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871

16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377

17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285

18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667

19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318

20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402

21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876

22 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150

23 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247

24 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267

25 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155

26 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320

27 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438

28 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193

29 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505

30 LAWML [5times5] 299 474 621 747 863 955 1046 1127 1198 1275

31 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223







Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267

5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573

6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333

7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779

8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231

9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155

10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060

11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499

12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389

13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680

14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652

15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864

16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356

17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264

18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706

19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287

20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349

21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809

22 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177

23 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512

24 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425

25 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083

26 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212

27 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517

28 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487

29 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524

30 LAWML [5times5] 293 472 607 732 852 966 1070 1166 1263 1338

31 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315







Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267

5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716

6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570

7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114

11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667

12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593

13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723

14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649

15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894

16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514

17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484

18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751

19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514

20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606

21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735

22 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474

23 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498

24 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592

25 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792

26 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503

27 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588

28 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353

29 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682

30 LAWML [5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531

31 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531







Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555

5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216

6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991

7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994

11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899

12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818

13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963

14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953

15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106

16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851

17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764

18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027

19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958

20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953

21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740

22 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582

23 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834

24 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866

25 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424

26 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568

27 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752

28 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443

29 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815

30 LAWML [5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663

31 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650







Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951

5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419

6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539

7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340

8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621

9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637

10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098

11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503

12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557

13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417

14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458

15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239

16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566

17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613

18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385

19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598

20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557

21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451

22 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178

23 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636

24 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621

25 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021

26 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953

27 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530

28 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661

29 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484

30 LAWML [5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622

31 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649







Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163

5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578

6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687

7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460

8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732

9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760

10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261

11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588

12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638

13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488

14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525

15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392

16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665

17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702

18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476

19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689

20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662

21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908

22 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289

23 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568

24 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617

25 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400

26 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484

27 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579

28 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022

29 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575

30 LAWML [5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675

31 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689







Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345

5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610

6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669

7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569

8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732

9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734

10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385

11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602

12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628

13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578

14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636

15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501

16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670

17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680

18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565

19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662

20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620

21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339

22 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328

23 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673

24 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627

25 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926

26 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443

27 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638

28 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541

29 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592

30 LAWML [5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656

31 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658







Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024

5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227

6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360

7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314

8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398

9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411

10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201

11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395

12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434

13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358

14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396

15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284

16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425

17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469

18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316

19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329

20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312

21 NL-Means 09957 09943 098 65

09716 09516 09285 09010 08737 08423 08127

22 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138

23 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424

24 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401

25 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005

26 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136

27 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491

28 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233

29 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433

30 LAWML [5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517

31 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521




Sl No

Denoising Images

Filters


1 Mean [3times3] 262 290 410 668

2 Mean [5times5] 443 408 642 946

3 Mean [7times7] 573 520 793 1035

4 Median [3times3] 132 153 252 438

5 Median [5times5] 270 239 443 693

6 Median [7times7] 395 311 499 744

7 ATM [3times3] 262 290 410 668

8 ATM [5times5] 443 408 642 946

9 ATM [7times7] 573 520 793 1035

10 Wiener [3times3] 186 204 318 387

11 Wiener [5times5] 367 351 540 637

12 Wiener [7times7] 464 387 576 668

13 AD 204 237 295 497

14 TV 211 234 334 573

15 Lee [3times3] 00118 109 00336 00583

16 Lee [5times5] 00530 114 01109 02057

17 Lee [7times7] 01315 201 01853 110

18 Bilateral [3times3] 288 308 423 680

19 Bilateral [5times5] 497 433 663 966

20 Bilateral [7times7] 601 545 826 1104

21 NL-Means 117 137 186 211

22 VisuShrink 318 423 471 637

23 SureShrink 517 673 770 1007

24 BayesShrink 00232 00273 00194 00190

25 OracleShrink 00285 00267 00242 00238

26 OracleThresh 00285 00267 00242 00238


466times10-10

334times10-10

497times10-10

28 SmoothShrink 660 752 645 790


466times10-10

334times10-10

497times10-10


466times10-10

334times10-10

497times10-10


466times10-10

334times10-10

497times10-10






1 Mean [3times3] 318 701 1713

2 Mean [5times5] 323 712 1749

3 Mean [7times7] 327 720 1776

4 Median [3times3] 402 742 2445

5 Median [5times5] 409 747 2469

6 Median [7times7] 415 812 2490

7 ATM [3times3] 732 1677 3018

8 ATM [5times5] 809 1723 3056

9 ATM [7times7] 813 1784 3084

10 Wiener [3times3] 787 1559 2806

11 Wiener [5times5] 807 1598 2876

12 Wiener [7times7] 843 1670 3006

13 AD ------ ------- ------

14 TV ------ ------- ------

15 Lee [3times3] 874 1426 3509

16 Lee [5times5] 887 1446 3545

17 Lee [7times7] 968 1579 3779

18 Bilateral [3times3] 536 1100 3265

19 Bilateral [5times5] 583 1353 3520

20 Bilateral [7times7] 588 1359 3639

21 NL-Means 44667 99620 221838

22 VisuShrink 0540 119 392







29 LAWML [3times3] 367 809 2669

30 LAWML [5times5] 370 815 2689

31 LAWML [7times7] 374 823 2715





(a) Lena


(d) Barbara

σn

PS

NR

(d

B)


PS

NR

(d

B)


SN

R (

dB

)


PS

NR

(d

B)

(a) (b)

(c) (d)

σn

σn σn




(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

RM

SE


RM

SE


(a) (b)

RM

SE


RM

SE

(c) (d)


σn σn

σn σn





(a) Lena (b) Pepper


UQ


UQ

I


QI


UQ

I


(a) (b)

(c) (d)

σn σn

σn σn



(b)

(f)

(j)

(n)

(a)

(e)

(i)

(m)

(q)

(r)

(c)

(d)

(g)

(h)

(k)

(l)

(o)

(p)

(s)









(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)


AWGN σn = 15








(a) (b) (c) (d) (e) (f) (g)

(h) (i) (j) (k) (l)

(m)

(l) (m) (n)

(o) (p) (q) (r) (s)









(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m) (n) (o) (p)

(q) (r) (s)








(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)









(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)


AWGN σn = 40








(a)

(b) (c)

(d)

(f) (g)

(h)

(i)

(e)

(j) (k) (l) (m) (n)

(o) (p) (q) (r) (s)









(d)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)









28 Conclusion
























domain filters












research work

Chapter 3

Development of


Image Filters



Preview















3












Simulation Results

Conclusion













power








much


The AWWF Theory

The AWWF Algorithm

Window Selection



311 The AWWF Theory







































Step-1



Step-2




Step-3







medium



Step-4


shown in Fig 34


sub-section






Sobel operator


Blurred Image

Edge Image

p

q






q

p

Wiener

Filtering

p1 OR q1









homogenous regions





pixels




used is 5times5















Simulation Results

Conclusion


















( ) ( )2 2



max

1 sd

dw

d= minus (32)









( )1

2 2 2

1 1| ( ) |gd g x y g x y = minus (33)


by

2

2exp

2

g

g

g

dw

σ

minus=

(34)





gw as




( )( ) ( )

ˆ

( )

a b

s a t b

a b

s a t b

w s t g x s y t

f x y

w s t

= minus = minus

= minus = minus

+ +

=

sum sum

sum sum (36)










(a) (b)








Experiment 1








Experiment 2








be taken as 1











(a) Lena image

(b) Goldhill image

0 1 2 3 4 515

20

25

30

σ = 30

σ = 40

σ = 50n

n

n

gσ

PS

NR

(d

B)

(a)

0 1 2 3 4 516

18

20

22

24

26

28

σ = 30

σ = 40

σ = 50

n

n

n

PS

NR

(d

B)

gσ

(b)



0 1 2 3 4 507

075

08

085

09

095

1

σ = 30

σ = 40

σ = 50

n

n

n

UQ

I

gσ

(a)

gσ

UQ

I

0 1 2 3 4 508

085

09

095

1

σ = 30

σ = 40

σ = 50

n

n

n

(b)


(a) Lena image

(b) Goldhill image































NL-Means filter








analysis











Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094

5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382

6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496

7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322

8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586

9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613

10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186

11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469

12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534

13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393

14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412

15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268

16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534

17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595

18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368

19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573

20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519

21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636

22 AWWF 3488 3336 3178 3056 2929 2813 2741 2688 2601 2585

23 CSF [3times3] 3719 3287 2971 2735 2551 2397 2269 2155 2060 1970

24 CSF [5times5] 3371 3280 3158 3031 2911 2796 2688 2598 2507 2432

25 CSF [7times7] 3015 2987 2962 2932 2896 2847 2801 2749 2699 2646






Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102

5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419

6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562

7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312

8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632

9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687

10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185

11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460

12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526

13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361

14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376

15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271

16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547

17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609

18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348

19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592

20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552

21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651

22 AWWF 3516 3396 3258 3101 3011 2891 2821 2743 2710 2638

23 CSF [3times3] 3680 3275 2968 2739 2552 2400 2271 2159 2063 1973

24 CSF [5times5] 3499 3381 3235 3084 2949 2819 2705 2607 2514 2434

25 CSF [7times7] 3217 3126 3091 3044 2991 2925 2861 2792 2730 2696






Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102

5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343

6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420

7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162

11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368

12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407

13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340

14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378

15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258

16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451

17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469

18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325

19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451

20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400

21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668

22 AWWF 3434 3234 3087 2918 2815 2720 2638 2539 2510 2446

23 CSF [3times3] 3615 3250 2960 2738 2559 2411 2282 2171 2079 1992

24 CSF [5times5] 3189 3127 3041 2940 2838 2741 2641 2552 2464 2389

25 CSF [7times7] 2914 2854 2836 2809 2776 2730 2692 2644 2590 2534






Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998

5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121

6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214

7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3657 3167 2865 2821 2750 2606 2489 2390 2297 2213

11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255

12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293

13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226

14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231

15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166

16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277

17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319

18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199

19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229

20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231

21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667

22 AWWF 3319 3169 3028 2954 2798 2671 2585 2475 2360 2273

23 CSF [3times3] 3188 3013 2922 2851 2698 2666 2551 2445 2249 2169

24 CSF [5times5] 2865 2820 2792 2756 2714 2671 2618 2557 2504 2455

25 CSF [7times7] 2796 2744 2739 2729 2716 2701 2683 2662 2633 2607






Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287

5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642

6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438

7 ATM [3times3] 511 589 696 821 963 1106 1267 1428 1593 1759

8 ATM [5times5] 828 844 869 910 956 1004 1071 1134 1208 1298

9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257

10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057

11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484

12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377

13 AD 470 688 772 874 989 1109 1236 1369 1491 1621

14 TV 428 555 663 782 902 1032 1167 1298 1445 1586

15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871

16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377

17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285

18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667

19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318

20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402

21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876

22 AWWF 459 545 655 754 874 999 1086 1152 1275 1295

23 CSF [3times3] 352 578 831 1094 1351 1614 1869 2131 2379 2639

24 CSF [5times5] 526 583 670 777 892 1017 1152 1280 1420 1550

25 CSF [7times7] 792 818 841 869 907 961 1012 1076 1139 1211






Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267

5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573

6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333

7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779

8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231

9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155

10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060

11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499

12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389

13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680

14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652

15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864

16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356

17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264

18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706

19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287

20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349

21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809

22 AWWF 445 510 596 716 795 912 989 1083 1124 1221

23 CSF [3times3] 368 586 836 1088 1349 1606 1864 2121 2371 2629

24 CSF [5times5] 453 517 614 731 854 991 1132 1267 1410 1545

25 CSF [7times7] 628 696 724 765 813 877 9460 1022 1099 1142







Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267

5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716

6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570

7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114

11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667

12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593

13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723

14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649

15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894

16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514

17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484

18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751

19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514

20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606

21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735

22 AWWF 489 614 729 884 997 1111 1221 1369 1415 1524

23 CSF [3times3] 397 604 844 1088 1338 1588 1841 2093 2328 2573

24 CSF [5times5] 648 696 767 861 971 1086 1218 1349 1494 1629

25 CSF [7times7] 890 953 971 1004 1042 1099 1147 1213 1290 1377







Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555

5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216

6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991

7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994

11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899

12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818

13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963

14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953

15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106

16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851

17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764

18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027

19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958

20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953

21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740

22 AWWF 558 663 780 849 1017 1175 1298 1473 1683 1861

23 CSF [3times3] 649 793 879 956 1139 1183 1351 1527 1912 2098

24 CSF [5times5] 941 991 1022 1065 1119 1175 1249 1341 1425 1509

25 CSF [7times7] 1019 1081 1088 1101 1116 1137 1160 1188 1229 1267







Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951

5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419

6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539

7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340

8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621

9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637

10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098

11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503

12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557

13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417

14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458

15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239

16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566

17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613

18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385

19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598

20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557

21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451

22 AWWF 09953 09934 09898 09865 09820 09765 09721 09690 09620 09568

23 CSF [3times3] 09973 09949 09849 09742 09611 09452 09272 09067 08854 08614

24 CSF [5times5] 09938 09924 09900 09866 09822 09771 09710 09640 09555 09469

25 CSF [7times7] 09912 09848 09839 09828 09813 09789 09765 09735 09700 09659







Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163

5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578

6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687

7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460

8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732

9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760

10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261

11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588

12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638

13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488

14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525

15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392

16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665

17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702

18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476

19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689

20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662

21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908

22 AWWF 09974 09960 09941 09912 09888 09852 09791 09745 09700 09656

23 CSF [3times3] 09976 09962 09879 09796 09689 09561 09412 09246 09068 08862

24 CSF [5times5] 09964 09952 09949 09915 09871 09828 09778 09716 09652 09571

25 CSF [7times7] 09925 09913 09906 09895 09889 09861 09838 09810 09785 09766







Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345

5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610

6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669

7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569

8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732

9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734

10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385

11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602

12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628

13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578

14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636

15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501

16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670

17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680

18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565

19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662

20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620

21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339

22 AWWF 09961 09950 09938 09895 09872 09840 09786 09750 09733 09713

23 CSF [3times3] 09979 09961 09940 09843 09762 09666 09550 09418 09282 09126

24 CSF [5times5] 09944 09935 09920 09899 09873 09847 09797 09749 09693 09630

25 CSF [7times7] 09886 09877 09871 09862 09850 09832 09815 09792 09762 09751







Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024

5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227

6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360

7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314

8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398

9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411

10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201

11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395

12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434

13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358

14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396

15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284

16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425

17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469

18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316

19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329

20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312

21 NL-Means 09957 09943 09865 09716 09516 09285 09010 08737 08423 08127

22 AWWF 09943 09918 09893 09836 09748 09690 09614 09568 09492 09453

23 CSF [3times3] 09964 09945 09895 09773 09721 09666 09536 09485 09313 09261

24 CSF [5times5] 09913 09896 09866 09838 09793 09779 09692 09576 09517 09458

25 CSF [7times7] 09834 09818 09799 09783 09779 09752 09717 09659 09600 09534




Sl No

Denoising Images

Filters


1 Mean [3times3] 262 290 410 668

2 Mean [5times5] 443 408 642 946

3 Mean [7times7] 573 520 793 1035

4 Median [3times3] 132 153 252 438

5 Median [5times5] 270 239 443 693

6 Median [7times7] 395 311 499 744

7 ATM [3times3] 262 290 410 668

8 ATM [5times5] 443 408 642 946

9 ATM [7times7] 573 520 793 1035

10 Wiener [3times3] 186 204 318 387

11 Wiener [5times5] 367 351 540 637

12 Wiener [7times7] 464 387 576 668

13 AD 204 237 295 497

14 TV 211 234 334 573

15 Lee [3times3] 00118 109 00336 00583

16 Lee [5times5] 00530 114 01109 02057

17 Lee [7times7] 01315 201 01853 110

18 Bilateral [3times3] 288 308 423 680

19 Bilateral [5times5] 497 433 663 966

20 Bilateral [7times7] 601 545 826 1104

21 NL-Means 117 137 186 211

22 AWWF 183 206 321 387

23 CSF [3times3] 122 142 183 318

24 CSF [5times5] 272 257 402 675

25 CSF [7times7] 4437 390 619 907







1 Mean [3times3] 318 701 1713

2 Mean [5times5] 323 712 1749

3 Mean [7times7] 327 720 1776

4 Median [3times3] 402 742 2445

5 Median [5times5] 409 747 2469

6 Median [7times7] 415 812 2490

7 ATM [3times3] 732 1677 3018

8 ATM [5times5] 809 1723 3056

9 ATM [7times7] 813 1784 3084

10 Wiener [3times3] 787 1559 2806

11 Wiener [5times5] 807 1598 2876

12 Wiener [7times7] 843 1670 3006

13 AD ------ ------- ------

14 TV ------ ------- ------

15 Lee [3times3] 874 1426 3509

16 Lee [5times5] 887 1446 3545

17 Lee [7times7] 968 1579 3779

18 Bilateral [3times3] 536 1100 3265

19 Bilateral [5times5] 583 1353 3520

20 Bilateral [7times7] 588 1359 3639

21 NL-Means 44667 99620 221838

22 AWWF 1181 2417 4546

23 CSF [3times3] 338 706 1866

24 CSF [5times5] 343 717 1898

25 CSF [7times7] 352 729 1930





(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

PS

NR

(d

B)


PS

NR

(d

B)

(a) (b)

σn σn


PS

NR

(d

B)


SN

R (

dB

)

(c) (d)

σn σn





(a) Lena (b) Pepper


RM

SE


RM

SE


(a) (b)

σn σn


RM

SE


RM

SE

(c) (d)

σn σn




(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara


UQ

I


UQ

I

(a) (b)

σn σn

UQ

I

UQ

I


(c) (d)

σn σn



(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)


with AWGN σn = 15







(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k) (l) (m)


AWGN σn = 15







(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

(m)


AWGN σn = 40







(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k)

(l) (m)













(d)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(l)

(m)



34 Conclusion







condition




















image Pepper















others







Chapter 4

Development of

Transform-Domain

Filters



Preview
















4













filtered image











Simulation Results

Conclusion




Filter











bull Mask Selection












= times (41)








2

2

( ) exp2

exp

2

exp2

kxf x A

xA

k

xA

c

σ

σ

= minus

minus =

minus =

(42)



k = a constant






and rests are zeros




INPUT NOISY

IMAGE

7times7

window

DCT

Edge Detection

Percentage of


Selection


FILTERED IMAGE

Masking matrices

IDCT





412 Mask Selection








1 5

2 5 8

3 8 12

4 12 18

5 18 24

6 24 30

7 30

Mask if PEP

Mask if PEP

Mask if PEP

Mask Mask if PEP

Mask if PEP

Mask if PEP

Mask if PEP

le lt le lt le

= lt le lt le

lt le

lt

(43)













In (42) for x = 0 f (0) = A


Hence A = 1
















in Section 44



002 004 006 008 0127

28

29

30

31

Lena

Pepper

Goldhill

Pea

k S

ign

al

to N

ois

e R

ati

o (

dB

)

parameter c

(a)



(a) σn = 20

(b) σn = 30

002 004 006 008 0125

26

27

28

29

Lena

Pepper

Goldhill

Pea

k S

ign

al

to N

ois

e R

ati

o (

dB

)

(b)

parameter c























The Proposed Method






































Step ndash 1



Step ndash 2



Step ndash 3





Step ndash 4




Step ndash 5



Step ndash 6
















Noise level of AWGN

Sl No



Low

(σnle10)

Moderate

(10lt σnle30)

High

(30lt σnle50)



























The Proposed Scheme










as

2

2 2

ˆˆ

ˆk

k k

k n

w yσ

σ σ=

+ (44)

where ˆk

w and k


region of a

particular subband





( )

( )

2

2 2

0(k)

2 2

(k)

arg max P Y(j) |

1max 0 Y j

k

j

n

jM

σσ σ

σ

geisin

isin

=

= minus

prod

sum

N

N

(45)



















shown in Fig 43

Input

DWT

Get a sub-image by




ML Estimation




IDWT

ˆ ( )f x y

Y

Y

( ) ( ) ( )g x y f x y x yη= +

Noisy Image

Output



























performing filters













best performer


















No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148

5 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621

6 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607

7 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815

8 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542

9 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497

10 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131

11 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458

12 LAWML[5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602

13 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638

14 GS-DCT 3376 3313 3188 3098 3001 2911 2746 2706 2689 2611

15 TV-DWT 3465 3376 3229 3056 296 2844 2736 2667 2558 2477

16 RM-DWT 3910 3472 3236 3069 2948 2858 2781 2723 2655 2602







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137

5 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454

6 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505

7 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835

8 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564

9 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451

10 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728

11 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447

12 LAWML[5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560

13 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575

14 GS-DCT 3379 3310 3259 3100 2976 2855 2766 2621 2610 2562

15 TV-DWT 3278 3183 3075 297 2865 2772 2675 2593 2507 2438

16 RM-DWT 3918 3481 3189 3083 2971 2852 2748 2687 2523 2454







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026

5 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462

6 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409

7 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921

8 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724

9 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411

10 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762

11 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361

12 LAWML[5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443

13 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443

14 GS-DCT 3325 3161 3089 2956 2821 2716 2623 2518 2474 2401

15 TV-DWT 2782 2693 2645 2594 254 2488 2434 2379 2327 2277

16 RM-DWT 3812 3331 3076 2922 2800 2719 2635 2555 2497 2442







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989

5 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286

6 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271

7 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044

8 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708

9 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326

10 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739

11 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295

12 LAWML[5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371

13 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378

14 GS-DCT 3376 3195 3085 2995 2808 2649 2544 2439 2416 2321

15 TV-DWT 2712 2693 2645 2594 254 2488 2434 2379 2327 2277

16 RM-DWT 3793 3310 3012 2834 2689 2588 2496 2431 2372 2325







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150

5 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247

6 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267

7 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155

8 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320

9 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438

10 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193

11 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505

12 LAWML[5times5] 299 475 621 747 863 955 1046 1127 1198 1275

13 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223

14 GS-DCT 558 562 649 720 805 893 1080 1131 1153 1261

15 TV-DWT 472 523 619 756 844 965 1092 1183 1341 1472

16 RM-DWT 282 468 614 744 856 949 1037 1109 1199 1275







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177

5 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512

6 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425

7 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083

8 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212

9 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517

10 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487

11 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524

12 LAWML[5times5] 293 472 607 732 852 966 1070 1166 1263 1338

13 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315

14 GS-DCT 521 564 598 718 828 952 1055 1247 1263 1335

15 TV-DWT 585 653 739 834 941 1048 1172 1288 1422 1540

16 RM-DWT 280 463 648 732 833 956 1077 1156 1396 1512







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 174

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474

5 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498

6 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592

7 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792

8 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503

9 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588

10 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353

11 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682

12 LAWML[5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531

13 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531

14 GS-DCT 554 669 727 848 990 1118 1244 1404 1477 1607

15 TV-DWT 1036 1148 1213 1286 1369 1453 1547 1648 175 1853

16 RM-DWT 316 550 738 882 1015 1114 1227 1346 1438 1533







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582

5 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834

6 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866

7 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424

8 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568

9 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752

10 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443

11 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815

12 LAWML[5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663

13 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650

14 GS-DCT 523 644 731 811 1005 1207 1363 1538 1579 1762

15 TV-DWT 1123 1148 1213 1286 1369 1453 1547 1648 1751 1853

16 RM-DWT 323 564 795 976 1153 1295 1440 1552 1661 1754







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178

5 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636

6 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621

7 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021

8 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953

9 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530

10 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661

11 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484

12 LAWML[5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622

13 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649

14 GS-DCT 09944 09937 09911 09896 09856 09813 09740 09720 09626 09578

15 TV-DWT 09968 09938 09925 09877 09843 09788 09724 09652 09570 09481

16 RM-DWT 09985 09954 09917 09878 09844 09808 09766 09692 09654 09596







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289

5 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568

6 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617

7 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400

8 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484

9 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579

10 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022

11 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575

12 LAWML[5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675

13 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689

14 GS-DCT 09971 09960 09954 09921 09883 09822 09754 09721 09689 09635

15 TV-DWT 09953 09932 09908 09878 09839 09797 09741 09684 09613 09544

16 RM-DWT 09991 09971 09885 09868 09853 09833 09798 09752 09708 09639







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328

5 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673

6 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627

7 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926

8 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443

9 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638

10 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541

11 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592

12 LAWML[5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656

13 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658

14 GS-DCT 09958 09949 09939 09913 09881 09845 09789 09756 09703 09648

15 TV-DWT 09976 09954 09935 09902 09873 09841 09779 09768 09718 09654

16 RM-DWT 09992 09961 09926 09889 09859 09788 09759 09698 09659 09599







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138

5 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424

6 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401

7 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005

8 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136

9 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491

10 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233

11 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433

12 LAWML[5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517

13 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521

14 GS-DCT 09945 09933 09913 09867 09823 09764 09701 09645 09532 09512

15 TV-DWT 09801 09783 09755 09724 09685 09643 09593 09537 09478 09413

16 RM-DWT 09989 09951 09898 09859 09807 09759 09700 09647 09573 09511






Filters


1 Mean [3times3]

262 290 410 668

2 Mean [5times5]

443 408 642 946

3 Mean [7times7]

573 520 793 1035

4 VisuShrink

318 423 471 637

5 SureShrink

517 673 770 1007

6 BayesShrink

00232 00273 00194 00190

7 OracleShrink

00285 00267 00242 00238

8 OracleThresh

00285 00267 00242 00238

9 NeighShrink

408times10-10

466times10-10

334times10-10

497times10-10

10 SmoothShrink

660 752 64515 790

11 LAWML [3times3]

408times10-10

466times10-10

334times10-10

497times10-10

12 LAWML[5times5]

408times10-10

466times10-10

334times10-10

497times10-10

13 LAWML [7times7]

408times10-10

466times10-10

334times10-10

497times10-10

14 GS-DCT

05737 072675 067065 07930

15 TV-DWT

201 226 341 479

16 RM-DWT

408times10-10

466times10-10

334times10-10

497times10-10






SYSTEM-1

SYSTEM-2

SYSTEM-3

1 Mean [3times3] 318 701 2313

2 Mean [5times5] 323 712 2349

3 Mean [7times7] 327 720 2376








11 LAWML [3times3] 367 809 2669

12 LAWML[5times5] 370 815 2689

13 LAWML [7times7] 374 823 2715

14 GS-DCT 1381 3038 7025

15 TV-DWT 04261 09375 309

16 RM-DWT 515 1134 3742




PS

NR

(d

B)


PS

NR

(d

B)

PS

NR

(d

B)


PS

NR

(d

B)


(a) (b)

(c) (d)


(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

σn

σn σn

σn




RM

SE

RM

SE


RM

SE


RM

SE

(a) (b)

(c) (d)


(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

σn σn

σn σn



UQ

I


UQ

I

UQ

I


UQ

I


(a) (b)

(c) (d)



(a) Lena (b) Pepper


σn σn

σn σn



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)







(l)

(m)

(n)



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)


σn = 15






(l)

(m)

(n)



(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)







(h) (i) (j)

(m) (k)

(l)

(m) (n)



(a) (b) (c)

(d)

(e) (f) (g) (h)

(i) (j) (k)







(l)

(m) (n)



(a) (b) (c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)






(l)

(m) (n)



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)







(l)

(m) (n)



(a)

(b) (c)

(d) (e)

(g) (h) (i) (j)

(k)







(f)

(m) (n) (l)









(a) (b) (c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m) (n)



45 Conclusion















applications







Chapter 5

Development of

Some Color Image

Denoising Filters



Preview














5















Filter

Simulation Results

Conclusion















(a)

Filter R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

Input

Color Image

(RGB)

Output

Color Image

(RGB)

Filter

Filter




Filter R-Channel

G-Channel

RG

B ndash

C

T

ran

sfo

rma

tio

n

C ndash

RG

B

T

ran

sfo

rma

tio

n

B-Channel

(b)

R-Channel

G-Channel

B-Channel Filter

Filter

Input

Color Image

(RGB)

Output Color Image

(RGB)











029900000 058700000 014400000

016873000 033126400 050000000

050000000 041866800 008131200

Y R

Cb G

Cr B


(51)




expression [1]

1

1

1

C R

M G

Y B

= minus

(52)


1

3

1 1

3 3

1 1

3 3

116 16

500

200

n n

n n

YL

Yn

X Ya

X Y

Y Zb

Y Z

= minus

= minus

= minus

(53)





0412 0358 0180

0213 0715 0072

0019 0119 0950

X R G B

Y R G B

Z R G B

= + +

= + +

= + +

(54)




















RGB color space

YCbCr color space

CMY color space

CIE LAB color space





Sl

No

Denoising

Filters

10

25

40

10

25

40

10

25

40

10

25

40

1 M-MF [3times3] 3350 2868 2572 3745 3326 3003 3311 2849 2555 3240 2789 2499

2 M-MF [5times5] 3029 2888 2701 3437 3322 3159 2990 2869 2684 2919 2809 2628

3 M-MF [7times7] 2820 2771 2660 3242 3195 3110 2781 2753 2643 2710 2692 2587

4 M-LAWML [3times3] 3425 2925 2583 3897 3416 3159 3386 2916 2566 3315 2846 2510

5 M-LAWML [5times5] 3455 3011 2712 3857 3341 3008 3416 2993 2695 3345 2932 2639

6 M-LAWML [7times7] 3496 3048 2755 3824 3266 2793 3457 3028 2738 3386 2969 2682

7 MCSF [3times3] 3357 2654 2245 3764 3044 2659 3318 2631 2228 3247 2575 2172

8 MCSF [5times5] 3330 3049 2686 3751 3417 3080 3291 3030 2669 3220 2970 2613

9 MCSF [7times7] 3101 2998 2835 3458 3357 3204 3062 2979 2818 2991 2919 2762

10 MRM-DWT 3502 3011 2765 3987 3388 3149 3463 2992 2748 3392 2932 2692









YC

bC

r

RG

B

CM

Y

CIE

La

b

CP

SN

R (

dB

)

(a)

CM

Y

RG

B

YC

bC

r

CIE

La

b

CP

SN

R (

dB

)

(b)

YC

bC

r

RG

B

CIE

La

b

CM

Y

CP

SN

R (

dB

) (c)











schematic in Fig 53








Input

Color Image

(RGB)

Mean

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

Mean

Filter

Mean

Filter

(a)

Mean

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

Mean

Filter

Mean

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)















Input

Color Image

(RGB)

LAWML

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

LAWML

Filter

LAWML

Filter

(a)

LAWML

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

LAWML

Filter

LAWML

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)
















schematic in Fig 55





Input

Color Image

(RGB)

CSF

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

CSF

Filter

CSF

Filter

(a)

CSF

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

CSF

Filter

CSF

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)







DWT-domain Filter







Fig 56





Input

Color Image

(RGB)

RM-DWT

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

RM-DWT

Filter

RM-DWT

Filter

(a)

RM-DWT

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

RM-DWT

Filter

RM-DWT

Filter

Input

Color Image

(RGB)

Output Color Image

(RGB)

















(30ltσnle50)









highlighted



































analysis






from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 3470 3350 3227 3078 2868 2778 2686 2572 2495 2458

2 M-MF[5times5] 3051 3029 2977 2902 2888 2855 2783 2701 2659 2599

3 M-MF[7times7] 2829 2820 2789 2776 2761 2714 2689 2660 2645 2591

4 M-LAWML [3times3] 3501 3425 3263 3078 2925 2777 2662 2583 2513 2476

5 M-LAWML[5times5] 3513 3455 3336 3161 3011 2893 2769 2712 2682 2623

6 M-LAWML [7times7] 3537 3496 3344 3179 3048 2905 2867 2755 2698 2658

7 MCSF [3times3] 3488 3357 3077 2845 2654 2477 2355 2245 2189 2083

8 MCSF [5times5] 3402 3388 3375 3179 3049 2876 2774 2686 2595 2541

9 MCSF [7times7] 3331 3101 3085 3039 2998 2952 2942 2835 2789 2733

10 MRM-DWT 3587 3502 3373 3175 3046 2908 2876 2765 2698 2661



from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 3346 3176 3087 2942 2831 2725 2629 2538 2458 2388

2 M-MF[5times5] 3271 3097 3065 3009 2956 2894 2835 2776 2713 2673

3 M-MF[7times7] 3162 2914 2916 2859 2834 2812 2773 2737 2734 2682

4 M-LAWML [3times3] 3538 3501 3254 3076 2934 2811 2714 2638 2574 2520

5 M-LAWML[5times5] 3579 3543 3325 3163 3031 2922 2833 2758 2689 2639

6 M-LAWML [7times7] 3593 3545 3327 3170 3049 2939 2849 2777 2703 2657

7 MCSF [3times3] 3443 3346 3039 281 2623 2471 2342 223 2134 2044

8 MCSF [5times5] 3462 3464 3327 3174 3032 2902 2788 269 2597 2517

9 MCSF [7times7] 3432 3313 3278 3131 3078 3012 2948 2879 2817 2783

10 MRM-DWT 3596 3548 3318 3167 3053 2941 2856 2781 2712 2656





to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 469 538 620 737 938 1041 1157 1319 1442 1505

2 M-MF[5times5] 760 779 828 902 917 952 1035 1137 1194 1279

3 M-MF[7times7] 981 992 1028 1067 1049 1120 1153 1192 1213 1291

4 M-LAWML [3times3] 452 494 595 737 879 1042 1190 1303 1412 1474

5 M-LAWML[5times5] 446 477 547 669 796 912 1052 1123 1162 1244

6 M-LAWML [7times7] 434 455 542 656 763 899 939 1069 1141 1195

7 MCSF [3times3] 459 534 737 963 1201 1472 1694 1923 2051 2317

8 MCSF [5times5] 507 551 523 656 762 930 1046 1157 1285 1367

9 MCSF [7times7] 550 717 720 765 808 852 862 975 1028 1096

10 MRM-DWT 412 452 660 692 796 896 930 1056 1141 1191



from 5 to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 541 658 729 862 979 1106 1236 1372 1505 1631

2 M-MF[5times5] 590 721 748 798 848 911 978 1043 1122 1175

3 M-MF[7times7] 669 890 888 948 9762 1001 1047 10915 1095 1162

4 M-LAWML [3times3] 434 452 601 738 870 1002 1120 12233 1316 1401

5 M-LAWML[5times5] 414 431 554 668 778 882 977 10655 1153 1221

6 M-LAWML [7times7] 407 430 553 663 762 865 959 10424 1135 1196

7 MCSF [3times3] 484 541 770 1003 1244 1482 1722 19568 2185 2424

8 MCSF [5times5] 473 472 553 659 777 902 1029 11522 1282 1406

9 MCSF [7times7] 490 631 656 693 737 795 856 92692 995 1035

10 MRM-DWT 406 429 559 665 758 863 951 10376 1123 1198





UQI



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 09954 09936 09906 09863 09811 09746 09677 09593 09502 09392

2 M-MF[5times5] 09871 09853 09842 09826 09806 09784 09751 09715 09682 09628

3 M-MF[7times7] 09768 09755 09749 09741 09733 09717 09699 09675 09652 09617

4 M-LAWML [3times3] 09966 09959 09916 09864 09811 09754 0969 09627 09561 09498

5 M-LAWML[5times5] 09978 09965 09932 09892 09852 09812 09772 09727 09685 09637

6 M-LAWML [7times7] 09977 09966 09932 09898 09861 09827 09788 09747 09709 09665

7 MCSF [3times3] 09972 09963 09863 09756 09625 09466 09286 09081 08868 08628

8 MCSF [5times5] 09945 09939 09934 09899 09861 09828 09725 09655 09572 09484

9 MCSF [7times7] 09912 09903 09855 09844 09829 09805 09789 09751 09716 09675

10 MRM-DWT 09982 09973 09915 09881 09837 09786 09788 09747 09708 09663



UQI



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 09917 09901 09873 09836 09788 09731 09663 09587 09506 09410

2 M-MF[5times5] 09886 09878 09867 09849 09827 09800 09770 09731 09688 09639

3 M-MF[7times7] 09820 09815 09807 09794 09780 09760 09738 09708 09678 09641

4 M-LAWML [3times3] 09980 09950 09912 09867 09816 09758 09702 09639 09576 09505

5 M-LAWML[5times5] 09978 09906 09897 09883 09864 09842 09816 09782 09747 0971

6 M-LAWML [7times7] 09991 09983 09957 09929 09898 09861 09822 09783 09735 09697

7 MCSF [3times3] 09987 09983 099 09817 0971 09582 09433 09267 09089 08883

8 MCSF [5times5] 09979 09971 09968 09934 09898 09847 09797 09735 09671 0959

9 MCSF [7times7] 09921 09913 09906 09895 09889 09862 09838 09810 09785 09766

10 MRM-DWT 09993 09986 09961 09929 09890 09861 09821 09776 09731 09695





from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 3863 3745 3602 3460 3326 3209 3099 3003 2917 2838

2 M-MF[5times5] 3456 3437 3407 3366 3322 3267 3216 3159 3100 3046

3 M-MF[7times7] 3249 3242 3230 3217 3195 3172 3143 3110 3076 3040

4 M-LAWML [3times3] 4173 3897 3683 3537 3416 3323 3236 3159 3088 3019

5 M-LAWML[5times5] 4145 3857 3608 3456 3341 3224 3099 3008 2938 2840

6 M-LAWML [7times7] 4129 3824 3555 3385 3266 3107 2963 2793 2782 2694

7 MCSF [3times3] 4078 3864 3455 3224 3044 2895 2767 2659 2567 2484

8 MCSF [5times5] 3976 3781 3774 3617 3417 3276 3174 3080 2991 2913

9 MCSF [7times7] 3786 3458 3432 3398 3357 3343 3260 3204 3150 3095

10 MRM-DWT 4372 3987 3652 3508 3388 3308 3224 3149 3076 3016




CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 3656 3581 3475 3364 3253 3152 3052 2967 2884 2812

2 M-MF[5times5] 3520 3494 3454 3403 3346 3286 3222 3156 3094 3030

3 M-MF[7times7] 3324 3312 3294 3271 3241 3206 3170 3126 3083 3032

4 M-LAWML [3times3] 4121 3811 3611 3453 3333 3224 3131 3047 2960 2881

5 M-LAWML[5times5] 4105 3781 3575 3390 3261 3127 3028 2929 2835 2760

6 M-LAWML [7times7] 4087 3747 3505 3354 3195 3047 2926 2812 2724 2595

7 MCSF [3times3] 4018 3743 3446 3220 3042 2893 2772 2665 2572 2491

8 MCSF [5times5] 3945 3821 3696 3540 3418 3282 3174 3077 2985 2904

9 MCSF [7times7] 3832 3565 3524 3474 3414 3355 3290 3221 3156 3087

10 MRM-DWT 4212 3895 3676 3535 3402 3314 3212 3130 3050 2974





from 5 to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 298 342 403 474 554 633 719 803 887 971

2 M-MF[5times5] 477 487 504 529 556 592 622 671 718 764

3 M-MF[7times7] 605 610 618 628 644 661 683 710 738 770

4 M-LAWML [3times3] 208 287 367 434 499 555 614 671 728 788

5 M-LAWML[5times5] 215 300 400 477 544 623 719 798 866 969

6 M-LAWML [7times7] 219 312 425 517 593 712 841 1023 1036 1146

7 MCSF [3times3] 232 334 477 623 766 912 1054 1194 1327 1460

8 MCSF [5times5] 262 327 330 391 498 586 659 735 814 891

9 MCSF [7times7] 326 475 490 509 534 543 597 637 678 722

10 MRM-DWT 166 258 389 449 515 565 617 681 738 793




RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 378 413 466 530 602 676 759 837 921 1001

2 M-MF[5times5] 443 456 478 507 541 580 624 673 723 779

3 M-MF[7times7] 555 563 574 590 611 636 663 697 732 777

4 M-LAWML [3times3] 221 316 399 478 549 623 693 763 844 924

5 M-LAWML[5times5] 225 328 415 514 597 696 780 875 975 1063

6 M-LAWML [7times7] 230 341 450 536 644 763 878 1001 1108 1285

7 MCSF [3times3] 249 342 482 625 768 912 1048 1185 1319 1448

8 MCSF [5times5] 271 313 361 433 498 582 659 737 820 900

9 MCSF [7times7] 309 420 441 467 500 535 577 625 673 729

10 MRM-DWT 199 287 370 435 507 561 631 694 761 830





UQI


No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 09926 09903 09865 09813 09747 09671 09579 09475

09366 09245

2 M-MF[5times5] 09807 09799 09784 09764 09739 09704 09667 09623 09570 09515

3 M-MF[7times7] 09686 09681 09673 09663 09646 09627 09601 09572 09540 09504

4

M-LAWML

[3times3] 09977 09945 09910 09870 09834 09796 09751 09705 09656 09598

5

M-

LAWML[5times5] 09975 09939 09894 09848 09803 09739 09659 09577 09506 09384

6

M-LAWML [7times7] 09974 09935 09880 09820 09764 09665 09533 09280 09288 09131

7 MCSF [3times3] 09943 09908 09815 09687 09533 09354 09149 08928 08701 08457

8 MCSF [5times5] 09924 09920 09918 09871 09837 09717 09641 09559 09462 09361

9 MCSF [7times7] 09912 09901 09896 09861 09819 09798 09776 09727 09668 09613

10 MRM-DWT 09982 09953 09873 09832 09789 09788 09744 09699 09644 09596



UQI



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 09917 09901 09873 09836 09787 09731 09661 09588 09501 09411

2 M-MF[5times5] 09886 09879 09866 09849 09827 09802 09769 09731 09689 09640

3 M-MF[7times7] 09820 09815 09806 09795 09780 09760 09739 09710 09680 09641

4 M-LAWML [3times3] 09956 09932 09904 09872 09837 09806 09752 09703 09641 09571

5 M-LAWML[5times5] 09955 09929 09908 09855 09812 09750 09689 09613 09524 09423

6 M-LAWML [7times7] 09954 09925 09884 09843 09783 09704 09607 09501 09385 09177

7 MCSF [3times3] 09960 09931 09865 09774 09661 09528 09380 09213 09035 08850

8 MCSF [5times5] 09950 09943 09922 09888 09849 09801 09744 09681 09605 09526

9 MCSF [7times7] 09903 09897 09886 09872 09853 09831 09804 09769 09732 09686

10 MRM-DWT 09976 09950 09920 09889 09852 09812 09762 09711 09653 09585





Sl

No

Images


1 M-MF [3times3] 265 308

2 M-MF[5times5] 446 425

3 M-MF[7times7] 573 563


456times10-10


456times10-10


456times10-10

7 MCSF [3times3] 124 150

8 MCSF [5times5] 275 270

9 MCSF [7times7] 438 400


456times10-10



Sl

No

Images


1 M-MF [3times3] 265 308

2 M-MF[5times5] 446 425

3 M-MF[7times7] 573 563


456times10-10


456times10-10


456times10-10

7 MCSF [3times3] 124 150

8 MCSF [5times5] 275 270

9 MCSF [7times7] 438 400


456times10-10






Filters


1 M-MF [3times3] 855 1539 4309

2 M-MF[5times5] 8966 1614 4519

3 M-MF[7times7] 945 1701 4762

4 M-LAWML [3times3] 1188 2139 5989

5 M-LAWML[5times5] 1198 2157 6039

6 M-LAWML [7times7] 1245 2242 6277

7 MCSF [3times3] 8711 1568 4390

8 MCSF [5times5] 928 1672 4681

9 MCSF [7times7] 1001 1803 5048

10 MRM-DWT 1307 2353 6588


Sl No Images

Denoising

Filters


1 M-MF [3times3] 1042 1564 4848

2 M-MF[5times5] 1104 1656 5133

3 M-MF[7times7] 1150 1726 5350

4 M-LAWML [3times3] 1624 2436 7551

5 M-LAWML[5times5] 1688 2532 7849

6 M-LAWML [7times7] 1792 2688 8332

7 MCSF [3times3] 1067 1601 4963

8 MCSF [5times5] 1148 1722 5338

9 MCSF [7times7] 1210 1816 5629

10 MRM-DWT 1984 2976 9225






Ex

ecu

tio

n T

ime

in s

econ

ds





CP

SN

R [

dB

]


CP

SN

R [

dB

] (a) (b)




(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)


(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image






(a) (b) (c)

(d) (e) (f)








(a) (b) (c)

(d) (e) (f)



(a) Original image






(a)

(b)

(c)

(d)

(e)

(f)


(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image





(a)

(b)

(c)

(d)

(e)

(f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image








(a) Original image




(c)

2

1

3

4

5

6

(a)

2

1

3

4

5

6

(d)

2

1

3

4

5

6

(b)

2

1

3

4

5

6



57 Conclusion



















































Chapter 6

Conclusion



Preview
















6












Conclusion




analyzed here


Images

































σn = 10

σn = 20

σn = 40


Mean 3270 589 09922 2978 826 09849 2696 1142 09700

ATM 3271 589 09922 2983 821 09851 2703 1134 09710

Wiener 3401 507 09943 3019 787 09861 2655 1198 09671

TV 3322 555 09931 3025 782 09864 2585 1298 09633

Lee 3347 540 09936 2974 828 09847 2677 1167 09688

Bilateral 3258 596 09921 2977 826 09849 2671 1175 09686

BayesShrink 3364 527 09938 3020 787 09863 2711 1124 09711

NeighShrink 3445 481 09949 3011 795 09861 2608 1264 09642

Ex

isti

ng

Fil

ters

LAWML 3459 474 09950 3086 729 09882 2732 1086 09721

AWWF 3336 545 09934 3056 754 09865 2688 1152 09690

CSF 3287 578 09949 3031 777 09866 2749 1076 09735

GS-DCT 3310 563 09902 3098 719 09896 2710 1124 09720

TV-DWT 3376 522 09936 3056 754 09855 2667 1180 09652 Pro

po

sed

Fil

ters

RM-DWT 3472 466 09954 3022 785 09815 2734 1083 09725





respectively)


Mean 262 720

ATM 262 1784

Wiener 186 1614

TV 211 -------

Lee 00118 1508

Bilateral 288 1347



Ex

isti

ng

F

ilte

rs

LAWML 408times10-10

809

AWWF 183 2417

CSF 122 729

GS-DCT 05737 3038

TV-DWT 2014 09375

Pro

po

sed

Fil

ters















noise conditions








Images


















space


σn = 10 σn = 20 σn = 40

Denoising

Filters

CPSNR

RMSE

UQI

CPSNR

RMSE

UQI

CPSNR

RMSE

UQI

M-MF [3times3] 3745 342 09903 3460 474 09813 3003 803 09475

M-MF [5times5] 3437 487 09799 3366 529 09764 3159 671 09623

M-MF [7times7] 3242 610 09681 3217 628 09663 3110 710 09572

M-LAWML[3times3] 3897 287 09945 3537 434 09870 3159 671 09705

M-LAWML[5times5] 3857 300 09939 3456 477 09848 3008 798 09577

Ex

isti

ng

F

ilte

rs

M-LAWML[7times7] 3824 312 09935 3385 517 09820 2793 1023 09280

MCSF [3times3] 3864 334 09908 3224 623 09687 2659 1194 08928

MCSF [5times5] 3781 327 09920 3617 391 09871 3080 735 09559

MCSF [7times7] 3458 475 09901 3398 509 09861 3204 637 09727

Pro

po

sed

Fil

ters

MRM-DWT 3987 258 09953 3508 449 09832 3149 681 09699





Denoising Filters

Method Noise

Execution Time

M-MF [3times3] 265 1564

M-MF [5times5] 446 1656

M-MF [7times7] 573 1726


-10

2436


-10 2532

Ex

isti

ng

F

ilte

rs


-10 2688

MCSF [3times3] 12495 1601

MCSF [5times5] 2754 1722

MCSF [7times7] 4386 1816

Pro

po

sed

Fil

ters

MRM-DWT 379times10

-10 2976









62 Conclusion
























conditions

























image denoising







Prentice-Hall 1989


1971













1999


Press 1996







REFERENCES















vol 3 pp 1499-1502 1996









54 no 1 pp 352-358 2005






vol 153 no 4 pp 261-269 2006



919-927 2008

REFERENCES




December 1999












2001






vol 16 no 10 pp 2565-2575 2007



406-421 2008



4281 2006



11 no 6 pp 403-416 2005

REFERENCES







46 2002




Kharagpur 2005






vol14 no 11 2005





2003



vol 24(12) pp 2061-2068 2003








REFERENCES










vol17 no 8 pp 1421-1430 2008






481-488 1995






1296 2007






2301-2311 2008



pp 364-376 2008

REFERENCES




1 no 2 pp 156-167 2007



pp 3-23 2006






29 pp 1136-1141 Dec 1981




vol 1 pp 25-28 1997








pp 1019-1021 1983


370 1984



FL pp 16-22 1987



639 1990

REFERENCES






846 1998





2002








2003





imaging pp 820-823 2004





vol 2 no 3 pp 165-168 1980





REFERENCES














1004 2005






57 no 1 pp 75-78 1995













REFERENCES




12 pp 839-842 2005



4 pp 514-523 2008






pp 117-130 2007



no 2 pp 597-630 2007







1200-1224 1995






no 9 pp 1532-1546 2000




REFERENCES





















vol 54 no 4 pp 1600-1606 2005



1056-1068 2008






2878 2006



2003 vol 1 pp I-101-I-104 2003

REFERENCES






vol 87 no 7 pp 1721-1734 2007



2205 2007



pp349-365 2007





16 no 8 pp 2080-2095 2007



16 no 2 pp 523-533 2007











2675 2006

REFERENCES




pp 1435-1447 2005








vol 15 no 11 pp 3362-3374 2006









3 pp 873-886 2008











REFERENCES




69 2008



15 no 9 pp 2575-2587 2006



1170 2006



vol 17 no 4 pp 482-492 2006



741-744 2005




vol 73 no 12 pp 1832-1835 1983





no 4 pp 550-563 2008



22 no 7 pp 837-845 2003





vol 3 pp 774-777 2000

REFERENCES







pp 479-482 2000















2008

























Punjab







Rourkela



NCNTE-2008 Mumbai

CERTFICATE












Engineering



Dr Sukadev Meher

Asst Professor





i

PREFACE

























Nilamani Bhoi


ii

ACKNOWLEDGEMENT












period






throughout



Nilamani Bhoi


iii






Communication Engg




PO-Kalamati







PUBLICATION





CONTENTS Page No

Certificate

Preface i

Acknowledgement ii


Contents iv

Abstract

vi



xii




15 Image Metrics 19



Preview




Filters

32





28 Conclusion 79

CONTENTS


v


Preview




34 Conclusion 122


Preview


127



Filter

137


45 Conclusion 167


Preview






DWT-domain Filter

183


57 Conclusion 209

6 Conclusion 211

Preview


62 Conclusion 221


References 223



Abstract



(AWGN)










possible





noise in an image












Abstract


vii













execution time




developed














Abstract


viii


of the image




























Abstract


ix




























suppressing AWGN



Abbreviations




4 SN Speckle Noise




8 LL Low-Low

9 LH Low-High

10 HL High-Low

11 HH High-High





16 MED Median








xi



24 HVS

Human Visual System


25 MF Mean Filter








Maximum Likelihood

DEVELOPED FILTERS










Symbols








7 TE Execution Time

8 MN Method Noise

9 2

nσ Noise Variance















xiii

22 ( )hT







28 C Color Space

Chapter 1

Introduction



Preview












Literature Review

Problem Statement

Image Metrics


Conclusion

1




















































( ) ( ) ( )f x y K i x y r x y= (11)


0 ( ) 1r x ylt lt (13)











(b)

(a)

(c)

(d)

Imaging

System

Sampler and

Quantizer

Digital Storage

System

Digital

Computer

Online

Buffer

Display

Device



Object

Transmitter

Recorder








used























etc











































noise are presented
















22

1 Vtn sdotlt











form










noise












( ) ( )AWGN G











f is same or very



represented by SPN



represented as

SPN

with probability 1

( ) 0 2

1 2

f(xy) p d

f x y p d

p d

= minus

= = =

(16)



of density d RVIN


RVIN



f(xy) p df x y

x y p dη

= minus=

=

(17)












( ) ( )tSttnSN

)( η= (18)

( ) ( ) ( ) ( ) SN



digital image SN



















( ) ( ) ( )g x y f x y x yη= + (110)














































































































sense















equations















































projection









































applications















domain






15 Image Metrics













( )1 1

2ˆ ( ) ( )

M N

x y

f x y f x y

M NMSE = =

minus

times

sumsum= (111)

MSERMSE = (112)


( )1 1

ˆ ( ) ( )

M N

x y

f x y f x y

M NMAE = =

minus

times

sumsum= (113)




as






1

10

110 log

3c

c R G B

CPSNR MSE

minus

isin

= sdot

sum dB (115)













is defined by

where

( ) ( )ˆ ˆ

2 2 22

ˆ ˆ

ˆ 22

ˆ

ff f f

f ff f

f fUQI

f f

σ σ σ


++

1 1

1 1

1( )

1ˆ ˆ( )

M N

x y

M N

x y

f f x yM N

f f x yM N

= =

= =

=times

=times

sumsum

sumsum

( )

( )

22

1 1

22

ˆ

1 1

1( )

1

1 ˆ ˆ( )1

M N

f

x y

M N

fx y

f x y fM N

f x y fM N

σ

σ

= =

= =

= minustimes minus

= minustimes minus

sumsum

sumsum

( )( )ˆ

1 1

1 ˆ ˆ( ) ( )1

M N

f fx y

f x y f f x y fM N

σ= =


sumsum

(119)

(120)

(121)

(118)

(117)

(116)












fσ =f

σ




Method Noise





undesirable




1 =1

M

( )x y

x y==

times

sumsumM N

M N

N

N (122)




( )ˆ ( ) ( )f x y T f x y= (124)


Execution Time







access time etc










the filters



Processor









Preview



Literature Review

Problem Statement

Image Metrics


Conclusion


Preview




Bilateral Filter



Simulation Results

Conclusion


Preview



Simulation Results

Conclusion


Preview






Simulation Results

Conclusion


Preview






Simulation Results

Conclusion



Conclusion


17 Conclusion












Chapter 2

Study of Image

Denoising Filters



Preview
















2











Bilateral Filter



Simulation Results

Conclusion









































operation [42]













α lowest and the

2




( )

1ˆ( ) ( )xy

r

s t S


=minus

sum (21)













221 Wiener Filter

















by

( )2

2 2ˆ ( ) ( )

f

f n

f x y g g x y gσ

σ σ= + minus

+ (22)






variance 2

gσ are defined by

1( )

a b

s a t b


= sum sum (23)


and

( )22 1

( )1

a b

g

s a t b

g s t gL

σ= minus = minus




gσ with a priori



nσ from 2

gσ with the














signal processing

222 Lee Filter








where

22 2

2

2 2

1 ( )

0

n

g n

g

g n

k x y

σσ σ

σ

σ σ

minus gt

= le

(26)













sharpening [83-87]










2tg C g= nabla (27)

where t









2

( )[ ( ) ( )]

( )

t


t

C x y t g C g

part= = nabla

part


(28)











2

2( ) exp

sU s

k

= minus

(29)

or

2

1( )

1

U ss

k

=

+

(210)



as given by

[ ]1( ) ( ) ( ) ( ) ( ) ( )nn n


where 1( )ng x y



( )( )N N

C U g x y= nabla

( ) ( 1 ) ( )N






( )( )E E

C U g x y= nabla




+=





















(214)

( ) ( )( )

( ) ( )( )

( )

1

22

22

( ) ( )

( )

( ) ( ) ( )

( )

( ) ( ) ( )

( ) ( )

n n

n

SN

n n n

S E W

n

EW

n n n

E S N

n n

g x y g x y

g x yt


g x y

g x y m g x y g x y

t g x y g x yλ

+ =

nabla∆


nabla


minus ∆ minus



where

( )

( ) min mod( )

sgn sgnmin

2

m a b a b

a ba b

=

+ =

(215)

where

1 0sgn( )

1 0

xx

x

ge=

minus lt (216)


constant


2

tc

h

∆le (217)



+=



24 Bilateral Filter








functions)






122 2

1 1( ) ( )gd g x y g x y = minus (218)


2

1exp

2

g

g

g

dw

σ

= minus

(219)




distance given by

( ) ( )2 2





2

1exp

2

sd

d

dw

σ

= minus

(221)


dw


gw and dw

b g dw w w= (222)



( ) ( )ˆ ( )

( )

a b

b

s a t b

a b

b

s a t b

w s t g x s y t

f x y

w s t

=minus =minus

=minus =minus

+ +

=sum sum

sum sum (223)
















penalized



















( ) [ ]1 1

1 1

( )

ˆ ( ) ( ) ( ) ( ) ( )x y


= = sum (224)

[ ] [ ]1 1

1 1 1 1

( )

0 ( ) ( ) 1 ( ) ( ) 1x y


le le =sum (225)


p

q1

q2










[ ][ ]1 1

1 1 2

( ) ( )1( ) ( ) exp

p

d x y x yw x y x y

Z h

= minus

(226)

[ ]

1 1

1 1

2( )

( ) ( )expp

x y

d x y x yZ

hforall

= minus

sum (227)




[ ] ( )( ) ( )( )1 1

2

1 1 ( ) ( )

sim

x y x yR

























respectively [8889]








segmentation [97]


















(DWT)






Forward

WT


WT

Input

Image

Output

Image



























(a) decomposition

(b) reconstruction

f(n)

d1(n) H0 darr2

G0 darr2

H0 darr2

G0 darr2

a1(n)

d2(n)

a2(n)

(a)

f(n)

d1(n)

H1

darr2 G1

darr2

a1(n)

d2(n)

a2(n)

H1

darr2 G1

darr2

(b)



LL2 HL2

HL1

LH2 HH2

LH1 HH1


Transform


Image




















263 VisuShrink




where 2


image













264 SureShrink









( )22 2

1

1( ) 2 min

L

h n n i h i h

i

SURE T Y i Y T Y TL

σ σ=


sum (232)

where 2





265 BayesShrink





2ˆ

ˆn

B

F

Tσ

σ= (233)




ˆF



( )

1ˆ

06745

ij

n ij






Yσ can be found

empirically by

2 2

2 1

1ˆ

n

Y i j

i j

Yn

σ=

= sum (236)

In case 2 2ˆ ˆn Y

σ σge ˆF



( )maxB ijT Y=







( )2

1

arg min ( )h

h

n

OS T ij ijT

i j

T Y Fξ=

= minussum (237)



( )2

1

arg min ( )h

h

n

OT T ij ijT

i j

T Y Fζ=

= minussum (238)




as


and

( ) T

x x x Tζ = gt1 (240)


267 NeighShrink










2

21 U

ij

ij

T

S+

Γ = minus

(241)




1 12 2

1 1

j i

ij m n

n j m i

S Y+ +

= minus = minus

= sum sum (242)







counterpart ijY as


268 SmoothShrink










Step-1



d1

d2

d3

d4




Step-2



1 23 4nn d ijd Y Y n∆ = minus = (244)


th direction

Step-3


( )arg mindn

nY

d= ∆K (245)

Step-4



îjF =K (246)



269 LAWML








( )2

2 2

0( )

2 2

( )

ˆ ( ) arg max ( )

1max 0 ( )

j N k

n

j N k

k P Y j

Y jL

σσ σ

σ

geisin

isin

=

= minus

prod

sum (247)




nσ σ+ L is






by

2

2 2

ˆ ( )ˆ ( ) ( )ˆ ( ) n

kF k Y k

k

σ

σ σ= sdot

+ (248)



























performance




















Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094

5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382

6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496

7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322

8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586

9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613

10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186

11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469

12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534

13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393

14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412

15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268

16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534

17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595

18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368

19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573

20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519

21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636

22 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148

23 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621

24 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607

25 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815

26 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542

27 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497

28 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131

29 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458

30 LAWML [5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602

31 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638







Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102

5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419

6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562

7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312

8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632

9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687

10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185

11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460

12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526

13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361

14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376

15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271

16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547

17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609

18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348

19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592

20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552

21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651

22 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137

23 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454

24 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505

25 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835

26 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564

27 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451

28 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728

29 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447

30 LAWML [5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560

31 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575







Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102

5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343

6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420

7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162

11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368

12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407

13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340

14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378

15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258

16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451

17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469

18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325

19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451

20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400

21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668

22 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026

23 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462

24 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409

25 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921

26 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724

27 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411

28 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762

29 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361

30 LAWML [5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443

31 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443







Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998

5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121

6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214

7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3657 3167 2865 2921 2750 2606 2489 2390 2297 2213

11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255

12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293

13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226

14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231

15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166

16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277

17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319

18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199

19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229

20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231

21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667

22 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989

23 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286

24 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271

25 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044

26 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708

27 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326

28 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739

29 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295

30 LAWML [5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371

31 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378







Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287

5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642

6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438

7 ATM [3times3] 511 589 696 821 9639 1106 1267 1428 1593 1759

8 ATM [5times5] 828 844 869 910 9562 1004 1071 1134 1208 1298

9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257

10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057

11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484

12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377

13 AD 470 688 772 874 989 1109 1236 1369 1491 1621

14 TV 428 555 663 782 902 1032 1167 1298 1445 1586

15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871

16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377

17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285

18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667

19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318

20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402

21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876

22 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150

23 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247

24 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267

25 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155

26 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320

27 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438

28 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193

29 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505

30 LAWML [5times5] 299 474 621 747 863 955 1046 1127 1198 1275

31 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223







Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267

5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573

6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333

7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779

8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231

9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155

10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060

11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499

12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389

13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680

14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652

15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864

16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356

17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264

18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706

19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287

20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349

21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809

22 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177

23 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512

24 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425

25 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083

26 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212

27 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517

28 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487

29 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524

30 LAWML [5times5] 293 472 607 732 852 966 1070 1166 1263 1338

31 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315







Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267

5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716

6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570

7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114

11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667

12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593

13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723

14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649

15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894

16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514

17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484

18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751

19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514

20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606

21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735

22 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474

23 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498

24 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592

25 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792

26 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503

27 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588

28 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353

29 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682

30 LAWML [5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531

31 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531







Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555

5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216

6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991

7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994

11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899

12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818

13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963

14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953

15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106

16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851

17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764

18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027

19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958

20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953

21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740

22 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582

23 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834

24 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866

25 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424

26 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568

27 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752

28 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443

29 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815

30 LAWML [5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663

31 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650







Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951

5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419

6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539

7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340

8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621

9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637

10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098

11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503

12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557

13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417

14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458

15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239

16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566

17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613

18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385

19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598

20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557

21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451

22 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178

23 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636

24 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621

25 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021

26 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953

27 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530

28 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661

29 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484

30 LAWML [5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622

31 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649







Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163

5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578

6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687

7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460

8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732

9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760

10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261

11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588

12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638

13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488

14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525

15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392

16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665

17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702

18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476

19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689

20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662

21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908

22 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289

23 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568

24 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617

25 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400

26 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484

27 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579

28 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022

29 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575

30 LAWML [5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675

31 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689







Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345

5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610

6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669

7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569

8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732

9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734

10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385

11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602

12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628

13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578

14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636

15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501

16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670

17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680

18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565

19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662

20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620

21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339

22 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328

23 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673

24 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627

25 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926

26 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443

27 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638

28 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541

29 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592

30 LAWML [5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656

31 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658







Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024

5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227

6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360

7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314

8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398

9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411

10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201

11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395

12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434

13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358

14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396

15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284

16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425

17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469

18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316

19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329

20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312

21 NL-Means 09957 09943 098 65

09716 09516 09285 09010 08737 08423 08127

22 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138

23 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424

24 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401

25 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005

26 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136

27 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491

28 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233

29 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433

30 LAWML [5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517

31 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521




Sl No

Denoising Images

Filters


1 Mean [3times3] 262 290 410 668

2 Mean [5times5] 443 408 642 946

3 Mean [7times7] 573 520 793 1035

4 Median [3times3] 132 153 252 438

5 Median [5times5] 270 239 443 693

6 Median [7times7] 395 311 499 744

7 ATM [3times3] 262 290 410 668

8 ATM [5times5] 443 408 642 946

9 ATM [7times7] 573 520 793 1035

10 Wiener [3times3] 186 204 318 387

11 Wiener [5times5] 367 351 540 637

12 Wiener [7times7] 464 387 576 668

13 AD 204 237 295 497

14 TV 211 234 334 573

15 Lee [3times3] 00118 109 00336 00583

16 Lee [5times5] 00530 114 01109 02057

17 Lee [7times7] 01315 201 01853 110

18 Bilateral [3times3] 288 308 423 680

19 Bilateral [5times5] 497 433 663 966

20 Bilateral [7times7] 601 545 826 1104

21 NL-Means 117 137 186 211

22 VisuShrink 318 423 471 637

23 SureShrink 517 673 770 1007

24 BayesShrink 00232 00273 00194 00190

25 OracleShrink 00285 00267 00242 00238

26 OracleThresh 00285 00267 00242 00238


466times10-10

334times10-10

497times10-10

28 SmoothShrink 660 752 645 790


466times10-10

334times10-10

497times10-10


466times10-10

334times10-10

497times10-10


466times10-10

334times10-10

497times10-10






1 Mean [3times3] 318 701 1713

2 Mean [5times5] 323 712 1749

3 Mean [7times7] 327 720 1776

4 Median [3times3] 402 742 2445

5 Median [5times5] 409 747 2469

6 Median [7times7] 415 812 2490

7 ATM [3times3] 732 1677 3018

8 ATM [5times5] 809 1723 3056

9 ATM [7times7] 813 1784 3084

10 Wiener [3times3] 787 1559 2806

11 Wiener [5times5] 807 1598 2876

12 Wiener [7times7] 843 1670 3006

13 AD ------ ------- ------

14 TV ------ ------- ------

15 Lee [3times3] 874 1426 3509

16 Lee [5times5] 887 1446 3545

17 Lee [7times7] 968 1579 3779

18 Bilateral [3times3] 536 1100 3265

19 Bilateral [5times5] 583 1353 3520

20 Bilateral [7times7] 588 1359 3639

21 NL-Means 44667 99620 221838

22 VisuShrink 0540 119 392







29 LAWML [3times3] 367 809 2669

30 LAWML [5times5] 370 815 2689

31 LAWML [7times7] 374 823 2715





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(d

B)

(a) (b)

(c) (d)

σn

σn σn




(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

RM

SE


RM

SE


(a) (b)

RM

SE


RM

SE

(c) (d)


σn σn

σn σn





(a) Lena (b) Pepper


UQ


UQ

I


QI


UQ

I


(a) (b)

(c) (d)

σn σn

σn σn



(b)

(f)

(j)

(n)

(a)

(e)

(i)

(m)

(q)

(r)

(c)

(d)

(g)

(h)

(k)

(l)

(o)

(p)

(s)









(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)


AWGN σn = 15








(a) (b) (c) (d) (e) (f) (g)

(h) (i) (j) (k) (l)

(m)

(l) (m) (n)

(o) (p) (q) (r) (s)









(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m) (n) (o) (p)

(q) (r) (s)








(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)









(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)


AWGN σn = 40








(a)

(b) (c)

(d)

(f) (g)

(h)

(i)

(e)

(j) (k) (l) (m) (n)

(o) (p) (q) (r) (s)









(d)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)









28 Conclusion
























domain filters












research work

Chapter 3

Development of


Image Filters



Preview















3












Simulation Results

Conclusion













power








much


The AWWF Theory

The AWWF Algorithm

Window Selection



311 The AWWF Theory







































Step-1



Step-2




Step-3







medium



Step-4


shown in Fig 34


sub-section






Sobel operator


Blurred Image

Edge Image

p

q






q

p

Wiener

Filtering

p1 OR q1









homogenous regions





pixels




used is 5times5















Simulation Results

Conclusion


















( ) ( )2 2



max

1 sd

dw

d= minus (32)









( )1

2 2 2

1 1| ( ) |gd g x y g x y = minus (33)


by

2

2exp

2

g

g

g

dw

σ

minus=

(34)





gw as




( )( ) ( )

ˆ

( )

a b

s a t b

a b

s a t b

w s t g x s y t

f x y

w s t

= minus = minus

= minus = minus

+ +

=

sum sum

sum sum (36)










(a) (b)








Experiment 1








Experiment 2








be taken as 1











(a) Lena image

(b) Goldhill image

0 1 2 3 4 515

20

25

30

σ = 30

σ = 40

σ = 50n

n

n

gσ

PS

NR

(d

B)

(a)

0 1 2 3 4 516

18

20

22

24

26

28

σ = 30

σ = 40

σ = 50

n

n

n

PS

NR

(d

B)

gσ

(b)



0 1 2 3 4 507

075

08

085

09

095

1

σ = 30

σ = 40

σ = 50

n

n

n

UQ

I

gσ

(a)

gσ

UQ

I

0 1 2 3 4 508

085

09

095

1

σ = 30

σ = 40

σ = 50

n

n

n

(b)


(a) Lena image

(b) Goldhill image































NL-Means filter








analysis











Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094

5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382

6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496

7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322

8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586

9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613

10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186

11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469

12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534

13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393

14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412

15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268

16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534

17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595

18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368

19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573

20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519

21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636

22 AWWF 3488 3336 3178 3056 2929 2813 2741 2688 2601 2585

23 CSF [3times3] 3719 3287 2971 2735 2551 2397 2269 2155 2060 1970

24 CSF [5times5] 3371 3280 3158 3031 2911 2796 2688 2598 2507 2432

25 CSF [7times7] 3015 2987 2962 2932 2896 2847 2801 2749 2699 2646






Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102

5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419

6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562

7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312

8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632

9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687

10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185

11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460

12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526

13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361

14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376

15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271

16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547

17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609

18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348

19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592

20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552

21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651

22 AWWF 3516 3396 3258 3101 3011 2891 2821 2743 2710 2638

23 CSF [3times3] 3680 3275 2968 2739 2552 2400 2271 2159 2063 1973

24 CSF [5times5] 3499 3381 3235 3084 2949 2819 2705 2607 2514 2434

25 CSF [7times7] 3217 3126 3091 3044 2991 2925 2861 2792 2730 2696






Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102

5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343

6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420

7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162

11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368

12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407

13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340

14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378

15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258

16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451

17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469

18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325

19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451

20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400

21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668

22 AWWF 3434 3234 3087 2918 2815 2720 2638 2539 2510 2446

23 CSF [3times3] 3615 3250 2960 2738 2559 2411 2282 2171 2079 1992

24 CSF [5times5] 3189 3127 3041 2940 2838 2741 2641 2552 2464 2389

25 CSF [7times7] 2914 2854 2836 2809 2776 2730 2692 2644 2590 2534






Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998

5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121

6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214

7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3657 3167 2865 2821 2750 2606 2489 2390 2297 2213

11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255

12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293

13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226

14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231

15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166

16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277

17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319

18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199

19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229

20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231

21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667

22 AWWF 3319 3169 3028 2954 2798 2671 2585 2475 2360 2273

23 CSF [3times3] 3188 3013 2922 2851 2698 2666 2551 2445 2249 2169

24 CSF [5times5] 2865 2820 2792 2756 2714 2671 2618 2557 2504 2455

25 CSF [7times7] 2796 2744 2739 2729 2716 2701 2683 2662 2633 2607






Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287

5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642

6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438

7 ATM [3times3] 511 589 696 821 963 1106 1267 1428 1593 1759

8 ATM [5times5] 828 844 869 910 956 1004 1071 1134 1208 1298

9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257

10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057

11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484

12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377

13 AD 470 688 772 874 989 1109 1236 1369 1491 1621

14 TV 428 555 663 782 902 1032 1167 1298 1445 1586

15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871

16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377

17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285

18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667

19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318

20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402

21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876

22 AWWF 459 545 655 754 874 999 1086 1152 1275 1295

23 CSF [3times3] 352 578 831 1094 1351 1614 1869 2131 2379 2639

24 CSF [5times5] 526 583 670 777 892 1017 1152 1280 1420 1550

25 CSF [7times7] 792 818 841 869 907 961 1012 1076 1139 1211






Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267

5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573

6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333

7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779

8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231

9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155

10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060

11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499

12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389

13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680

14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652

15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864

16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356

17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264

18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706

19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287

20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349

21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809

22 AWWF 445 510 596 716 795 912 989 1083 1124 1221

23 CSF [3times3] 368 586 836 1088 1349 1606 1864 2121 2371 2629

24 CSF [5times5] 453 517 614 731 854 991 1132 1267 1410 1545

25 CSF [7times7] 628 696 724 765 813 877 9460 1022 1099 1142







Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267

5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716

6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570

7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114

11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667

12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593

13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723

14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649

15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894

16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514

17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484

18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751

19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514

20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606

21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735

22 AWWF 489 614 729 884 997 1111 1221 1369 1415 1524

23 CSF [3times3] 397 604 844 1088 1338 1588 1841 2093 2328 2573

24 CSF [5times5] 648 696 767 861 971 1086 1218 1349 1494 1629

25 CSF [7times7] 890 953 971 1004 1042 1099 1147 1213 1290 1377







Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555

5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216

6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991

7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994

11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899

12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818

13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963

14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953

15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106

16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851

17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764

18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027

19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958

20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953

21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740

22 AWWF 558 663 780 849 1017 1175 1298 1473 1683 1861

23 CSF [3times3] 649 793 879 956 1139 1183 1351 1527 1912 2098

24 CSF [5times5] 941 991 1022 1065 1119 1175 1249 1341 1425 1509

25 CSF [7times7] 1019 1081 1088 1101 1116 1137 1160 1188 1229 1267







Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951

5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419

6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539

7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340

8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621

9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637

10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098

11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503

12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557

13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417

14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458

15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239

16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566

17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613

18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385

19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598

20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557

21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451

22 AWWF 09953 09934 09898 09865 09820 09765 09721 09690 09620 09568

23 CSF [3times3] 09973 09949 09849 09742 09611 09452 09272 09067 08854 08614

24 CSF [5times5] 09938 09924 09900 09866 09822 09771 09710 09640 09555 09469

25 CSF [7times7] 09912 09848 09839 09828 09813 09789 09765 09735 09700 09659







Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163

5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578

6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687

7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460

8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732

9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760

10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261

11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588

12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638

13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488

14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525

15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392

16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665

17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702

18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476

19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689

20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662

21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908

22 AWWF 09974 09960 09941 09912 09888 09852 09791 09745 09700 09656

23 CSF [3times3] 09976 09962 09879 09796 09689 09561 09412 09246 09068 08862

24 CSF [5times5] 09964 09952 09949 09915 09871 09828 09778 09716 09652 09571

25 CSF [7times7] 09925 09913 09906 09895 09889 09861 09838 09810 09785 09766







Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345

5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610

6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669

7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569

8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732

9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734

10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385

11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602

12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628

13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578

14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636

15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501

16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670

17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680

18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565

19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662

20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620

21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339

22 AWWF 09961 09950 09938 09895 09872 09840 09786 09750 09733 09713

23 CSF [3times3] 09979 09961 09940 09843 09762 09666 09550 09418 09282 09126

24 CSF [5times5] 09944 09935 09920 09899 09873 09847 09797 09749 09693 09630

25 CSF [7times7] 09886 09877 09871 09862 09850 09832 09815 09792 09762 09751







Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024

5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227

6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360

7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314

8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398

9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411

10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201

11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395

12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434

13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358

14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396

15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284

16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425

17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469

18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316

19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329

20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312

21 NL-Means 09957 09943 09865 09716 09516 09285 09010 08737 08423 08127

22 AWWF 09943 09918 09893 09836 09748 09690 09614 09568 09492 09453

23 CSF [3times3] 09964 09945 09895 09773 09721 09666 09536 09485 09313 09261

24 CSF [5times5] 09913 09896 09866 09838 09793 09779 09692 09576 09517 09458

25 CSF [7times7] 09834 09818 09799 09783 09779 09752 09717 09659 09600 09534




Sl No

Denoising Images

Filters


1 Mean [3times3] 262 290 410 668

2 Mean [5times5] 443 408 642 946

3 Mean [7times7] 573 520 793 1035

4 Median [3times3] 132 153 252 438

5 Median [5times5] 270 239 443 693

6 Median [7times7] 395 311 499 744

7 ATM [3times3] 262 290 410 668

8 ATM [5times5] 443 408 642 946

9 ATM [7times7] 573 520 793 1035

10 Wiener [3times3] 186 204 318 387

11 Wiener [5times5] 367 351 540 637

12 Wiener [7times7] 464 387 576 668

13 AD 204 237 295 497

14 TV 211 234 334 573

15 Lee [3times3] 00118 109 00336 00583

16 Lee [5times5] 00530 114 01109 02057

17 Lee [7times7] 01315 201 01853 110

18 Bilateral [3times3] 288 308 423 680

19 Bilateral [5times5] 497 433 663 966

20 Bilateral [7times7] 601 545 826 1104

21 NL-Means 117 137 186 211

22 AWWF 183 206 321 387

23 CSF [3times3] 122 142 183 318

24 CSF [5times5] 272 257 402 675

25 CSF [7times7] 4437 390 619 907







1 Mean [3times3] 318 701 1713

2 Mean [5times5] 323 712 1749

3 Mean [7times7] 327 720 1776

4 Median [3times3] 402 742 2445

5 Median [5times5] 409 747 2469

6 Median [7times7] 415 812 2490

7 ATM [3times3] 732 1677 3018

8 ATM [5times5] 809 1723 3056

9 ATM [7times7] 813 1784 3084

10 Wiener [3times3] 787 1559 2806

11 Wiener [5times5] 807 1598 2876

12 Wiener [7times7] 843 1670 3006

13 AD ------ ------- ------

14 TV ------ ------- ------

15 Lee [3times3] 874 1426 3509

16 Lee [5times5] 887 1446 3545

17 Lee [7times7] 968 1579 3779

18 Bilateral [3times3] 536 1100 3265

19 Bilateral [5times5] 583 1353 3520

20 Bilateral [7times7] 588 1359 3639

21 NL-Means 44667 99620 221838

22 AWWF 1181 2417 4546

23 CSF [3times3] 338 706 1866

24 CSF [5times5] 343 717 1898

25 CSF [7times7] 352 729 1930





(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

PS

NR

(d

B)


PS

NR

(d

B)

(a) (b)

σn σn


PS

NR

(d

B)


SN

R (

dB

)

(c) (d)

σn σn





(a) Lena (b) Pepper


RM

SE


RM

SE


(a) (b)

σn σn


RM

SE


RM

SE

(c) (d)

σn σn




(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara


UQ

I


UQ

I

(a) (b)

σn σn

UQ

I

UQ

I


(c) (d)

σn σn



(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)


with AWGN σn = 15







(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k) (l) (m)


AWGN σn = 15







(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

(m)


AWGN σn = 40







(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k)

(l) (m)













(d)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(l)

(m)



34 Conclusion







condition




















image Pepper















others







Chapter 4

Development of

Transform-Domain

Filters



Preview
















4













filtered image











Simulation Results

Conclusion




Filter











bull Mask Selection












= times (41)








2

2

( ) exp2

exp

2

exp2

kxf x A

xA

k

xA

c

σ

σ

= minus

minus =

minus =

(42)



k = a constant






and rests are zeros




INPUT NOISY

IMAGE

7times7

window

DCT

Edge Detection

Percentage of


Selection


FILTERED IMAGE

Masking matrices

IDCT





412 Mask Selection








1 5

2 5 8

3 8 12

4 12 18

5 18 24

6 24 30

7 30

Mask if PEP

Mask if PEP

Mask if PEP

Mask Mask if PEP

Mask if PEP

Mask if PEP

Mask if PEP

le lt le lt le

= lt le lt le

lt le

lt

(43)













In (42) for x = 0 f (0) = A


Hence A = 1
















in Section 44



002 004 006 008 0127

28

29

30

31

Lena

Pepper

Goldhill

Pea

k S

ign

al

to N

ois

e R

ati

o (

dB

)

parameter c

(a)



(a) σn = 20

(b) σn = 30

002 004 006 008 0125

26

27

28

29

Lena

Pepper

Goldhill

Pea

k S

ign

al

to N

ois

e R

ati

o (

dB

)

(b)

parameter c























The Proposed Method






































Step ndash 1



Step ndash 2



Step ndash 3





Step ndash 4




Step ndash 5



Step ndash 6
















Noise level of AWGN

Sl No



Low

(σnle10)

Moderate

(10lt σnle30)

High

(30lt σnle50)



























The Proposed Scheme










as

2

2 2

ˆˆ

ˆk

k k

k n

w yσ

σ σ=

+ (44)

where ˆk

w and k


region of a

particular subband





( )

( )

2

2 2

0(k)

2 2

(k)

arg max P Y(j) |

1max 0 Y j

k

j

n

jM

σσ σ

σ

geisin

isin

=

= minus

prod

sum

N

N

(45)



















shown in Fig 43

Input

DWT

Get a sub-image by




ML Estimation




IDWT

ˆ ( )f x y

Y

Y

( ) ( ) ( )g x y f x y x yη= +

Noisy Image

Output



























performing filters













best performer


















No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148

5 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621

6 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607

7 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815

8 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542

9 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497

10 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131

11 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458

12 LAWML[5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602

13 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638

14 GS-DCT 3376 3313 3188 3098 3001 2911 2746 2706 2689 2611

15 TV-DWT 3465 3376 3229 3056 296 2844 2736 2667 2558 2477

16 RM-DWT 3910 3472 3236 3069 2948 2858 2781 2723 2655 2602







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137

5 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454

6 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505

7 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835

8 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564

9 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451

10 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728

11 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447

12 LAWML[5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560

13 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575

14 GS-DCT 3379 3310 3259 3100 2976 2855 2766 2621 2610 2562

15 TV-DWT 3278 3183 3075 297 2865 2772 2675 2593 2507 2438

16 RM-DWT 3918 3481 3189 3083 2971 2852 2748 2687 2523 2454







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026

5 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462

6 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409

7 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921

8 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724

9 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411

10 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762

11 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361

12 LAWML[5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443

13 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443

14 GS-DCT 3325 3161 3089 2956 2821 2716 2623 2518 2474 2401

15 TV-DWT 2782 2693 2645 2594 254 2488 2434 2379 2327 2277

16 RM-DWT 3812 3331 3076 2922 2800 2719 2635 2555 2497 2442







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989

5 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286

6 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271

7 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044

8 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708

9 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326

10 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739

11 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295

12 LAWML[5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371

13 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378

14 GS-DCT 3376 3195 3085 2995 2808 2649 2544 2439 2416 2321

15 TV-DWT 2712 2693 2645 2594 254 2488 2434 2379 2327 2277

16 RM-DWT 3793 3310 3012 2834 2689 2588 2496 2431 2372 2325







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150

5 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247

6 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267

7 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155

8 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320

9 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438

10 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193

11 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505

12 LAWML[5times5] 299 475 621 747 863 955 1046 1127 1198 1275

13 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223

14 GS-DCT 558 562 649 720 805 893 1080 1131 1153 1261

15 TV-DWT 472 523 619 756 844 965 1092 1183 1341 1472

16 RM-DWT 282 468 614 744 856 949 1037 1109 1199 1275







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177

5 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512

6 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425

7 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083

8 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212

9 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517

10 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487

11 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524

12 LAWML[5times5] 293 472 607 732 852 966 1070 1166 1263 1338

13 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315

14 GS-DCT 521 564 598 718 828 952 1055 1247 1263 1335

15 TV-DWT 585 653 739 834 941 1048 1172 1288 1422 1540

16 RM-DWT 280 463 648 732 833 956 1077 1156 1396 1512







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 174

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474

5 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498

6 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592

7 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792

8 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503

9 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588

10 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353

11 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682

12 LAWML[5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531

13 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531

14 GS-DCT 554 669 727 848 990 1118 1244 1404 1477 1607

15 TV-DWT 1036 1148 1213 1286 1369 1453 1547 1648 175 1853

16 RM-DWT 316 550 738 882 1015 1114 1227 1346 1438 1533







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582

5 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834

6 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866

7 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424

8 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568

9 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752

10 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443

11 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815

12 LAWML[5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663

13 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650

14 GS-DCT 523 644 731 811 1005 1207 1363 1538 1579 1762

15 TV-DWT 1123 1148 1213 1286 1369 1453 1547 1648 1751 1853

16 RM-DWT 323 564 795 976 1153 1295 1440 1552 1661 1754







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178

5 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636

6 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621

7 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021

8 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953

9 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530

10 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661

11 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484

12 LAWML[5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622

13 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649

14 GS-DCT 09944 09937 09911 09896 09856 09813 09740 09720 09626 09578

15 TV-DWT 09968 09938 09925 09877 09843 09788 09724 09652 09570 09481

16 RM-DWT 09985 09954 09917 09878 09844 09808 09766 09692 09654 09596







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289

5 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568

6 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617

7 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400

8 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484

9 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579

10 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022

11 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575

12 LAWML[5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675

13 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689

14 GS-DCT 09971 09960 09954 09921 09883 09822 09754 09721 09689 09635

15 TV-DWT 09953 09932 09908 09878 09839 09797 09741 09684 09613 09544

16 RM-DWT 09991 09971 09885 09868 09853 09833 09798 09752 09708 09639







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328

5 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673

6 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627

7 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926

8 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443

9 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638

10 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541

11 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592

12 LAWML[5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656

13 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658

14 GS-DCT 09958 09949 09939 09913 09881 09845 09789 09756 09703 09648

15 TV-DWT 09976 09954 09935 09902 09873 09841 09779 09768 09718 09654

16 RM-DWT 09992 09961 09926 09889 09859 09788 09759 09698 09659 09599







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138

5 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424

6 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401

7 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005

8 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136

9 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491

10 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233

11 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433

12 LAWML[5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517

13 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521

14 GS-DCT 09945 09933 09913 09867 09823 09764 09701 09645 09532 09512

15 TV-DWT 09801 09783 09755 09724 09685 09643 09593 09537 09478 09413

16 RM-DWT 09989 09951 09898 09859 09807 09759 09700 09647 09573 09511






Filters


1 Mean [3times3]

262 290 410 668

2 Mean [5times5]

443 408 642 946

3 Mean [7times7]

573 520 793 1035

4 VisuShrink

318 423 471 637

5 SureShrink

517 673 770 1007

6 BayesShrink

00232 00273 00194 00190

7 OracleShrink

00285 00267 00242 00238

8 OracleThresh

00285 00267 00242 00238

9 NeighShrink

408times10-10

466times10-10

334times10-10

497times10-10

10 SmoothShrink

660 752 64515 790

11 LAWML [3times3]

408times10-10

466times10-10

334times10-10

497times10-10

12 LAWML[5times5]

408times10-10

466times10-10

334times10-10

497times10-10

13 LAWML [7times7]

408times10-10

466times10-10

334times10-10

497times10-10

14 GS-DCT

05737 072675 067065 07930

15 TV-DWT

201 226 341 479

16 RM-DWT

408times10-10

466times10-10

334times10-10

497times10-10






SYSTEM-1

SYSTEM-2

SYSTEM-3

1 Mean [3times3] 318 701 2313

2 Mean [5times5] 323 712 2349

3 Mean [7times7] 327 720 2376








11 LAWML [3times3] 367 809 2669

12 LAWML[5times5] 370 815 2689

13 LAWML [7times7] 374 823 2715

14 GS-DCT 1381 3038 7025

15 TV-DWT 04261 09375 309

16 RM-DWT 515 1134 3742




PS

NR

(d

B)


PS

NR

(d

B)

PS

NR

(d

B)


PS

NR

(d

B)


(a) (b)

(c) (d)


(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

σn

σn σn

σn




RM

SE

RM

SE


RM

SE


RM

SE

(a) (b)

(c) (d)


(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

σn σn

σn σn



UQ

I


UQ

I

UQ

I


UQ

I


(a) (b)

(c) (d)



(a) Lena (b) Pepper


σn σn

σn σn



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)







(l)

(m)

(n)



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)


σn = 15






(l)

(m)

(n)



(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)







(h) (i) (j)

(m) (k)

(l)

(m) (n)



(a) (b) (c)

(d)

(e) (f) (g) (h)

(i) (j) (k)







(l)

(m) (n)



(a) (b) (c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)






(l)

(m) (n)



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)







(l)

(m) (n)



(a)

(b) (c)

(d) (e)

(g) (h) (i) (j)

(k)







(f)

(m) (n) (l)









(a) (b) (c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m) (n)



45 Conclusion















applications







Chapter 5

Development of

Some Color Image

Denoising Filters



Preview














5















Filter

Simulation Results

Conclusion















(a)

Filter R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

Input

Color Image

(RGB)

Output

Color Image

(RGB)

Filter

Filter




Filter R-Channel

G-Channel

RG

B ndash

C

T

ran

sfo

rma

tio

n

C ndash

RG

B

T

ran

sfo

rma

tio

n

B-Channel

(b)

R-Channel

G-Channel

B-Channel Filter

Filter

Input

Color Image

(RGB)

Output Color Image

(RGB)











029900000 058700000 014400000

016873000 033126400 050000000

050000000 041866800 008131200

Y R

Cb G

Cr B


(51)




expression [1]

1

1

1

C R

M G

Y B

= minus

(52)


1

3

1 1

3 3

1 1

3 3

116 16

500

200

n n

n n

YL

Yn

X Ya

X Y

Y Zb

Y Z

= minus

= minus

= minus

(53)





0412 0358 0180

0213 0715 0072

0019 0119 0950

X R G B

Y R G B

Z R G B

= + +

= + +

= + +

(54)




















RGB color space

YCbCr color space

CMY color space

CIE LAB color space





Sl

No

Denoising

Filters

10

25

40

10

25

40

10

25

40

10

25

40

1 M-MF [3times3] 3350 2868 2572 3745 3326 3003 3311 2849 2555 3240 2789 2499

2 M-MF [5times5] 3029 2888 2701 3437 3322 3159 2990 2869 2684 2919 2809 2628

3 M-MF [7times7] 2820 2771 2660 3242 3195 3110 2781 2753 2643 2710 2692 2587

4 M-LAWML [3times3] 3425 2925 2583 3897 3416 3159 3386 2916 2566 3315 2846 2510

5 M-LAWML [5times5] 3455 3011 2712 3857 3341 3008 3416 2993 2695 3345 2932 2639

6 M-LAWML [7times7] 3496 3048 2755 3824 3266 2793 3457 3028 2738 3386 2969 2682

7 MCSF [3times3] 3357 2654 2245 3764 3044 2659 3318 2631 2228 3247 2575 2172

8 MCSF [5times5] 3330 3049 2686 3751 3417 3080 3291 3030 2669 3220 2970 2613

9 MCSF [7times7] 3101 2998 2835 3458 3357 3204 3062 2979 2818 2991 2919 2762

10 MRM-DWT 3502 3011 2765 3987 3388 3149 3463 2992 2748 3392 2932 2692









YC

bC

r

RG

B

CM

Y

CIE

La

b

CP

SN

R (

dB

)

(a)

CM

Y

RG

B

YC

bC

r

CIE

La

b

CP

SN

R (

dB

)

(b)

YC

bC

r

RG

B

CIE

La

b

CM

Y

CP

SN

R (

dB

) (c)











schematic in Fig 53








Input

Color Image

(RGB)

Mean

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

Mean

Filter

Mean

Filter

(a)

Mean

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

Mean

Filter

Mean

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)















Input

Color Image

(RGB)

LAWML

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

LAWML

Filter

LAWML

Filter

(a)

LAWML

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

LAWML

Filter

LAWML

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)
















schematic in Fig 55





Input

Color Image

(RGB)

CSF

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

CSF

Filter

CSF

Filter

(a)

CSF

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

CSF

Filter

CSF

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)







DWT-domain Filter







Fig 56





Input

Color Image

(RGB)

RM-DWT

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

RM-DWT

Filter

RM-DWT

Filter

(a)

RM-DWT

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

RM-DWT

Filter

RM-DWT

Filter

Input

Color Image

(RGB)

Output Color Image

(RGB)

















(30ltσnle50)









highlighted



































analysis






from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 3470 3350 3227 3078 2868 2778 2686 2572 2495 2458

2 M-MF[5times5] 3051 3029 2977 2902 2888 2855 2783 2701 2659 2599

3 M-MF[7times7] 2829 2820 2789 2776 2761 2714 2689 2660 2645 2591

4 M-LAWML [3times3] 3501 3425 3263 3078 2925 2777 2662 2583 2513 2476

5 M-LAWML[5times5] 3513 3455 3336 3161 3011 2893 2769 2712 2682 2623

6 M-LAWML [7times7] 3537 3496 3344 3179 3048 2905 2867 2755 2698 2658

7 MCSF [3times3] 3488 3357 3077 2845 2654 2477 2355 2245 2189 2083

8 MCSF [5times5] 3402 3388 3375 3179 3049 2876 2774 2686 2595 2541

9 MCSF [7times7] 3331 3101 3085 3039 2998 2952 2942 2835 2789 2733

10 MRM-DWT 3587 3502 3373 3175 3046 2908 2876 2765 2698 2661



from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 3346 3176 3087 2942 2831 2725 2629 2538 2458 2388

2 M-MF[5times5] 3271 3097 3065 3009 2956 2894 2835 2776 2713 2673

3 M-MF[7times7] 3162 2914 2916 2859 2834 2812 2773 2737 2734 2682

4 M-LAWML [3times3] 3538 3501 3254 3076 2934 2811 2714 2638 2574 2520

5 M-LAWML[5times5] 3579 3543 3325 3163 3031 2922 2833 2758 2689 2639

6 M-LAWML [7times7] 3593 3545 3327 3170 3049 2939 2849 2777 2703 2657

7 MCSF [3times3] 3443 3346 3039 281 2623 2471 2342 223 2134 2044

8 MCSF [5times5] 3462 3464 3327 3174 3032 2902 2788 269 2597 2517

9 MCSF [7times7] 3432 3313 3278 3131 3078 3012 2948 2879 2817 2783

10 MRM-DWT 3596 3548 3318 3167 3053 2941 2856 2781 2712 2656





to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 469 538 620 737 938 1041 1157 1319 1442 1505

2 M-MF[5times5] 760 779 828 902 917 952 1035 1137 1194 1279

3 M-MF[7times7] 981 992 1028 1067 1049 1120 1153 1192 1213 1291

4 M-LAWML [3times3] 452 494 595 737 879 1042 1190 1303 1412 1474

5 M-LAWML[5times5] 446 477 547 669 796 912 1052 1123 1162 1244

6 M-LAWML [7times7] 434 455 542 656 763 899 939 1069 1141 1195

7 MCSF [3times3] 459 534 737 963 1201 1472 1694 1923 2051 2317

8 MCSF [5times5] 507 551 523 656 762 930 1046 1157 1285 1367

9 MCSF [7times7] 550 717 720 765 808 852 862 975 1028 1096

10 MRM-DWT 412 452 660 692 796 896 930 1056 1141 1191



from 5 to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 541 658 729 862 979 1106 1236 1372 1505 1631

2 M-MF[5times5] 590 721 748 798 848 911 978 1043 1122 1175

3 M-MF[7times7] 669 890 888 948 9762 1001 1047 10915 1095 1162

4 M-LAWML [3times3] 434 452 601 738 870 1002 1120 12233 1316 1401

5 M-LAWML[5times5] 414 431 554 668 778 882 977 10655 1153 1221

6 M-LAWML [7times7] 407 430 553 663 762 865 959 10424 1135 1196

7 MCSF [3times3] 484 541 770 1003 1244 1482 1722 19568 2185 2424

8 MCSF [5times5] 473 472 553 659 777 902 1029 11522 1282 1406

9 MCSF [7times7] 490 631 656 693 737 795 856 92692 995 1035

10 MRM-DWT 406 429 559 665 758 863 951 10376 1123 1198





UQI



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 09954 09936 09906 09863 09811 09746 09677 09593 09502 09392

2 M-MF[5times5] 09871 09853 09842 09826 09806 09784 09751 09715 09682 09628

3 M-MF[7times7] 09768 09755 09749 09741 09733 09717 09699 09675 09652 09617

4 M-LAWML [3times3] 09966 09959 09916 09864 09811 09754 0969 09627 09561 09498

5 M-LAWML[5times5] 09978 09965 09932 09892 09852 09812 09772 09727 09685 09637

6 M-LAWML [7times7] 09977 09966 09932 09898 09861 09827 09788 09747 09709 09665

7 MCSF [3times3] 09972 09963 09863 09756 09625 09466 09286 09081 08868 08628

8 MCSF [5times5] 09945 09939 09934 09899 09861 09828 09725 09655 09572 09484

9 MCSF [7times7] 09912 09903 09855 09844 09829 09805 09789 09751 09716 09675

10 MRM-DWT 09982 09973 09915 09881 09837 09786 09788 09747 09708 09663



UQI



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 09917 09901 09873 09836 09788 09731 09663 09587 09506 09410

2 M-MF[5times5] 09886 09878 09867 09849 09827 09800 09770 09731 09688 09639

3 M-MF[7times7] 09820 09815 09807 09794 09780 09760 09738 09708 09678 09641

4 M-LAWML [3times3] 09980 09950 09912 09867 09816 09758 09702 09639 09576 09505

5 M-LAWML[5times5] 09978 09906 09897 09883 09864 09842 09816 09782 09747 0971

6 M-LAWML [7times7] 09991 09983 09957 09929 09898 09861 09822 09783 09735 09697

7 MCSF [3times3] 09987 09983 099 09817 0971 09582 09433 09267 09089 08883

8 MCSF [5times5] 09979 09971 09968 09934 09898 09847 09797 09735 09671 0959

9 MCSF [7times7] 09921 09913 09906 09895 09889 09862 09838 09810 09785 09766

10 MRM-DWT 09993 09986 09961 09929 09890 09861 09821 09776 09731 09695





from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 3863 3745 3602 3460 3326 3209 3099 3003 2917 2838

2 M-MF[5times5] 3456 3437 3407 3366 3322 3267 3216 3159 3100 3046

3 M-MF[7times7] 3249 3242 3230 3217 3195 3172 3143 3110 3076 3040

4 M-LAWML [3times3] 4173 3897 3683 3537 3416 3323 3236 3159 3088 3019

5 M-LAWML[5times5] 4145 3857 3608 3456 3341 3224 3099 3008 2938 2840

6 M-LAWML [7times7] 4129 3824 3555 3385 3266 3107 2963 2793 2782 2694

7 MCSF [3times3] 4078 3864 3455 3224 3044 2895 2767 2659 2567 2484

8 MCSF [5times5] 3976 3781 3774 3617 3417 3276 3174 3080 2991 2913

9 MCSF [7times7] 3786 3458 3432 3398 3357 3343 3260 3204 3150 3095

10 MRM-DWT 4372 3987 3652 3508 3388 3308 3224 3149 3076 3016




CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 3656 3581 3475 3364 3253 3152 3052 2967 2884 2812

2 M-MF[5times5] 3520 3494 3454 3403 3346 3286 3222 3156 3094 3030

3 M-MF[7times7] 3324 3312 3294 3271 3241 3206 3170 3126 3083 3032

4 M-LAWML [3times3] 4121 3811 3611 3453 3333 3224 3131 3047 2960 2881

5 M-LAWML[5times5] 4105 3781 3575 3390 3261 3127 3028 2929 2835 2760

6 M-LAWML [7times7] 4087 3747 3505 3354 3195 3047 2926 2812 2724 2595

7 MCSF [3times3] 4018 3743 3446 3220 3042 2893 2772 2665 2572 2491

8 MCSF [5times5] 3945 3821 3696 3540 3418 3282 3174 3077 2985 2904

9 MCSF [7times7] 3832 3565 3524 3474 3414 3355 3290 3221 3156 3087

10 MRM-DWT 4212 3895 3676 3535 3402 3314 3212 3130 3050 2974





from 5 to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 298 342 403 474 554 633 719 803 887 971

2 M-MF[5times5] 477 487 504 529 556 592 622 671 718 764

3 M-MF[7times7] 605 610 618 628 644 661 683 710 738 770

4 M-LAWML [3times3] 208 287 367 434 499 555 614 671 728 788

5 M-LAWML[5times5] 215 300 400 477 544 623 719 798 866 969

6 M-LAWML [7times7] 219 312 425 517 593 712 841 1023 1036 1146

7 MCSF [3times3] 232 334 477 623 766 912 1054 1194 1327 1460

8 MCSF [5times5] 262 327 330 391 498 586 659 735 814 891

9 MCSF [7times7] 326 475 490 509 534 543 597 637 678 722

10 MRM-DWT 166 258 389 449 515 565 617 681 738 793




RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 378 413 466 530 602 676 759 837 921 1001

2 M-MF[5times5] 443 456 478 507 541 580 624 673 723 779

3 M-MF[7times7] 555 563 574 590 611 636 663 697 732 777

4 M-LAWML [3times3] 221 316 399 478 549 623 693 763 844 924

5 M-LAWML[5times5] 225 328 415 514 597 696 780 875 975 1063

6 M-LAWML [7times7] 230 341 450 536 644 763 878 1001 1108 1285

7 MCSF [3times3] 249 342 482 625 768 912 1048 1185 1319 1448

8 MCSF [5times5] 271 313 361 433 498 582 659 737 820 900

9 MCSF [7times7] 309 420 441 467 500 535 577 625 673 729

10 MRM-DWT 199 287 370 435 507 561 631 694 761 830





UQI


No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 09926 09903 09865 09813 09747 09671 09579 09475

09366 09245

2 M-MF[5times5] 09807 09799 09784 09764 09739 09704 09667 09623 09570 09515

3 M-MF[7times7] 09686 09681 09673 09663 09646 09627 09601 09572 09540 09504

4

M-LAWML

[3times3] 09977 09945 09910 09870 09834 09796 09751 09705 09656 09598

5

M-

LAWML[5times5] 09975 09939 09894 09848 09803 09739 09659 09577 09506 09384

6

M-LAWML [7times7] 09974 09935 09880 09820 09764 09665 09533 09280 09288 09131

7 MCSF [3times3] 09943 09908 09815 09687 09533 09354 09149 08928 08701 08457

8 MCSF [5times5] 09924 09920 09918 09871 09837 09717 09641 09559 09462 09361

9 MCSF [7times7] 09912 09901 09896 09861 09819 09798 09776 09727 09668 09613

10 MRM-DWT 09982 09953 09873 09832 09789 09788 09744 09699 09644 09596



UQI



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 09917 09901 09873 09836 09787 09731 09661 09588 09501 09411

2 M-MF[5times5] 09886 09879 09866 09849 09827 09802 09769 09731 09689 09640

3 M-MF[7times7] 09820 09815 09806 09795 09780 09760 09739 09710 09680 09641

4 M-LAWML [3times3] 09956 09932 09904 09872 09837 09806 09752 09703 09641 09571

5 M-LAWML[5times5] 09955 09929 09908 09855 09812 09750 09689 09613 09524 09423

6 M-LAWML [7times7] 09954 09925 09884 09843 09783 09704 09607 09501 09385 09177

7 MCSF [3times3] 09960 09931 09865 09774 09661 09528 09380 09213 09035 08850

8 MCSF [5times5] 09950 09943 09922 09888 09849 09801 09744 09681 09605 09526

9 MCSF [7times7] 09903 09897 09886 09872 09853 09831 09804 09769 09732 09686

10 MRM-DWT 09976 09950 09920 09889 09852 09812 09762 09711 09653 09585





Sl

No

Images


1 M-MF [3times3] 265 308

2 M-MF[5times5] 446 425

3 M-MF[7times7] 573 563


456times10-10


456times10-10


456times10-10

7 MCSF [3times3] 124 150

8 MCSF [5times5] 275 270

9 MCSF [7times7] 438 400


456times10-10



Sl

No

Images


1 M-MF [3times3] 265 308

2 M-MF[5times5] 446 425

3 M-MF[7times7] 573 563


456times10-10


456times10-10


456times10-10

7 MCSF [3times3] 124 150

8 MCSF [5times5] 275 270

9 MCSF [7times7] 438 400


456times10-10






Filters


1 M-MF [3times3] 855 1539 4309

2 M-MF[5times5] 8966 1614 4519

3 M-MF[7times7] 945 1701 4762

4 M-LAWML [3times3] 1188 2139 5989

5 M-LAWML[5times5] 1198 2157 6039

6 M-LAWML [7times7] 1245 2242 6277

7 MCSF [3times3] 8711 1568 4390

8 MCSF [5times5] 928 1672 4681

9 MCSF [7times7] 1001 1803 5048

10 MRM-DWT 1307 2353 6588


Sl No Images

Denoising

Filters


1 M-MF [3times3] 1042 1564 4848

2 M-MF[5times5] 1104 1656 5133

3 M-MF[7times7] 1150 1726 5350

4 M-LAWML [3times3] 1624 2436 7551

5 M-LAWML[5times5] 1688 2532 7849

6 M-LAWML [7times7] 1792 2688 8332

7 MCSF [3times3] 1067 1601 4963

8 MCSF [5times5] 1148 1722 5338

9 MCSF [7times7] 1210 1816 5629

10 MRM-DWT 1984 2976 9225






Ex

ecu

tio

n T

ime

in s

econ

ds





CP

SN

R [

dB

]


CP

SN

R [

dB

] (a) (b)




(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)


(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image






(a) (b) (c)

(d) (e) (f)








(a) (b) (c)

(d) (e) (f)



(a) Original image






(a)

(b)

(c)

(d)

(e)

(f)


(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image





(a)

(b)

(c)

(d)

(e)

(f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image








(a) Original image




(c)

2

1

3

4

5

6

(a)

2

1

3

4

5

6

(d)

2

1

3

4

5

6

(b)

2

1

3

4

5

6



57 Conclusion



















































Chapter 6

Conclusion



Preview
















6












Conclusion




analyzed here


Images

































σn = 10

σn = 20

σn = 40


Mean 3270 589 09922 2978 826 09849 2696 1142 09700

ATM 3271 589 09922 2983 821 09851 2703 1134 09710

Wiener 3401 507 09943 3019 787 09861 2655 1198 09671

TV 3322 555 09931 3025 782 09864 2585 1298 09633

Lee 3347 540 09936 2974 828 09847 2677 1167 09688

Bilateral 3258 596 09921 2977 826 09849 2671 1175 09686

BayesShrink 3364 527 09938 3020 787 09863 2711 1124 09711

NeighShrink 3445 481 09949 3011 795 09861 2608 1264 09642

Ex

isti

ng

Fil

ters

LAWML 3459 474 09950 3086 729 09882 2732 1086 09721

AWWF 3336 545 09934 3056 754 09865 2688 1152 09690

CSF 3287 578 09949 3031 777 09866 2749 1076 09735

GS-DCT 3310 563 09902 3098 719 09896 2710 1124 09720

TV-DWT 3376 522 09936 3056 754 09855 2667 1180 09652 Pro

po

sed

Fil

ters

RM-DWT 3472 466 09954 3022 785 09815 2734 1083 09725





respectively)


Mean 262 720

ATM 262 1784

Wiener 186 1614

TV 211 -------

Lee 00118 1508

Bilateral 288 1347



Ex

isti

ng

F

ilte

rs

LAWML 408times10-10

809

AWWF 183 2417

CSF 122 729

GS-DCT 05737 3038

TV-DWT 2014 09375

Pro

po

sed

Fil

ters















noise conditions








Images


















space


σn = 10 σn = 20 σn = 40

Denoising

Filters

CPSNR

RMSE

UQI

CPSNR

RMSE

UQI

CPSNR

RMSE

UQI

M-MF [3times3] 3745 342 09903 3460 474 09813 3003 803 09475

M-MF [5times5] 3437 487 09799 3366 529 09764 3159 671 09623

M-MF [7times7] 3242 610 09681 3217 628 09663 3110 710 09572

M-LAWML[3times3] 3897 287 09945 3537 434 09870 3159 671 09705

M-LAWML[5times5] 3857 300 09939 3456 477 09848 3008 798 09577

Ex

isti

ng

F

ilte

rs

M-LAWML[7times7] 3824 312 09935 3385 517 09820 2793 1023 09280

MCSF [3times3] 3864 334 09908 3224 623 09687 2659 1194 08928

MCSF [5times5] 3781 327 09920 3617 391 09871 3080 735 09559

MCSF [7times7] 3458 475 09901 3398 509 09861 3204 637 09727

Pro

po

sed

Fil

ters

MRM-DWT 3987 258 09953 3508 449 09832 3149 681 09699





Denoising Filters

Method Noise

Execution Time

M-MF [3times3] 265 1564

M-MF [5times5] 446 1656

M-MF [7times7] 573 1726


-10

2436


-10 2532

Ex

isti

ng

F

ilte

rs


-10 2688

MCSF [3times3] 12495 1601

MCSF [5times5] 2754 1722

MCSF [7times7] 4386 1816

Pro

po

sed

Fil

ters

MRM-DWT 379times10

-10 2976









62 Conclusion
























conditions

























image denoising







Prentice-Hall 1989


1971













1999


Press 1996







REFERENCES















vol 3 pp 1499-1502 1996









54 no 1 pp 352-358 2005






vol 153 no 4 pp 261-269 2006



919-927 2008

REFERENCES




December 1999












2001






vol 16 no 10 pp 2565-2575 2007



406-421 2008



4281 2006



11 no 6 pp 403-416 2005

REFERENCES







46 2002




Kharagpur 2005






vol14 no 11 2005





2003



vol 24(12) pp 2061-2068 2003








REFERENCES










vol17 no 8 pp 1421-1430 2008






481-488 1995






1296 2007






2301-2311 2008



pp 364-376 2008

REFERENCES




1 no 2 pp 156-167 2007



pp 3-23 2006






29 pp 1136-1141 Dec 1981




vol 1 pp 25-28 1997








pp 1019-1021 1983


370 1984



FL pp 16-22 1987



639 1990

REFERENCES






846 1998





2002








2003





imaging pp 820-823 2004





vol 2 no 3 pp 165-168 1980





REFERENCES














1004 2005






57 no 1 pp 75-78 1995













REFERENCES




12 pp 839-842 2005



4 pp 514-523 2008






pp 117-130 2007



no 2 pp 597-630 2007







1200-1224 1995






no 9 pp 1532-1546 2000




REFERENCES





















vol 54 no 4 pp 1600-1606 2005



1056-1068 2008






2878 2006



2003 vol 1 pp I-101-I-104 2003

REFERENCES






vol 87 no 7 pp 1721-1734 2007



2205 2007



pp349-365 2007





16 no 8 pp 2080-2095 2007



16 no 2 pp 523-533 2007











2675 2006

REFERENCES




pp 1435-1447 2005








vol 15 no 11 pp 3362-3374 2006









3 pp 873-886 2008











REFERENCES




69 2008



15 no 9 pp 2575-2587 2006



1170 2006



vol 17 no 4 pp 482-492 2006



741-744 2005




vol 73 no 12 pp 1832-1835 1983





no 4 pp 550-563 2008



22 no 7 pp 837-845 2003





vol 3 pp 774-777 2000

REFERENCES







pp 479-482 2000















2008

























Punjab







Rourkela



NCNTE-2008 Mumbai


i

PREFACE

























Nilamani Bhoi


ii

ACKNOWLEDGEMENT












period






throughout



Nilamani Bhoi


iii






Communication Engg




PO-Kalamati







PUBLICATION





CONTENTS Page No

Certificate

Preface i

Acknowledgement ii


Contents iv

Abstract

vi



xii




15 Image Metrics 19



Preview




Filters

32





28 Conclusion 79

CONTENTS


v


Preview




34 Conclusion 122


Preview


127



Filter

137


45 Conclusion 167


Preview






DWT-domain Filter

183


57 Conclusion 209

6 Conclusion 211

Preview


62 Conclusion 221


References 223



Abstract



(AWGN)










possible





noise in an image












Abstract


vii













execution time




developed














Abstract


viii


of the image




























Abstract


ix




























suppressing AWGN



Abbreviations




4 SN Speckle Noise




8 LL Low-Low

9 LH Low-High

10 HL High-Low

11 HH High-High





16 MED Median








xi



24 HVS

Human Visual System


25 MF Mean Filter








Maximum Likelihood

DEVELOPED FILTERS










Symbols








7 TE Execution Time

8 MN Method Noise

9 2

nσ Noise Variance















xiii

22 ( )hT







28 C Color Space

Chapter 1

Introduction



Preview












Literature Review

Problem Statement

Image Metrics


Conclusion

1




















































( ) ( ) ( )f x y K i x y r x y= (11)


0 ( ) 1r x ylt lt (13)











(b)

(a)

(c)

(d)

Imaging

System

Sampler and

Quantizer

Digital Storage

System

Digital

Computer

Online

Buffer

Display

Device



Object

Transmitter

Recorder








used























etc











































noise are presented
















22

1 Vtn sdotlt











form










noise












( ) ( )AWGN G











f is same or very



represented by SPN



represented as

SPN

with probability 1

( ) 0 2

1 2

f(xy) p d

f x y p d

p d

= minus

= = =

(16)



of density d RVIN


RVIN



f(xy) p df x y

x y p dη

= minus=

=

(17)












( ) ( )tSttnSN

)( η= (18)

( ) ( ) ( ) ( ) SN



digital image SN



















( ) ( ) ( )g x y f x y x yη= + (110)














































































































sense















equations















































projection









































applications















domain






15 Image Metrics













( )1 1

2ˆ ( ) ( )

M N

x y

f x y f x y

M NMSE = =

minus

times

sumsum= (111)

MSERMSE = (112)


( )1 1

ˆ ( ) ( )

M N

x y

f x y f x y

M NMAE = =

minus

times

sumsum= (113)




as






1

10

110 log

3c

c R G B

CPSNR MSE

minus

isin

= sdot

sum dB (115)













is defined by

where

( ) ( )ˆ ˆ

2 2 22

ˆ ˆ

ˆ 22

ˆ

ff f f

f ff f

f fUQI

f f

σ σ σ


++

1 1

1 1

1( )

1ˆ ˆ( )

M N

x y

M N

x y

f f x yM N

f f x yM N

= =

= =

=times

=times

sumsum

sumsum

( )

( )

22

1 1

22

ˆ

1 1

1( )

1

1 ˆ ˆ( )1

M N

f

x y

M N

fx y

f x y fM N

f x y fM N

σ

σ

= =

= =

= minustimes minus

= minustimes minus

sumsum

sumsum

( )( )ˆ

1 1

1 ˆ ˆ( ) ( )1

M N

f fx y

f x y f f x y fM N

σ= =


sumsum

(119)

(120)

(121)

(118)

(117)

(116)












fσ =f

σ




Method Noise





undesirable




1 =1

M

( )x y

x y==

times

sumsumM N

M N

N

N (122)




( )ˆ ( ) ( )f x y T f x y= (124)


Execution Time







access time etc










the filters



Processor









Preview



Literature Review

Problem Statement

Image Metrics


Conclusion


Preview




Bilateral Filter



Simulation Results

Conclusion


Preview



Simulation Results

Conclusion


Preview






Simulation Results

Conclusion


Preview






Simulation Results

Conclusion



Conclusion


17 Conclusion












Chapter 2

Study of Image

Denoising Filters



Preview
















2











Bilateral Filter



Simulation Results

Conclusion









































operation [42]













α lowest and the

2




( )

1ˆ( ) ( )xy

r

s t S


=minus

sum (21)













221 Wiener Filter

















by

( )2

2 2ˆ ( ) ( )

f

f n

f x y g g x y gσ

σ σ= + minus

+ (22)






variance 2

gσ are defined by

1( )

a b

s a t b


= sum sum (23)


and

( )22 1

( )1

a b

g

s a t b

g s t gL

σ= minus = minus




gσ with a priori



nσ from 2

gσ with the














signal processing

222 Lee Filter








where

22 2

2

2 2

1 ( )

0

n

g n

g

g n

k x y

σσ σ

σ

σ σ

minus gt

= le

(26)













sharpening [83-87]










2tg C g= nabla (27)

where t









2

( )[ ( ) ( )]

( )

t


t

C x y t g C g

part= = nabla

part


(28)











2

2( ) exp

sU s

k

= minus

(29)

or

2

1( )

1

U ss

k

=

+

(210)



as given by

[ ]1( ) ( ) ( ) ( ) ( ) ( )nn n


where 1( )ng x y



( )( )N N

C U g x y= nabla

( ) ( 1 ) ( )N






( )( )E E

C U g x y= nabla




+=





















(214)

( ) ( )( )

( ) ( )( )

( )

1

22

22

( ) ( )

( )

( ) ( ) ( )

( )

( ) ( ) ( )

( ) ( )

n n

n

SN

n n n

S E W

n

EW

n n n

E S N

n n

g x y g x y

g x yt


g x y

g x y m g x y g x y

t g x y g x yλ

+ =

nabla∆


nabla


minus ∆ minus



where

( )

( ) min mod( )

sgn sgnmin

2

m a b a b

a ba b

=

+ =

(215)

where

1 0sgn( )

1 0

xx

x

ge=

minus lt (216)


constant


2

tc

h

∆le (217)



+=



24 Bilateral Filter








functions)






122 2

1 1( ) ( )gd g x y g x y = minus (218)


2

1exp

2

g

g

g

dw

σ

= minus

(219)




distance given by

( ) ( )2 2





2

1exp

2

sd

d

dw

σ

= minus

(221)


dw


gw and dw

b g dw w w= (222)



( ) ( )ˆ ( )

( )

a b

b

s a t b

a b

b

s a t b

w s t g x s y t

f x y

w s t

=minus =minus

=minus =minus

+ +

=sum sum

sum sum (223)
















penalized



















( ) [ ]1 1

1 1

( )

ˆ ( ) ( ) ( ) ( ) ( )x y


= = sum (224)

[ ] [ ]1 1

1 1 1 1

( )

0 ( ) ( ) 1 ( ) ( ) 1x y


le le =sum (225)


p

q1

q2










[ ][ ]1 1

1 1 2

( ) ( )1( ) ( ) exp

p

d x y x yw x y x y

Z h

= minus

(226)

[ ]

1 1

1 1

2( )

( ) ( )expp

x y

d x y x yZ

hforall

= minus

sum (227)




[ ] ( )( ) ( )( )1 1

2

1 1 ( ) ( )

sim

x y x yR

























respectively [8889]








segmentation [97]


















(DWT)






Forward

WT


WT

Input

Image

Output

Image



























(a) decomposition

(b) reconstruction

f(n)

d1(n) H0 darr2

G0 darr2

H0 darr2

G0 darr2

a1(n)

d2(n)

a2(n)

(a)

f(n)

d1(n)

H1

darr2 G1

darr2

a1(n)

d2(n)

a2(n)

H1

darr2 G1

darr2

(b)



LL2 HL2

HL1

LH2 HH2

LH1 HH1


Transform


Image




















263 VisuShrink




where 2


image













264 SureShrink









( )22 2

1

1( ) 2 min

L

h n n i h i h

i

SURE T Y i Y T Y TL

σ σ=


sum (232)

where 2





265 BayesShrink





2ˆ

ˆn

B

F

Tσ

σ= (233)




ˆF



( )

1ˆ

06745

ij

n ij






Yσ can be found

empirically by

2 2

2 1

1ˆ

n

Y i j

i j

Yn

σ=

= sum (236)

In case 2 2ˆ ˆn Y

σ σge ˆF



( )maxB ijT Y=







( )2

1

arg min ( )h

h

n

OS T ij ijT

i j

T Y Fξ=

= minussum (237)



( )2

1

arg min ( )h

h

n

OT T ij ijT

i j

T Y Fζ=

= minussum (238)




as


and

( ) T

x x x Tζ = gt1 (240)


267 NeighShrink










2

21 U

ij

ij

T

S+

Γ = minus

(241)




1 12 2

1 1

j i

ij m n

n j m i

S Y+ +

= minus = minus

= sum sum (242)







counterpart ijY as


268 SmoothShrink










Step-1



d1

d2

d3

d4




Step-2



1 23 4nn d ijd Y Y n∆ = minus = (244)


th direction

Step-3


( )arg mindn

nY

d= ∆K (245)

Step-4



îjF =K (246)



269 LAWML








( )2

2 2

0( )

2 2

( )

ˆ ( ) arg max ( )

1max 0 ( )

j N k

n

j N k

k P Y j

Y jL

σσ σ

σ

geisin

isin

=

= minus

prod

sum (247)




nσ σ+ L is






by

2

2 2

ˆ ( )ˆ ( ) ( )ˆ ( ) n

kF k Y k

k

σ

σ σ= sdot

+ (248)



























performance




















Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094

5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382

6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496

7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322

8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586

9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613

10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186

11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469

12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534

13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393

14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412

15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268

16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534

17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595

18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368

19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573

20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519

21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636

22 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148

23 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621

24 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607

25 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815

26 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542

27 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497

28 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131

29 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458

30 LAWML [5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602

31 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638







Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102

5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419

6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562

7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312

8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632

9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687

10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185

11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460

12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526

13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361

14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376

15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271

16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547

17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609

18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348

19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592

20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552

21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651

22 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137

23 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454

24 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505

25 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835

26 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564

27 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451

28 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728

29 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447

30 LAWML [5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560

31 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575







Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102

5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343

6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420

7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162

11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368

12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407

13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340

14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378

15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258

16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451

17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469

18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325

19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451

20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400

21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668

22 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026

23 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462

24 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409

25 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921

26 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724

27 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411

28 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762

29 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361

30 LAWML [5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443

31 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443







Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998

5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121

6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214

7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3657 3167 2865 2921 2750 2606 2489 2390 2297 2213

11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255

12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293

13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226

14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231

15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166

16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277

17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319

18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199

19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229

20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231

21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667

22 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989

23 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286

24 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271

25 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044

26 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708

27 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326

28 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739

29 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295

30 LAWML [5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371

31 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378







Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287

5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642

6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438

7 ATM [3times3] 511 589 696 821 9639 1106 1267 1428 1593 1759

8 ATM [5times5] 828 844 869 910 9562 1004 1071 1134 1208 1298

9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257

10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057

11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484

12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377

13 AD 470 688 772 874 989 1109 1236 1369 1491 1621

14 TV 428 555 663 782 902 1032 1167 1298 1445 1586

15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871

16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377

17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285

18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667

19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318

20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402

21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876

22 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150

23 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247

24 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267

25 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155

26 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320

27 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438

28 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193

29 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505

30 LAWML [5times5] 299 474 621 747 863 955 1046 1127 1198 1275

31 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223







Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267

5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573

6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333

7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779

8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231

9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155

10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060

11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499

12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389

13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680

14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652

15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864

16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356

17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264

18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706

19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287

20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349

21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809

22 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177

23 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512

24 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425

25 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083

26 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212

27 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517

28 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487

29 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524

30 LAWML [5times5] 293 472 607 732 852 966 1070 1166 1263 1338

31 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315







Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267

5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716

6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570

7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114

11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667

12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593

13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723

14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649

15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894

16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514

17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484

18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751

19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514

20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606

21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735

22 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474

23 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498

24 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592

25 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792

26 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503

27 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588

28 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353

29 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682

30 LAWML [5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531

31 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531







Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555

5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216

6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991

7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994

11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899

12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818

13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963

14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953

15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106

16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851

17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764

18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027

19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958

20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953

21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740

22 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582

23 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834

24 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866

25 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424

26 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568

27 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752

28 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443

29 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815

30 LAWML [5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663

31 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650







Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951

5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419

6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539

7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340

8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621

9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637

10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098

11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503

12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557

13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417

14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458

15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239

16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566

17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613

18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385

19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598

20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557

21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451

22 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178

23 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636

24 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621

25 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021

26 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953

27 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530

28 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661

29 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484

30 LAWML [5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622

31 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649







Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163

5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578

6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687

7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460

8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732

9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760

10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261

11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588

12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638

13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488

14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525

15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392

16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665

17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702

18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476

19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689

20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662

21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908

22 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289

23 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568

24 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617

25 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400

26 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484

27 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579

28 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022

29 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575

30 LAWML [5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675

31 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689







Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345

5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610

6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669

7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569

8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732

9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734

10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385

11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602

12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628

13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578

14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636

15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501

16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670

17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680

18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565

19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662

20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620

21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339

22 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328

23 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673

24 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627

25 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926

26 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443

27 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638

28 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541

29 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592

30 LAWML [5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656

31 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658







Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024

5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227

6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360

7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314

8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398

9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411

10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201

11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395

12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434

13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358

14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396

15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284

16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425

17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469

18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316

19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329

20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312

21 NL-Means 09957 09943 098 65

09716 09516 09285 09010 08737 08423 08127

22 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138

23 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424

24 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401

25 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005

26 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136

27 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491

28 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233

29 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433

30 LAWML [5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517

31 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521




Sl No

Denoising Images

Filters


1 Mean [3times3] 262 290 410 668

2 Mean [5times5] 443 408 642 946

3 Mean [7times7] 573 520 793 1035

4 Median [3times3] 132 153 252 438

5 Median [5times5] 270 239 443 693

6 Median [7times7] 395 311 499 744

7 ATM [3times3] 262 290 410 668

8 ATM [5times5] 443 408 642 946

9 ATM [7times7] 573 520 793 1035

10 Wiener [3times3] 186 204 318 387

11 Wiener [5times5] 367 351 540 637

12 Wiener [7times7] 464 387 576 668

13 AD 204 237 295 497

14 TV 211 234 334 573

15 Lee [3times3] 00118 109 00336 00583

16 Lee [5times5] 00530 114 01109 02057

17 Lee [7times7] 01315 201 01853 110

18 Bilateral [3times3] 288 308 423 680

19 Bilateral [5times5] 497 433 663 966

20 Bilateral [7times7] 601 545 826 1104

21 NL-Means 117 137 186 211

22 VisuShrink 318 423 471 637

23 SureShrink 517 673 770 1007

24 BayesShrink 00232 00273 00194 00190

25 OracleShrink 00285 00267 00242 00238

26 OracleThresh 00285 00267 00242 00238


466times10-10

334times10-10

497times10-10

28 SmoothShrink 660 752 645 790


466times10-10

334times10-10

497times10-10


466times10-10

334times10-10

497times10-10


466times10-10

334times10-10

497times10-10






1 Mean [3times3] 318 701 1713

2 Mean [5times5] 323 712 1749

3 Mean [7times7] 327 720 1776

4 Median [3times3] 402 742 2445

5 Median [5times5] 409 747 2469

6 Median [7times7] 415 812 2490

7 ATM [3times3] 732 1677 3018

8 ATM [5times5] 809 1723 3056

9 ATM [7times7] 813 1784 3084

10 Wiener [3times3] 787 1559 2806

11 Wiener [5times5] 807 1598 2876

12 Wiener [7times7] 843 1670 3006

13 AD ------ ------- ------

14 TV ------ ------- ------

15 Lee [3times3] 874 1426 3509

16 Lee [5times5] 887 1446 3545

17 Lee [7times7] 968 1579 3779

18 Bilateral [3times3] 536 1100 3265

19 Bilateral [5times5] 583 1353 3520

20 Bilateral [7times7] 588 1359 3639

21 NL-Means 44667 99620 221838

22 VisuShrink 0540 119 392







29 LAWML [3times3] 367 809 2669

30 LAWML [5times5] 370 815 2689

31 LAWML [7times7] 374 823 2715





(a) Lena


(d) Barbara

σn

PS

NR

(d

B)


PS

NR

(d

B)


SN

R (

dB

)


PS

NR

(d

B)

(a) (b)

(c) (d)

σn

σn σn




(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

RM

SE


RM

SE


(a) (b)

RM

SE


RM

SE

(c) (d)


σn σn

σn σn





(a) Lena (b) Pepper


UQ


UQ

I


QI


UQ

I


(a) (b)

(c) (d)

σn σn

σn σn



(b)

(f)

(j)

(n)

(a)

(e)

(i)

(m)

(q)

(r)

(c)

(d)

(g)

(h)

(k)

(l)

(o)

(p)

(s)









(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)


AWGN σn = 15








(a) (b) (c) (d) (e) (f) (g)

(h) (i) (j) (k) (l)

(m)

(l) (m) (n)

(o) (p) (q) (r) (s)









(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m) (n) (o) (p)

(q) (r) (s)








(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)









(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)


AWGN σn = 40








(a)

(b) (c)

(d)

(f) (g)

(h)

(i)

(e)

(j) (k) (l) (m) (n)

(o) (p) (q) (r) (s)









(d)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)









28 Conclusion
























domain filters












research work

Chapter 3

Development of


Image Filters



Preview















3












Simulation Results

Conclusion













power








much


The AWWF Theory

The AWWF Algorithm

Window Selection



311 The AWWF Theory







































Step-1



Step-2




Step-3







medium



Step-4


shown in Fig 34


sub-section






Sobel operator


Blurred Image

Edge Image

p

q






q

p

Wiener

Filtering

p1 OR q1









homogenous regions





pixels




used is 5times5















Simulation Results

Conclusion


















( ) ( )2 2



max

1 sd

dw

d= minus (32)









( )1

2 2 2

1 1| ( ) |gd g x y g x y = minus (33)


by

2

2exp

2

g

g

g

dw

σ

minus=

(34)





gw as




( )( ) ( )

ˆ

( )

a b

s a t b

a b

s a t b

w s t g x s y t

f x y

w s t

= minus = minus

= minus = minus

+ +

=

sum sum

sum sum (36)










(a) (b)








Experiment 1








Experiment 2








be taken as 1











(a) Lena image

(b) Goldhill image

0 1 2 3 4 515

20

25

30

σ = 30

σ = 40

σ = 50n

n

n

gσ

PS

NR

(d

B)

(a)

0 1 2 3 4 516

18

20

22

24

26

28

σ = 30

σ = 40

σ = 50

n

n

n

PS

NR

(d

B)

gσ

(b)



0 1 2 3 4 507

075

08

085

09

095

1

σ = 30

σ = 40

σ = 50

n

n

n

UQ

I

gσ

(a)

gσ

UQ

I

0 1 2 3 4 508

085

09

095

1

σ = 30

σ = 40

σ = 50

n

n

n

(b)


(a) Lena image

(b) Goldhill image































NL-Means filter








analysis











Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094

5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382

6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496

7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322

8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586

9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613

10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186

11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469

12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534

13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393

14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412

15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268

16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534

17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595

18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368

19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573

20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519

21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636

22 AWWF 3488 3336 3178 3056 2929 2813 2741 2688 2601 2585

23 CSF [3times3] 3719 3287 2971 2735 2551 2397 2269 2155 2060 1970

24 CSF [5times5] 3371 3280 3158 3031 2911 2796 2688 2598 2507 2432

25 CSF [7times7] 3015 2987 2962 2932 2896 2847 2801 2749 2699 2646






Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102

5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419

6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562

7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312

8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632

9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687

10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185

11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460

12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526

13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361

14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376

15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271

16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547

17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609

18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348

19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592

20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552

21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651

22 AWWF 3516 3396 3258 3101 3011 2891 2821 2743 2710 2638

23 CSF [3times3] 3680 3275 2968 2739 2552 2400 2271 2159 2063 1973

24 CSF [5times5] 3499 3381 3235 3084 2949 2819 2705 2607 2514 2434

25 CSF [7times7] 3217 3126 3091 3044 2991 2925 2861 2792 2730 2696






Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102

5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343

6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420

7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162

11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368

12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407

13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340

14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378

15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258

16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451

17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469

18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325

19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451

20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400

21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668

22 AWWF 3434 3234 3087 2918 2815 2720 2638 2539 2510 2446

23 CSF [3times3] 3615 3250 2960 2738 2559 2411 2282 2171 2079 1992

24 CSF [5times5] 3189 3127 3041 2940 2838 2741 2641 2552 2464 2389

25 CSF [7times7] 2914 2854 2836 2809 2776 2730 2692 2644 2590 2534






Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998

5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121

6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214

7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3657 3167 2865 2821 2750 2606 2489 2390 2297 2213

11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255

12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293

13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226

14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231

15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166

16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277

17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319

18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199

19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229

20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231

21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667

22 AWWF 3319 3169 3028 2954 2798 2671 2585 2475 2360 2273

23 CSF [3times3] 3188 3013 2922 2851 2698 2666 2551 2445 2249 2169

24 CSF [5times5] 2865 2820 2792 2756 2714 2671 2618 2557 2504 2455

25 CSF [7times7] 2796 2744 2739 2729 2716 2701 2683 2662 2633 2607






Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287

5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642

6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438

7 ATM [3times3] 511 589 696 821 963 1106 1267 1428 1593 1759

8 ATM [5times5] 828 844 869 910 956 1004 1071 1134 1208 1298

9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257

10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057

11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484

12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377

13 AD 470 688 772 874 989 1109 1236 1369 1491 1621

14 TV 428 555 663 782 902 1032 1167 1298 1445 1586

15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871

16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377

17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285

18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667

19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318

20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402

21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876

22 AWWF 459 545 655 754 874 999 1086 1152 1275 1295

23 CSF [3times3] 352 578 831 1094 1351 1614 1869 2131 2379 2639

24 CSF [5times5] 526 583 670 777 892 1017 1152 1280 1420 1550

25 CSF [7times7] 792 818 841 869 907 961 1012 1076 1139 1211






Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267

5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573

6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333

7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779

8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231

9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155

10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060

11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499

12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389

13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680

14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652

15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864

16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356

17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264

18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706

19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287

20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349

21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809

22 AWWF 445 510 596 716 795 912 989 1083 1124 1221

23 CSF [3times3] 368 586 836 1088 1349 1606 1864 2121 2371 2629

24 CSF [5times5] 453 517 614 731 854 991 1132 1267 1410 1545

25 CSF [7times7] 628 696 724 765 813 877 9460 1022 1099 1142







Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267

5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716

6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570

7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114

11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667

12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593

13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723

14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649

15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894

16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514

17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484

18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751

19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514

20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606

21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735

22 AWWF 489 614 729 884 997 1111 1221 1369 1415 1524

23 CSF [3times3] 397 604 844 1088 1338 1588 1841 2093 2328 2573

24 CSF [5times5] 648 696 767 861 971 1086 1218 1349 1494 1629

25 CSF [7times7] 890 953 971 1004 1042 1099 1147 1213 1290 1377







Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555

5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216

6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991

7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994

11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899

12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818

13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963

14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953

15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106

16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851

17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764

18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027

19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958

20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953

21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740

22 AWWF 558 663 780 849 1017 1175 1298 1473 1683 1861

23 CSF [3times3] 649 793 879 956 1139 1183 1351 1527 1912 2098

24 CSF [5times5] 941 991 1022 1065 1119 1175 1249 1341 1425 1509

25 CSF [7times7] 1019 1081 1088 1101 1116 1137 1160 1188 1229 1267







Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951

5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419

6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539

7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340

8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621

9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637

10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098

11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503

12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557

13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417

14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458

15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239

16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566

17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613

18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385

19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598

20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557

21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451

22 AWWF 09953 09934 09898 09865 09820 09765 09721 09690 09620 09568

23 CSF [3times3] 09973 09949 09849 09742 09611 09452 09272 09067 08854 08614

24 CSF [5times5] 09938 09924 09900 09866 09822 09771 09710 09640 09555 09469

25 CSF [7times7] 09912 09848 09839 09828 09813 09789 09765 09735 09700 09659







Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163

5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578

6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687

7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460

8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732

9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760

10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261

11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588

12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638

13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488

14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525

15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392

16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665

17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702

18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476

19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689

20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662

21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908

22 AWWF 09974 09960 09941 09912 09888 09852 09791 09745 09700 09656

23 CSF [3times3] 09976 09962 09879 09796 09689 09561 09412 09246 09068 08862

24 CSF [5times5] 09964 09952 09949 09915 09871 09828 09778 09716 09652 09571

25 CSF [7times7] 09925 09913 09906 09895 09889 09861 09838 09810 09785 09766







Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345

5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610

6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669

7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569

8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732

9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734

10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385

11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602

12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628

13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578

14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636

15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501

16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670

17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680

18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565

19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662

20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620

21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339

22 AWWF 09961 09950 09938 09895 09872 09840 09786 09750 09733 09713

23 CSF [3times3] 09979 09961 09940 09843 09762 09666 09550 09418 09282 09126

24 CSF [5times5] 09944 09935 09920 09899 09873 09847 09797 09749 09693 09630

25 CSF [7times7] 09886 09877 09871 09862 09850 09832 09815 09792 09762 09751







Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024

5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227

6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360

7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314

8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398

9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411

10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201

11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395

12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434

13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358

14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396

15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284

16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425

17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469

18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316

19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329

20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312

21 NL-Means 09957 09943 09865 09716 09516 09285 09010 08737 08423 08127

22 AWWF 09943 09918 09893 09836 09748 09690 09614 09568 09492 09453

23 CSF [3times3] 09964 09945 09895 09773 09721 09666 09536 09485 09313 09261

24 CSF [5times5] 09913 09896 09866 09838 09793 09779 09692 09576 09517 09458

25 CSF [7times7] 09834 09818 09799 09783 09779 09752 09717 09659 09600 09534




Sl No

Denoising Images

Filters


1 Mean [3times3] 262 290 410 668

2 Mean [5times5] 443 408 642 946

3 Mean [7times7] 573 520 793 1035

4 Median [3times3] 132 153 252 438

5 Median [5times5] 270 239 443 693

6 Median [7times7] 395 311 499 744

7 ATM [3times3] 262 290 410 668

8 ATM [5times5] 443 408 642 946

9 ATM [7times7] 573 520 793 1035

10 Wiener [3times3] 186 204 318 387

11 Wiener [5times5] 367 351 540 637

12 Wiener [7times7] 464 387 576 668

13 AD 204 237 295 497

14 TV 211 234 334 573

15 Lee [3times3] 00118 109 00336 00583

16 Lee [5times5] 00530 114 01109 02057

17 Lee [7times7] 01315 201 01853 110

18 Bilateral [3times3] 288 308 423 680

19 Bilateral [5times5] 497 433 663 966

20 Bilateral [7times7] 601 545 826 1104

21 NL-Means 117 137 186 211

22 AWWF 183 206 321 387

23 CSF [3times3] 122 142 183 318

24 CSF [5times5] 272 257 402 675

25 CSF [7times7] 4437 390 619 907







1 Mean [3times3] 318 701 1713

2 Mean [5times5] 323 712 1749

3 Mean [7times7] 327 720 1776

4 Median [3times3] 402 742 2445

5 Median [5times5] 409 747 2469

6 Median [7times7] 415 812 2490

7 ATM [3times3] 732 1677 3018

8 ATM [5times5] 809 1723 3056

9 ATM [7times7] 813 1784 3084

10 Wiener [3times3] 787 1559 2806

11 Wiener [5times5] 807 1598 2876

12 Wiener [7times7] 843 1670 3006

13 AD ------ ------- ------

14 TV ------ ------- ------

15 Lee [3times3] 874 1426 3509

16 Lee [5times5] 887 1446 3545

17 Lee [7times7] 968 1579 3779

18 Bilateral [3times3] 536 1100 3265

19 Bilateral [5times5] 583 1353 3520

20 Bilateral [7times7] 588 1359 3639

21 NL-Means 44667 99620 221838

22 AWWF 1181 2417 4546

23 CSF [3times3] 338 706 1866

24 CSF [5times5] 343 717 1898

25 CSF [7times7] 352 729 1930





(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

PS

NR

(d

B)


PS

NR

(d

B)

(a) (b)

σn σn


PS

NR

(d

B)


SN

R (

dB

)

(c) (d)

σn σn





(a) Lena (b) Pepper


RM

SE


RM

SE


(a) (b)

σn σn


RM

SE


RM

SE

(c) (d)

σn σn




(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara


UQ

I


UQ

I

(a) (b)

σn σn

UQ

I

UQ

I


(c) (d)

σn σn



(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)


with AWGN σn = 15







(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k) (l) (m)


AWGN σn = 15







(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

(m)


AWGN σn = 40







(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k)

(l) (m)













(d)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(l)

(m)



34 Conclusion







condition




















image Pepper















others







Chapter 4

Development of

Transform-Domain

Filters



Preview
















4













filtered image











Simulation Results

Conclusion




Filter











bull Mask Selection












= times (41)








2

2

( ) exp2

exp

2

exp2

kxf x A

xA

k

xA

c

σ

σ

= minus

minus =

minus =

(42)



k = a constant






and rests are zeros




INPUT NOISY

IMAGE

7times7

window

DCT

Edge Detection

Percentage of


Selection


FILTERED IMAGE

Masking matrices

IDCT





412 Mask Selection








1 5

2 5 8

3 8 12

4 12 18

5 18 24

6 24 30

7 30

Mask if PEP

Mask if PEP

Mask if PEP

Mask Mask if PEP

Mask if PEP

Mask if PEP

Mask if PEP

le lt le lt le

= lt le lt le

lt le

lt

(43)













In (42) for x = 0 f (0) = A


Hence A = 1
















in Section 44



002 004 006 008 0127

28

29

30

31

Lena

Pepper

Goldhill

Pea

k S

ign

al

to N

ois

e R

ati

o (

dB

)

parameter c

(a)



(a) σn = 20

(b) σn = 30

002 004 006 008 0125

26

27

28

29

Lena

Pepper

Goldhill

Pea

k S

ign

al

to N

ois

e R

ati

o (

dB

)

(b)

parameter c























The Proposed Method






































Step ndash 1



Step ndash 2



Step ndash 3





Step ndash 4




Step ndash 5



Step ndash 6
















Noise level of AWGN

Sl No



Low

(σnle10)

Moderate

(10lt σnle30)

High

(30lt σnle50)



























The Proposed Scheme










as

2

2 2

ˆˆ

ˆk

k k

k n

w yσ

σ σ=

+ (44)

where ˆk

w and k


region of a

particular subband





( )

( )

2

2 2

0(k)

2 2

(k)

arg max P Y(j) |

1max 0 Y j

k

j

n

jM

σσ σ

σ

geisin

isin

=

= minus

prod

sum

N

N

(45)



















shown in Fig 43

Input

DWT

Get a sub-image by




ML Estimation




IDWT

ˆ ( )f x y

Y

Y

( ) ( ) ( )g x y f x y x yη= +

Noisy Image

Output



























performing filters













best performer


















No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148

5 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621

6 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607

7 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815

8 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542

9 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497

10 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131

11 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458

12 LAWML[5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602

13 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638

14 GS-DCT 3376 3313 3188 3098 3001 2911 2746 2706 2689 2611

15 TV-DWT 3465 3376 3229 3056 296 2844 2736 2667 2558 2477

16 RM-DWT 3910 3472 3236 3069 2948 2858 2781 2723 2655 2602







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137

5 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454

6 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505

7 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835

8 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564

9 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451

10 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728

11 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447

12 LAWML[5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560

13 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575

14 GS-DCT 3379 3310 3259 3100 2976 2855 2766 2621 2610 2562

15 TV-DWT 3278 3183 3075 297 2865 2772 2675 2593 2507 2438

16 RM-DWT 3918 3481 3189 3083 2971 2852 2748 2687 2523 2454







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026

5 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462

6 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409

7 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921

8 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724

9 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411

10 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762

11 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361

12 LAWML[5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443

13 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443

14 GS-DCT 3325 3161 3089 2956 2821 2716 2623 2518 2474 2401

15 TV-DWT 2782 2693 2645 2594 254 2488 2434 2379 2327 2277

16 RM-DWT 3812 3331 3076 2922 2800 2719 2635 2555 2497 2442







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989

5 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286

6 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271

7 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044

8 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708

9 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326

10 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739

11 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295

12 LAWML[5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371

13 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378

14 GS-DCT 3376 3195 3085 2995 2808 2649 2544 2439 2416 2321

15 TV-DWT 2712 2693 2645 2594 254 2488 2434 2379 2327 2277

16 RM-DWT 3793 3310 3012 2834 2689 2588 2496 2431 2372 2325







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150

5 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247

6 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267

7 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155

8 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320

9 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438

10 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193

11 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505

12 LAWML[5times5] 299 475 621 747 863 955 1046 1127 1198 1275

13 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223

14 GS-DCT 558 562 649 720 805 893 1080 1131 1153 1261

15 TV-DWT 472 523 619 756 844 965 1092 1183 1341 1472

16 RM-DWT 282 468 614 744 856 949 1037 1109 1199 1275







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177

5 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512

6 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425

7 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083

8 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212

9 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517

10 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487

11 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524

12 LAWML[5times5] 293 472 607 732 852 966 1070 1166 1263 1338

13 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315

14 GS-DCT 521 564 598 718 828 952 1055 1247 1263 1335

15 TV-DWT 585 653 739 834 941 1048 1172 1288 1422 1540

16 RM-DWT 280 463 648 732 833 956 1077 1156 1396 1512







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 174

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474

5 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498

6 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592

7 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792

8 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503

9 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588

10 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353

11 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682

12 LAWML[5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531

13 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531

14 GS-DCT 554 669 727 848 990 1118 1244 1404 1477 1607

15 TV-DWT 1036 1148 1213 1286 1369 1453 1547 1648 175 1853

16 RM-DWT 316 550 738 882 1015 1114 1227 1346 1438 1533







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582

5 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834

6 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866

7 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424

8 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568

9 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752

10 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443

11 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815

12 LAWML[5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663

13 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650

14 GS-DCT 523 644 731 811 1005 1207 1363 1538 1579 1762

15 TV-DWT 1123 1148 1213 1286 1369 1453 1547 1648 1751 1853

16 RM-DWT 323 564 795 976 1153 1295 1440 1552 1661 1754







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178

5 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636

6 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621

7 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021

8 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953

9 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530

10 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661

11 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484

12 LAWML[5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622

13 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649

14 GS-DCT 09944 09937 09911 09896 09856 09813 09740 09720 09626 09578

15 TV-DWT 09968 09938 09925 09877 09843 09788 09724 09652 09570 09481

16 RM-DWT 09985 09954 09917 09878 09844 09808 09766 09692 09654 09596







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289

5 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568

6 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617

7 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400

8 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484

9 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579

10 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022

11 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575

12 LAWML[5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675

13 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689

14 GS-DCT 09971 09960 09954 09921 09883 09822 09754 09721 09689 09635

15 TV-DWT 09953 09932 09908 09878 09839 09797 09741 09684 09613 09544

16 RM-DWT 09991 09971 09885 09868 09853 09833 09798 09752 09708 09639







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328

5 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673

6 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627

7 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926

8 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443

9 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638

10 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541

11 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592

12 LAWML[5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656

13 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658

14 GS-DCT 09958 09949 09939 09913 09881 09845 09789 09756 09703 09648

15 TV-DWT 09976 09954 09935 09902 09873 09841 09779 09768 09718 09654

16 RM-DWT 09992 09961 09926 09889 09859 09788 09759 09698 09659 09599







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138

5 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424

6 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401

7 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005

8 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136

9 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491

10 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233

11 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433

12 LAWML[5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517

13 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521

14 GS-DCT 09945 09933 09913 09867 09823 09764 09701 09645 09532 09512

15 TV-DWT 09801 09783 09755 09724 09685 09643 09593 09537 09478 09413

16 RM-DWT 09989 09951 09898 09859 09807 09759 09700 09647 09573 09511






Filters


1 Mean [3times3]

262 290 410 668

2 Mean [5times5]

443 408 642 946

3 Mean [7times7]

573 520 793 1035

4 VisuShrink

318 423 471 637

5 SureShrink

517 673 770 1007

6 BayesShrink

00232 00273 00194 00190

7 OracleShrink

00285 00267 00242 00238

8 OracleThresh

00285 00267 00242 00238

9 NeighShrink

408times10-10

466times10-10

334times10-10

497times10-10

10 SmoothShrink

660 752 64515 790

11 LAWML [3times3]

408times10-10

466times10-10

334times10-10

497times10-10

12 LAWML[5times5]

408times10-10

466times10-10

334times10-10

497times10-10

13 LAWML [7times7]

408times10-10

466times10-10

334times10-10

497times10-10

14 GS-DCT

05737 072675 067065 07930

15 TV-DWT

201 226 341 479

16 RM-DWT

408times10-10

466times10-10

334times10-10

497times10-10






SYSTEM-1

SYSTEM-2

SYSTEM-3

1 Mean [3times3] 318 701 2313

2 Mean [5times5] 323 712 2349

3 Mean [7times7] 327 720 2376








11 LAWML [3times3] 367 809 2669

12 LAWML[5times5] 370 815 2689

13 LAWML [7times7] 374 823 2715

14 GS-DCT 1381 3038 7025

15 TV-DWT 04261 09375 309

16 RM-DWT 515 1134 3742




PS

NR

(d

B)


PS

NR

(d

B)

PS

NR

(d

B)


PS

NR

(d

B)


(a) (b)

(c) (d)


(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

σn

σn σn

σn




RM

SE

RM

SE


RM

SE


RM

SE

(a) (b)

(c) (d)


(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

σn σn

σn σn



UQ

I


UQ

I

UQ

I


UQ

I


(a) (b)

(c) (d)



(a) Lena (b) Pepper


σn σn

σn σn



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)







(l)

(m)

(n)



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)


σn = 15






(l)

(m)

(n)



(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)







(h) (i) (j)

(m) (k)

(l)

(m) (n)



(a) (b) (c)

(d)

(e) (f) (g) (h)

(i) (j) (k)







(l)

(m) (n)



(a) (b) (c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)






(l)

(m) (n)



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)







(l)

(m) (n)



(a)

(b) (c)

(d) (e)

(g) (h) (i) (j)

(k)







(f)

(m) (n) (l)









(a) (b) (c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m) (n)



45 Conclusion















applications







Chapter 5

Development of

Some Color Image

Denoising Filters



Preview














5















Filter

Simulation Results

Conclusion















(a)

Filter R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

Input

Color Image

(RGB)

Output

Color Image

(RGB)

Filter

Filter




Filter R-Channel

G-Channel

RG

B ndash

C

T

ran

sfo

rma

tio

n

C ndash

RG

B

T

ran

sfo

rma

tio

n

B-Channel

(b)

R-Channel

G-Channel

B-Channel Filter

Filter

Input

Color Image

(RGB)

Output Color Image

(RGB)











029900000 058700000 014400000

016873000 033126400 050000000

050000000 041866800 008131200

Y R

Cb G

Cr B


(51)




expression [1]

1

1

1

C R

M G

Y B

= minus

(52)


1

3

1 1

3 3

1 1

3 3

116 16

500

200

n n

n n

YL

Yn

X Ya

X Y

Y Zb

Y Z

= minus

= minus

= minus

(53)





0412 0358 0180

0213 0715 0072

0019 0119 0950

X R G B

Y R G B

Z R G B

= + +

= + +

= + +

(54)




















RGB color space

YCbCr color space

CMY color space

CIE LAB color space





Sl

No

Denoising

Filters

10

25

40

10

25

40

10

25

40

10

25

40

1 M-MF [3times3] 3350 2868 2572 3745 3326 3003 3311 2849 2555 3240 2789 2499

2 M-MF [5times5] 3029 2888 2701 3437 3322 3159 2990 2869 2684 2919 2809 2628

3 M-MF [7times7] 2820 2771 2660 3242 3195 3110 2781 2753 2643 2710 2692 2587

4 M-LAWML [3times3] 3425 2925 2583 3897 3416 3159 3386 2916 2566 3315 2846 2510

5 M-LAWML [5times5] 3455 3011 2712 3857 3341 3008 3416 2993 2695 3345 2932 2639

6 M-LAWML [7times7] 3496 3048 2755 3824 3266 2793 3457 3028 2738 3386 2969 2682

7 MCSF [3times3] 3357 2654 2245 3764 3044 2659 3318 2631 2228 3247 2575 2172

8 MCSF [5times5] 3330 3049 2686 3751 3417 3080 3291 3030 2669 3220 2970 2613

9 MCSF [7times7] 3101 2998 2835 3458 3357 3204 3062 2979 2818 2991 2919 2762

10 MRM-DWT 3502 3011 2765 3987 3388 3149 3463 2992 2748 3392 2932 2692









YC

bC

r

RG

B

CM

Y

CIE

La

b

CP

SN

R (

dB

)

(a)

CM

Y

RG

B

YC

bC

r

CIE

La

b

CP

SN

R (

dB

)

(b)

YC

bC

r

RG

B

CIE

La

b

CM

Y

CP

SN

R (

dB

) (c)











schematic in Fig 53








Input

Color Image

(RGB)

Mean

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

Mean

Filter

Mean

Filter

(a)

Mean

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

Mean

Filter

Mean

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)















Input

Color Image

(RGB)

LAWML

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

LAWML

Filter

LAWML

Filter

(a)

LAWML

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

LAWML

Filter

LAWML

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)
















schematic in Fig 55





Input

Color Image

(RGB)

CSF

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

CSF

Filter

CSF

Filter

(a)

CSF

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

CSF

Filter

CSF

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)







DWT-domain Filter







Fig 56





Input

Color Image

(RGB)

RM-DWT

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

RM-DWT

Filter

RM-DWT

Filter

(a)

RM-DWT

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

RM-DWT

Filter

RM-DWT

Filter

Input

Color Image

(RGB)

Output Color Image

(RGB)

















(30ltσnle50)









highlighted



































analysis






from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 3470 3350 3227 3078 2868 2778 2686 2572 2495 2458

2 M-MF[5times5] 3051 3029 2977 2902 2888 2855 2783 2701 2659 2599

3 M-MF[7times7] 2829 2820 2789 2776 2761 2714 2689 2660 2645 2591

4 M-LAWML [3times3] 3501 3425 3263 3078 2925 2777 2662 2583 2513 2476

5 M-LAWML[5times5] 3513 3455 3336 3161 3011 2893 2769 2712 2682 2623

6 M-LAWML [7times7] 3537 3496 3344 3179 3048 2905 2867 2755 2698 2658

7 MCSF [3times3] 3488 3357 3077 2845 2654 2477 2355 2245 2189 2083

8 MCSF [5times5] 3402 3388 3375 3179 3049 2876 2774 2686 2595 2541

9 MCSF [7times7] 3331 3101 3085 3039 2998 2952 2942 2835 2789 2733

10 MRM-DWT 3587 3502 3373 3175 3046 2908 2876 2765 2698 2661



from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 3346 3176 3087 2942 2831 2725 2629 2538 2458 2388

2 M-MF[5times5] 3271 3097 3065 3009 2956 2894 2835 2776 2713 2673

3 M-MF[7times7] 3162 2914 2916 2859 2834 2812 2773 2737 2734 2682

4 M-LAWML [3times3] 3538 3501 3254 3076 2934 2811 2714 2638 2574 2520

5 M-LAWML[5times5] 3579 3543 3325 3163 3031 2922 2833 2758 2689 2639

6 M-LAWML [7times7] 3593 3545 3327 3170 3049 2939 2849 2777 2703 2657

7 MCSF [3times3] 3443 3346 3039 281 2623 2471 2342 223 2134 2044

8 MCSF [5times5] 3462 3464 3327 3174 3032 2902 2788 269 2597 2517

9 MCSF [7times7] 3432 3313 3278 3131 3078 3012 2948 2879 2817 2783

10 MRM-DWT 3596 3548 3318 3167 3053 2941 2856 2781 2712 2656





to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 469 538 620 737 938 1041 1157 1319 1442 1505

2 M-MF[5times5] 760 779 828 902 917 952 1035 1137 1194 1279

3 M-MF[7times7] 981 992 1028 1067 1049 1120 1153 1192 1213 1291

4 M-LAWML [3times3] 452 494 595 737 879 1042 1190 1303 1412 1474

5 M-LAWML[5times5] 446 477 547 669 796 912 1052 1123 1162 1244

6 M-LAWML [7times7] 434 455 542 656 763 899 939 1069 1141 1195

7 MCSF [3times3] 459 534 737 963 1201 1472 1694 1923 2051 2317

8 MCSF [5times5] 507 551 523 656 762 930 1046 1157 1285 1367

9 MCSF [7times7] 550 717 720 765 808 852 862 975 1028 1096

10 MRM-DWT 412 452 660 692 796 896 930 1056 1141 1191



from 5 to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 541 658 729 862 979 1106 1236 1372 1505 1631

2 M-MF[5times5] 590 721 748 798 848 911 978 1043 1122 1175

3 M-MF[7times7] 669 890 888 948 9762 1001 1047 10915 1095 1162

4 M-LAWML [3times3] 434 452 601 738 870 1002 1120 12233 1316 1401

5 M-LAWML[5times5] 414 431 554 668 778 882 977 10655 1153 1221

6 M-LAWML [7times7] 407 430 553 663 762 865 959 10424 1135 1196

7 MCSF [3times3] 484 541 770 1003 1244 1482 1722 19568 2185 2424

8 MCSF [5times5] 473 472 553 659 777 902 1029 11522 1282 1406

9 MCSF [7times7] 490 631 656 693 737 795 856 92692 995 1035

10 MRM-DWT 406 429 559 665 758 863 951 10376 1123 1198





UQI



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 09954 09936 09906 09863 09811 09746 09677 09593 09502 09392

2 M-MF[5times5] 09871 09853 09842 09826 09806 09784 09751 09715 09682 09628

3 M-MF[7times7] 09768 09755 09749 09741 09733 09717 09699 09675 09652 09617

4 M-LAWML [3times3] 09966 09959 09916 09864 09811 09754 0969 09627 09561 09498

5 M-LAWML[5times5] 09978 09965 09932 09892 09852 09812 09772 09727 09685 09637

6 M-LAWML [7times7] 09977 09966 09932 09898 09861 09827 09788 09747 09709 09665

7 MCSF [3times3] 09972 09963 09863 09756 09625 09466 09286 09081 08868 08628

8 MCSF [5times5] 09945 09939 09934 09899 09861 09828 09725 09655 09572 09484

9 MCSF [7times7] 09912 09903 09855 09844 09829 09805 09789 09751 09716 09675

10 MRM-DWT 09982 09973 09915 09881 09837 09786 09788 09747 09708 09663



UQI



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 09917 09901 09873 09836 09788 09731 09663 09587 09506 09410

2 M-MF[5times5] 09886 09878 09867 09849 09827 09800 09770 09731 09688 09639

3 M-MF[7times7] 09820 09815 09807 09794 09780 09760 09738 09708 09678 09641

4 M-LAWML [3times3] 09980 09950 09912 09867 09816 09758 09702 09639 09576 09505

5 M-LAWML[5times5] 09978 09906 09897 09883 09864 09842 09816 09782 09747 0971

6 M-LAWML [7times7] 09991 09983 09957 09929 09898 09861 09822 09783 09735 09697

7 MCSF [3times3] 09987 09983 099 09817 0971 09582 09433 09267 09089 08883

8 MCSF [5times5] 09979 09971 09968 09934 09898 09847 09797 09735 09671 0959

9 MCSF [7times7] 09921 09913 09906 09895 09889 09862 09838 09810 09785 09766

10 MRM-DWT 09993 09986 09961 09929 09890 09861 09821 09776 09731 09695





from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 3863 3745 3602 3460 3326 3209 3099 3003 2917 2838

2 M-MF[5times5] 3456 3437 3407 3366 3322 3267 3216 3159 3100 3046

3 M-MF[7times7] 3249 3242 3230 3217 3195 3172 3143 3110 3076 3040

4 M-LAWML [3times3] 4173 3897 3683 3537 3416 3323 3236 3159 3088 3019

5 M-LAWML[5times5] 4145 3857 3608 3456 3341 3224 3099 3008 2938 2840

6 M-LAWML [7times7] 4129 3824 3555 3385 3266 3107 2963 2793 2782 2694

7 MCSF [3times3] 4078 3864 3455 3224 3044 2895 2767 2659 2567 2484

8 MCSF [5times5] 3976 3781 3774 3617 3417 3276 3174 3080 2991 2913

9 MCSF [7times7] 3786 3458 3432 3398 3357 3343 3260 3204 3150 3095

10 MRM-DWT 4372 3987 3652 3508 3388 3308 3224 3149 3076 3016




CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 3656 3581 3475 3364 3253 3152 3052 2967 2884 2812

2 M-MF[5times5] 3520 3494 3454 3403 3346 3286 3222 3156 3094 3030

3 M-MF[7times7] 3324 3312 3294 3271 3241 3206 3170 3126 3083 3032

4 M-LAWML [3times3] 4121 3811 3611 3453 3333 3224 3131 3047 2960 2881

5 M-LAWML[5times5] 4105 3781 3575 3390 3261 3127 3028 2929 2835 2760

6 M-LAWML [7times7] 4087 3747 3505 3354 3195 3047 2926 2812 2724 2595

7 MCSF [3times3] 4018 3743 3446 3220 3042 2893 2772 2665 2572 2491

8 MCSF [5times5] 3945 3821 3696 3540 3418 3282 3174 3077 2985 2904

9 MCSF [7times7] 3832 3565 3524 3474 3414 3355 3290 3221 3156 3087

10 MRM-DWT 4212 3895 3676 3535 3402 3314 3212 3130 3050 2974





from 5 to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 298 342 403 474 554 633 719 803 887 971

2 M-MF[5times5] 477 487 504 529 556 592 622 671 718 764

3 M-MF[7times7] 605 610 618 628 644 661 683 710 738 770

4 M-LAWML [3times3] 208 287 367 434 499 555 614 671 728 788

5 M-LAWML[5times5] 215 300 400 477 544 623 719 798 866 969

6 M-LAWML [7times7] 219 312 425 517 593 712 841 1023 1036 1146

7 MCSF [3times3] 232 334 477 623 766 912 1054 1194 1327 1460

8 MCSF [5times5] 262 327 330 391 498 586 659 735 814 891

9 MCSF [7times7] 326 475 490 509 534 543 597 637 678 722

10 MRM-DWT 166 258 389 449 515 565 617 681 738 793




RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 378 413 466 530 602 676 759 837 921 1001

2 M-MF[5times5] 443 456 478 507 541 580 624 673 723 779

3 M-MF[7times7] 555 563 574 590 611 636 663 697 732 777

4 M-LAWML [3times3] 221 316 399 478 549 623 693 763 844 924

5 M-LAWML[5times5] 225 328 415 514 597 696 780 875 975 1063

6 M-LAWML [7times7] 230 341 450 536 644 763 878 1001 1108 1285

7 MCSF [3times3] 249 342 482 625 768 912 1048 1185 1319 1448

8 MCSF [5times5] 271 313 361 433 498 582 659 737 820 900

9 MCSF [7times7] 309 420 441 467 500 535 577 625 673 729

10 MRM-DWT 199 287 370 435 507 561 631 694 761 830





UQI


No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 09926 09903 09865 09813 09747 09671 09579 09475

09366 09245

2 M-MF[5times5] 09807 09799 09784 09764 09739 09704 09667 09623 09570 09515

3 M-MF[7times7] 09686 09681 09673 09663 09646 09627 09601 09572 09540 09504

4

M-LAWML

[3times3] 09977 09945 09910 09870 09834 09796 09751 09705 09656 09598

5

M-

LAWML[5times5] 09975 09939 09894 09848 09803 09739 09659 09577 09506 09384

6

M-LAWML [7times7] 09974 09935 09880 09820 09764 09665 09533 09280 09288 09131

7 MCSF [3times3] 09943 09908 09815 09687 09533 09354 09149 08928 08701 08457

8 MCSF [5times5] 09924 09920 09918 09871 09837 09717 09641 09559 09462 09361

9 MCSF [7times7] 09912 09901 09896 09861 09819 09798 09776 09727 09668 09613

10 MRM-DWT 09982 09953 09873 09832 09789 09788 09744 09699 09644 09596



UQI



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 09917 09901 09873 09836 09787 09731 09661 09588 09501 09411

2 M-MF[5times5] 09886 09879 09866 09849 09827 09802 09769 09731 09689 09640

3 M-MF[7times7] 09820 09815 09806 09795 09780 09760 09739 09710 09680 09641

4 M-LAWML [3times3] 09956 09932 09904 09872 09837 09806 09752 09703 09641 09571

5 M-LAWML[5times5] 09955 09929 09908 09855 09812 09750 09689 09613 09524 09423

6 M-LAWML [7times7] 09954 09925 09884 09843 09783 09704 09607 09501 09385 09177

7 MCSF [3times3] 09960 09931 09865 09774 09661 09528 09380 09213 09035 08850

8 MCSF [5times5] 09950 09943 09922 09888 09849 09801 09744 09681 09605 09526

9 MCSF [7times7] 09903 09897 09886 09872 09853 09831 09804 09769 09732 09686

10 MRM-DWT 09976 09950 09920 09889 09852 09812 09762 09711 09653 09585





Sl

No

Images


1 M-MF [3times3] 265 308

2 M-MF[5times5] 446 425

3 M-MF[7times7] 573 563


456times10-10


456times10-10


456times10-10

7 MCSF [3times3] 124 150

8 MCSF [5times5] 275 270

9 MCSF [7times7] 438 400


456times10-10



Sl

No

Images


1 M-MF [3times3] 265 308

2 M-MF[5times5] 446 425

3 M-MF[7times7] 573 563


456times10-10


456times10-10


456times10-10

7 MCSF [3times3] 124 150

8 MCSF [5times5] 275 270

9 MCSF [7times7] 438 400


456times10-10






Filters


1 M-MF [3times3] 855 1539 4309

2 M-MF[5times5] 8966 1614 4519

3 M-MF[7times7] 945 1701 4762

4 M-LAWML [3times3] 1188 2139 5989

5 M-LAWML[5times5] 1198 2157 6039

6 M-LAWML [7times7] 1245 2242 6277

7 MCSF [3times3] 8711 1568 4390

8 MCSF [5times5] 928 1672 4681

9 MCSF [7times7] 1001 1803 5048

10 MRM-DWT 1307 2353 6588


Sl No Images

Denoising

Filters


1 M-MF [3times3] 1042 1564 4848

2 M-MF[5times5] 1104 1656 5133

3 M-MF[7times7] 1150 1726 5350

4 M-LAWML [3times3] 1624 2436 7551

5 M-LAWML[5times5] 1688 2532 7849

6 M-LAWML [7times7] 1792 2688 8332

7 MCSF [3times3] 1067 1601 4963

8 MCSF [5times5] 1148 1722 5338

9 MCSF [7times7] 1210 1816 5629

10 MRM-DWT 1984 2976 9225






Ex

ecu

tio

n T

ime

in s

econ

ds





CP

SN

R [

dB

]


CP

SN

R [

dB

] (a) (b)




(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)


(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image






(a) (b) (c)

(d) (e) (f)








(a) (b) (c)

(d) (e) (f)



(a) Original image






(a)

(b)

(c)

(d)

(e)

(f)


(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image





(a)

(b)

(c)

(d)

(e)

(f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image








(a) Original image




(c)

2

1

3

4

5

6

(a)

2

1

3

4

5

6

(d)

2

1

3

4

5

6

(b)

2

1

3

4

5

6



57 Conclusion



















































Chapter 6

Conclusion



Preview
















6












Conclusion




analyzed here


Images

































σn = 10

σn = 20

σn = 40


Mean 3270 589 09922 2978 826 09849 2696 1142 09700

ATM 3271 589 09922 2983 821 09851 2703 1134 09710

Wiener 3401 507 09943 3019 787 09861 2655 1198 09671

TV 3322 555 09931 3025 782 09864 2585 1298 09633

Lee 3347 540 09936 2974 828 09847 2677 1167 09688

Bilateral 3258 596 09921 2977 826 09849 2671 1175 09686

BayesShrink 3364 527 09938 3020 787 09863 2711 1124 09711

NeighShrink 3445 481 09949 3011 795 09861 2608 1264 09642

Ex

isti

ng

Fil

ters

LAWML 3459 474 09950 3086 729 09882 2732 1086 09721

AWWF 3336 545 09934 3056 754 09865 2688 1152 09690

CSF 3287 578 09949 3031 777 09866 2749 1076 09735

GS-DCT 3310 563 09902 3098 719 09896 2710 1124 09720

TV-DWT 3376 522 09936 3056 754 09855 2667 1180 09652 Pro

po

sed

Fil

ters

RM-DWT 3472 466 09954 3022 785 09815 2734 1083 09725





respectively)


Mean 262 720

ATM 262 1784

Wiener 186 1614

TV 211 -------

Lee 00118 1508

Bilateral 288 1347



Ex

isti

ng

F

ilte

rs

LAWML 408times10-10

809

AWWF 183 2417

CSF 122 729

GS-DCT 05737 3038

TV-DWT 2014 09375

Pro

po

sed

Fil

ters















noise conditions








Images


















space


σn = 10 σn = 20 σn = 40

Denoising

Filters

CPSNR

RMSE

UQI

CPSNR

RMSE

UQI

CPSNR

RMSE

UQI

M-MF [3times3] 3745 342 09903 3460 474 09813 3003 803 09475

M-MF [5times5] 3437 487 09799 3366 529 09764 3159 671 09623

M-MF [7times7] 3242 610 09681 3217 628 09663 3110 710 09572

M-LAWML[3times3] 3897 287 09945 3537 434 09870 3159 671 09705

M-LAWML[5times5] 3857 300 09939 3456 477 09848 3008 798 09577

Ex

isti

ng

F

ilte

rs

M-LAWML[7times7] 3824 312 09935 3385 517 09820 2793 1023 09280

MCSF [3times3] 3864 334 09908 3224 623 09687 2659 1194 08928

MCSF [5times5] 3781 327 09920 3617 391 09871 3080 735 09559

MCSF [7times7] 3458 475 09901 3398 509 09861 3204 637 09727

Pro

po

sed

Fil

ters

MRM-DWT 3987 258 09953 3508 449 09832 3149 681 09699





Denoising Filters

Method Noise

Execution Time

M-MF [3times3] 265 1564

M-MF [5times5] 446 1656

M-MF [7times7] 573 1726


-10

2436


-10 2532

Ex

isti

ng

F

ilte

rs


-10 2688

MCSF [3times3] 12495 1601

MCSF [5times5] 2754 1722

MCSF [7times7] 4386 1816

Pro

po

sed

Fil

ters

MRM-DWT 379times10

-10 2976









62 Conclusion
























conditions

























image denoising







Prentice-Hall 1989


1971













1999


Press 1996







REFERENCES















vol 3 pp 1499-1502 1996









54 no 1 pp 352-358 2005






vol 153 no 4 pp 261-269 2006



919-927 2008

REFERENCES




December 1999












2001






vol 16 no 10 pp 2565-2575 2007



406-421 2008



4281 2006



11 no 6 pp 403-416 2005

REFERENCES







46 2002




Kharagpur 2005






vol14 no 11 2005





2003



vol 24(12) pp 2061-2068 2003








REFERENCES










vol17 no 8 pp 1421-1430 2008






481-488 1995






1296 2007






2301-2311 2008



pp 364-376 2008

REFERENCES




1 no 2 pp 156-167 2007



pp 3-23 2006






29 pp 1136-1141 Dec 1981




vol 1 pp 25-28 1997








pp 1019-1021 1983


370 1984



FL pp 16-22 1987



639 1990

REFERENCES






846 1998





2002








2003





imaging pp 820-823 2004





vol 2 no 3 pp 165-168 1980





REFERENCES














1004 2005






57 no 1 pp 75-78 1995













REFERENCES




12 pp 839-842 2005



4 pp 514-523 2008






pp 117-130 2007



no 2 pp 597-630 2007







1200-1224 1995






no 9 pp 1532-1546 2000




REFERENCES





















vol 54 no 4 pp 1600-1606 2005



1056-1068 2008






2878 2006



2003 vol 1 pp I-101-I-104 2003

REFERENCES






vol 87 no 7 pp 1721-1734 2007



2205 2007



pp349-365 2007





16 no 8 pp 2080-2095 2007



16 no 2 pp 523-533 2007











2675 2006

REFERENCES




pp 1435-1447 2005








vol 15 no 11 pp 3362-3374 2006









3 pp 873-886 2008











REFERENCES




69 2008



15 no 9 pp 2575-2587 2006



1170 2006



vol 17 no 4 pp 482-492 2006



741-744 2005




vol 73 no 12 pp 1832-1835 1983





no 4 pp 550-563 2008



22 no 7 pp 837-845 2003





vol 3 pp 774-777 2000

REFERENCES







pp 479-482 2000















2008

























Punjab







Rourkela



NCNTE-2008 Mumbai


ii

ACKNOWLEDGEMENT












period






throughout



Nilamani Bhoi


iii






Communication Engg




PO-Kalamati







PUBLICATION





CONTENTS Page No

Certificate

Preface i

Acknowledgement ii


Contents iv

Abstract

vi



xii




15 Image Metrics 19



Preview




Filters

32





28 Conclusion 79

CONTENTS


v


Preview




34 Conclusion 122


Preview


127



Filter

137


45 Conclusion 167


Preview






DWT-domain Filter

183


57 Conclusion 209

6 Conclusion 211

Preview


62 Conclusion 221


References 223



Abstract



(AWGN)










possible





noise in an image












Abstract


vii













execution time




developed














Abstract


viii


of the image




























Abstract


ix




























suppressing AWGN



Abbreviations




4 SN Speckle Noise




8 LL Low-Low

9 LH Low-High

10 HL High-Low

11 HH High-High





16 MED Median








xi



24 HVS

Human Visual System


25 MF Mean Filter








Maximum Likelihood

DEVELOPED FILTERS










Symbols








7 TE Execution Time

8 MN Method Noise

9 2

nσ Noise Variance















xiii

22 ( )hT







28 C Color Space

Chapter 1

Introduction



Preview












Literature Review

Problem Statement

Image Metrics


Conclusion

1




















































( ) ( ) ( )f x y K i x y r x y= (11)


0 ( ) 1r x ylt lt (13)











(b)

(a)

(c)

(d)

Imaging

System

Sampler and

Quantizer

Digital Storage

System

Digital

Computer

Online

Buffer

Display

Device



Object

Transmitter

Recorder








used























etc











































noise are presented
















22

1 Vtn sdotlt











form










noise












( ) ( )AWGN G











f is same or very



represented by SPN



represented as

SPN

with probability 1

( ) 0 2

1 2

f(xy) p d

f x y p d

p d

= minus

= = =

(16)



of density d RVIN


RVIN



f(xy) p df x y

x y p dη

= minus=

=

(17)












( ) ( )tSttnSN

)( η= (18)

( ) ( ) ( ) ( ) SN



digital image SN



















( ) ( ) ( )g x y f x y x yη= + (110)














































































































sense















equations















































projection









































applications















domain






15 Image Metrics













( )1 1

2ˆ ( ) ( )

M N

x y

f x y f x y

M NMSE = =

minus

times

sumsum= (111)

MSERMSE = (112)


( )1 1

ˆ ( ) ( )

M N

x y

f x y f x y

M NMAE = =

minus

times

sumsum= (113)




as






1

10

110 log

3c

c R G B

CPSNR MSE

minus

isin

= sdot

sum dB (115)













is defined by

where

( ) ( )ˆ ˆ

2 2 22

ˆ ˆ

ˆ 22

ˆ

ff f f

f ff f

f fUQI

f f

σ σ σ


++

1 1

1 1

1( )

1ˆ ˆ( )

M N

x y

M N

x y

f f x yM N

f f x yM N

= =

= =

=times

=times

sumsum

sumsum

( )

( )

22

1 1

22

ˆ

1 1

1( )

1

1 ˆ ˆ( )1

M N

f

x y

M N

fx y

f x y fM N

f x y fM N

σ

σ

= =

= =

= minustimes minus

= minustimes minus

sumsum

sumsum

( )( )ˆ

1 1

1 ˆ ˆ( ) ( )1

M N

f fx y

f x y f f x y fM N

σ= =


sumsum

(119)

(120)

(121)

(118)

(117)

(116)












fσ =f

σ




Method Noise





undesirable




1 =1

M

( )x y

x y==

times

sumsumM N

M N

N

N (122)




( )ˆ ( ) ( )f x y T f x y= (124)


Execution Time







access time etc










the filters



Processor









Preview



Literature Review

Problem Statement

Image Metrics


Conclusion


Preview




Bilateral Filter



Simulation Results

Conclusion


Preview



Simulation Results

Conclusion


Preview






Simulation Results

Conclusion


Preview






Simulation Results

Conclusion



Conclusion


17 Conclusion












Chapter 2

Study of Image

Denoising Filters



Preview
















2











Bilateral Filter



Simulation Results

Conclusion









































operation [42]













α lowest and the

2




( )

1ˆ( ) ( )xy

r

s t S


=minus

sum (21)













221 Wiener Filter

















by

( )2

2 2ˆ ( ) ( )

f

f n

f x y g g x y gσ

σ σ= + minus

+ (22)






variance 2

gσ are defined by

1( )

a b

s a t b


= sum sum (23)


and

( )22 1

( )1

a b

g

s a t b

g s t gL

σ= minus = minus




gσ with a priori



nσ from 2

gσ with the














signal processing

222 Lee Filter








where

22 2

2

2 2

1 ( )

0

n

g n

g

g n

k x y

σσ σ

σ

σ σ

minus gt

= le

(26)













sharpening [83-87]










2tg C g= nabla (27)

where t









2

( )[ ( ) ( )]

( )

t


t

C x y t g C g

part= = nabla

part


(28)











2

2( ) exp

sU s

k

= minus

(29)

or

2

1( )

1

U ss

k

=

+

(210)



as given by

[ ]1( ) ( ) ( ) ( ) ( ) ( )nn n


where 1( )ng x y



( )( )N N

C U g x y= nabla

( ) ( 1 ) ( )N






( )( )E E

C U g x y= nabla




+=





















(214)

( ) ( )( )

( ) ( )( )

( )

1

22

22

( ) ( )

( )

( ) ( ) ( )

( )

( ) ( ) ( )

( ) ( )

n n

n

SN

n n n

S E W

n

EW

n n n

E S N

n n

g x y g x y

g x yt


g x y

g x y m g x y g x y

t g x y g x yλ

+ =

nabla∆


nabla


minus ∆ minus



where

( )

( ) min mod( )

sgn sgnmin

2

m a b a b

a ba b

=

+ =

(215)

where

1 0sgn( )

1 0

xx

x

ge=

minus lt (216)


constant


2

tc

h

∆le (217)



+=



24 Bilateral Filter








functions)






122 2

1 1( ) ( )gd g x y g x y = minus (218)


2

1exp

2

g

g

g

dw

σ

= minus

(219)




distance given by

( ) ( )2 2





2

1exp

2

sd

d

dw

σ

= minus

(221)


dw


gw and dw

b g dw w w= (222)



( ) ( )ˆ ( )

( )

a b

b

s a t b

a b

b

s a t b

w s t g x s y t

f x y

w s t

=minus =minus

=minus =minus

+ +

=sum sum

sum sum (223)
















penalized



















( ) [ ]1 1

1 1

( )

ˆ ( ) ( ) ( ) ( ) ( )x y


= = sum (224)

[ ] [ ]1 1

1 1 1 1

( )

0 ( ) ( ) 1 ( ) ( ) 1x y


le le =sum (225)


p

q1

q2










[ ][ ]1 1

1 1 2

( ) ( )1( ) ( ) exp

p

d x y x yw x y x y

Z h

= minus

(226)

[ ]

1 1

1 1

2( )

( ) ( )expp

x y

d x y x yZ

hforall

= minus

sum (227)




[ ] ( )( ) ( )( )1 1

2

1 1 ( ) ( )

sim

x y x yR

























respectively [8889]








segmentation [97]


















(DWT)






Forward

WT


WT

Input

Image

Output

Image



























(a) decomposition

(b) reconstruction

f(n)

d1(n) H0 darr2

G0 darr2

H0 darr2

G0 darr2

a1(n)

d2(n)

a2(n)

(a)

f(n)

d1(n)

H1

darr2 G1

darr2

a1(n)

d2(n)

a2(n)

H1

darr2 G1

darr2

(b)



LL2 HL2

HL1

LH2 HH2

LH1 HH1


Transform


Image




















263 VisuShrink




where 2


image













264 SureShrink









( )22 2

1

1( ) 2 min

L

h n n i h i h

i

SURE T Y i Y T Y TL

σ σ=


sum (232)

where 2





265 BayesShrink





2ˆ

ˆn

B

F

Tσ

σ= (233)




ˆF



( )

1ˆ

06745

ij

n ij






Yσ can be found

empirically by

2 2

2 1

1ˆ

n

Y i j

i j

Yn

σ=

= sum (236)

In case 2 2ˆ ˆn Y

σ σge ˆF



( )maxB ijT Y=







( )2

1

arg min ( )h

h

n

OS T ij ijT

i j

T Y Fξ=

= minussum (237)



( )2

1

arg min ( )h

h

n

OT T ij ijT

i j

T Y Fζ=

= minussum (238)




as


and

( ) T

x x x Tζ = gt1 (240)


267 NeighShrink










2

21 U

ij

ij

T

S+

Γ = minus

(241)




1 12 2

1 1

j i

ij m n

n j m i

S Y+ +

= minus = minus

= sum sum (242)







counterpart ijY as


268 SmoothShrink










Step-1



d1

d2

d3

d4




Step-2



1 23 4nn d ijd Y Y n∆ = minus = (244)


th direction

Step-3


( )arg mindn

nY

d= ∆K (245)

Step-4



îjF =K (246)



269 LAWML








( )2

2 2

0( )

2 2

( )

ˆ ( ) arg max ( )

1max 0 ( )

j N k

n

j N k

k P Y j

Y jL

σσ σ

σ

geisin

isin

=

= minus

prod

sum (247)




nσ σ+ L is






by

2

2 2

ˆ ( )ˆ ( ) ( )ˆ ( ) n

kF k Y k

k

σ

σ σ= sdot

+ (248)



























performance




















Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094

5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382

6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496

7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322

8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586

9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613

10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186

11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469

12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534

13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393

14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412

15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268

16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534

17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595

18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368

19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573

20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519

21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636

22 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148

23 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621

24 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607

25 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815

26 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542

27 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497

28 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131

29 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458

30 LAWML [5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602

31 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638







Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102

5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419

6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562

7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312

8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632

9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687

10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185

11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460

12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526

13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361

14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376

15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271

16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547

17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609

18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348

19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592

20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552

21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651

22 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137

23 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454

24 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505

25 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835

26 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564

27 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451

28 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728

29 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447

30 LAWML [5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560

31 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575







Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102

5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343

6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420

7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162

11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368

12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407

13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340

14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378

15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258

16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451

17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469

18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325

19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451

20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400

21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668

22 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026

23 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462

24 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409

25 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921

26 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724

27 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411

28 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762

29 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361

30 LAWML [5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443

31 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443







Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998

5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121

6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214

7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3657 3167 2865 2921 2750 2606 2489 2390 2297 2213

11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255

12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293

13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226

14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231

15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166

16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277

17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319

18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199

19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229

20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231

21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667

22 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989

23 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286

24 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271

25 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044

26 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708

27 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326

28 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739

29 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295

30 LAWML [5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371

31 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378







Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287

5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642

6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438

7 ATM [3times3] 511 589 696 821 9639 1106 1267 1428 1593 1759

8 ATM [5times5] 828 844 869 910 9562 1004 1071 1134 1208 1298

9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257

10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057

11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484

12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377

13 AD 470 688 772 874 989 1109 1236 1369 1491 1621

14 TV 428 555 663 782 902 1032 1167 1298 1445 1586

15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871

16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377

17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285

18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667

19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318

20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402

21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876

22 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150

23 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247

24 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267

25 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155

26 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320

27 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438

28 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193

29 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505

30 LAWML [5times5] 299 474 621 747 863 955 1046 1127 1198 1275

31 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223







Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267

5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573

6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333

7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779

8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231

9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155

10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060

11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499

12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389

13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680

14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652

15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864

16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356

17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264

18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706

19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287

20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349

21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809

22 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177

23 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512

24 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425

25 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083

26 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212

27 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517

28 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487

29 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524

30 LAWML [5times5] 293 472 607 732 852 966 1070 1166 1263 1338

31 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315







Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267

5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716

6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570

7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114

11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667

12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593

13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723

14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649

15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894

16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514

17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484

18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751

19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514

20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606

21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735

22 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474

23 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498

24 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592

25 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792

26 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503

27 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588

28 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353

29 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682

30 LAWML [5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531

31 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531







Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555

5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216

6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991

7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994

11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899

12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818

13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963

14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953

15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106

16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851

17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764

18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027

19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958

20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953

21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740

22 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582

23 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834

24 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866

25 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424

26 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568

27 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752

28 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443

29 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815

30 LAWML [5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663

31 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650







Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951

5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419

6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539

7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340

8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621

9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637

10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098

11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503

12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557

13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417

14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458

15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239

16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566

17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613

18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385

19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598

20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557

21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451

22 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178

23 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636

24 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621

25 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021

26 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953

27 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530

28 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661

29 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484

30 LAWML [5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622

31 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649







Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163

5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578

6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687

7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460

8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732

9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760

10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261

11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588

12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638

13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488

14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525

15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392

16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665

17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702

18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476

19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689

20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662

21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908

22 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289

23 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568

24 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617

25 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400

26 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484

27 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579

28 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022

29 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575

30 LAWML [5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675

31 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689







Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345

5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610

6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669

7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569

8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732

9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734

10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385

11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602

12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628

13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578

14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636

15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501

16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670

17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680

18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565

19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662

20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620

21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339

22 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328

23 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673

24 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627

25 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926

26 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443

27 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638

28 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541

29 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592

30 LAWML [5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656

31 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658







Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024

5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227

6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360

7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314

8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398

9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411

10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201

11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395

12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434

13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358

14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396

15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284

16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425

17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469

18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316

19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329

20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312

21 NL-Means 09957 09943 098 65

09716 09516 09285 09010 08737 08423 08127

22 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138

23 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424

24 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401

25 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005

26 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136

27 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491

28 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233

29 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433

30 LAWML [5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517

31 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521




Sl No

Denoising Images

Filters


1 Mean [3times3] 262 290 410 668

2 Mean [5times5] 443 408 642 946

3 Mean [7times7] 573 520 793 1035

4 Median [3times3] 132 153 252 438

5 Median [5times5] 270 239 443 693

6 Median [7times7] 395 311 499 744

7 ATM [3times3] 262 290 410 668

8 ATM [5times5] 443 408 642 946

9 ATM [7times7] 573 520 793 1035

10 Wiener [3times3] 186 204 318 387

11 Wiener [5times5] 367 351 540 637

12 Wiener [7times7] 464 387 576 668

13 AD 204 237 295 497

14 TV 211 234 334 573

15 Lee [3times3] 00118 109 00336 00583

16 Lee [5times5] 00530 114 01109 02057

17 Lee [7times7] 01315 201 01853 110

18 Bilateral [3times3] 288 308 423 680

19 Bilateral [5times5] 497 433 663 966

20 Bilateral [7times7] 601 545 826 1104

21 NL-Means 117 137 186 211

22 VisuShrink 318 423 471 637

23 SureShrink 517 673 770 1007

24 BayesShrink 00232 00273 00194 00190

25 OracleShrink 00285 00267 00242 00238

26 OracleThresh 00285 00267 00242 00238


466times10-10

334times10-10

497times10-10

28 SmoothShrink 660 752 645 790


466times10-10

334times10-10

497times10-10


466times10-10

334times10-10

497times10-10


466times10-10

334times10-10

497times10-10






1 Mean [3times3] 318 701 1713

2 Mean [5times5] 323 712 1749

3 Mean [7times7] 327 720 1776

4 Median [3times3] 402 742 2445

5 Median [5times5] 409 747 2469

6 Median [7times7] 415 812 2490

7 ATM [3times3] 732 1677 3018

8 ATM [5times5] 809 1723 3056

9 ATM [7times7] 813 1784 3084

10 Wiener [3times3] 787 1559 2806

11 Wiener [5times5] 807 1598 2876

12 Wiener [7times7] 843 1670 3006

13 AD ------ ------- ------

14 TV ------ ------- ------

15 Lee [3times3] 874 1426 3509

16 Lee [5times5] 887 1446 3545

17 Lee [7times7] 968 1579 3779

18 Bilateral [3times3] 536 1100 3265

19 Bilateral [5times5] 583 1353 3520

20 Bilateral [7times7] 588 1359 3639

21 NL-Means 44667 99620 221838

22 VisuShrink 0540 119 392







29 LAWML [3times3] 367 809 2669

30 LAWML [5times5] 370 815 2689

31 LAWML [7times7] 374 823 2715





(a) Lena


(d) Barbara

σn

PS

NR

(d

B)


PS

NR

(d

B)


SN

R (

dB

)


PS

NR

(d

B)

(a) (b)

(c) (d)

σn

σn σn




(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

RM

SE


RM

SE


(a) (b)

RM

SE


RM

SE

(c) (d)


σn σn

σn σn





(a) Lena (b) Pepper


UQ


UQ

I


QI


UQ

I


(a) (b)

(c) (d)

σn σn

σn σn



(b)

(f)

(j)

(n)

(a)

(e)

(i)

(m)

(q)

(r)

(c)

(d)

(g)

(h)

(k)

(l)

(o)

(p)

(s)









(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)


AWGN σn = 15








(a) (b) (c) (d) (e) (f) (g)

(h) (i) (j) (k) (l)

(m)

(l) (m) (n)

(o) (p) (q) (r) (s)









(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m) (n) (o) (p)

(q) (r) (s)








(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)









(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)


AWGN σn = 40








(a)

(b) (c)

(d)

(f) (g)

(h)

(i)

(e)

(j) (k) (l) (m) (n)

(o) (p) (q) (r) (s)









(d)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)









28 Conclusion
























domain filters












research work

Chapter 3

Development of


Image Filters



Preview















3












Simulation Results

Conclusion













power








much


The AWWF Theory

The AWWF Algorithm

Window Selection



311 The AWWF Theory







































Step-1



Step-2




Step-3







medium



Step-4


shown in Fig 34


sub-section






Sobel operator


Blurred Image

Edge Image

p

q






q

p

Wiener

Filtering

p1 OR q1









homogenous regions





pixels




used is 5times5















Simulation Results

Conclusion


















( ) ( )2 2



max

1 sd

dw

d= minus (32)









( )1

2 2 2

1 1| ( ) |gd g x y g x y = minus (33)


by

2

2exp

2

g

g

g

dw

σ

minus=

(34)





gw as




( )( ) ( )

ˆ

( )

a b

s a t b

a b

s a t b

w s t g x s y t

f x y

w s t

= minus = minus

= minus = minus

+ +

=

sum sum

sum sum (36)










(a) (b)








Experiment 1








Experiment 2








be taken as 1











(a) Lena image

(b) Goldhill image

0 1 2 3 4 515

20

25

30

σ = 30

σ = 40

σ = 50n

n

n

gσ

PS

NR

(d

B)

(a)

0 1 2 3 4 516

18

20

22

24

26

28

σ = 30

σ = 40

σ = 50

n

n

n

PS

NR

(d

B)

gσ

(b)



0 1 2 3 4 507

075

08

085

09

095

1

σ = 30

σ = 40

σ = 50

n

n

n

UQ

I

gσ

(a)

gσ

UQ

I

0 1 2 3 4 508

085

09

095

1

σ = 30

σ = 40

σ = 50

n

n

n

(b)


(a) Lena image

(b) Goldhill image































NL-Means filter








analysis











Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094

5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382

6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496

7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322

8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586

9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613

10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186

11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469

12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534

13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393

14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412

15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268

16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534

17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595

18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368

19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573

20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519

21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636

22 AWWF 3488 3336 3178 3056 2929 2813 2741 2688 2601 2585

23 CSF [3times3] 3719 3287 2971 2735 2551 2397 2269 2155 2060 1970

24 CSF [5times5] 3371 3280 3158 3031 2911 2796 2688 2598 2507 2432

25 CSF [7times7] 3015 2987 2962 2932 2896 2847 2801 2749 2699 2646






Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102

5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419

6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562

7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312

8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632

9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687

10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185

11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460

12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526

13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361

14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376

15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271

16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547

17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609

18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348

19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592

20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552

21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651

22 AWWF 3516 3396 3258 3101 3011 2891 2821 2743 2710 2638

23 CSF [3times3] 3680 3275 2968 2739 2552 2400 2271 2159 2063 1973

24 CSF [5times5] 3499 3381 3235 3084 2949 2819 2705 2607 2514 2434

25 CSF [7times7] 3217 3126 3091 3044 2991 2925 2861 2792 2730 2696






Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102

5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343

6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420

7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162

11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368

12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407

13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340

14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378

15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258

16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451

17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469

18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325

19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451

20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400

21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668

22 AWWF 3434 3234 3087 2918 2815 2720 2638 2539 2510 2446

23 CSF [3times3] 3615 3250 2960 2738 2559 2411 2282 2171 2079 1992

24 CSF [5times5] 3189 3127 3041 2940 2838 2741 2641 2552 2464 2389

25 CSF [7times7] 2914 2854 2836 2809 2776 2730 2692 2644 2590 2534






Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998

5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121

6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214

7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3657 3167 2865 2821 2750 2606 2489 2390 2297 2213

11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255

12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293

13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226

14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231

15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166

16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277

17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319

18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199

19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229

20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231

21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667

22 AWWF 3319 3169 3028 2954 2798 2671 2585 2475 2360 2273

23 CSF [3times3] 3188 3013 2922 2851 2698 2666 2551 2445 2249 2169

24 CSF [5times5] 2865 2820 2792 2756 2714 2671 2618 2557 2504 2455

25 CSF [7times7] 2796 2744 2739 2729 2716 2701 2683 2662 2633 2607






Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287

5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642

6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438

7 ATM [3times3] 511 589 696 821 963 1106 1267 1428 1593 1759

8 ATM [5times5] 828 844 869 910 956 1004 1071 1134 1208 1298

9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257

10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057

11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484

12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377

13 AD 470 688 772 874 989 1109 1236 1369 1491 1621

14 TV 428 555 663 782 902 1032 1167 1298 1445 1586

15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871

16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377

17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285

18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667

19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318

20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402

21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876

22 AWWF 459 545 655 754 874 999 1086 1152 1275 1295

23 CSF [3times3] 352 578 831 1094 1351 1614 1869 2131 2379 2639

24 CSF [5times5] 526 583 670 777 892 1017 1152 1280 1420 1550

25 CSF [7times7] 792 818 841 869 907 961 1012 1076 1139 1211






Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267

5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573

6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333

7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779

8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231

9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155

10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060

11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499

12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389

13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680

14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652

15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864

16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356

17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264

18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706

19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287

20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349

21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809

22 AWWF 445 510 596 716 795 912 989 1083 1124 1221

23 CSF [3times3] 368 586 836 1088 1349 1606 1864 2121 2371 2629

24 CSF [5times5] 453 517 614 731 854 991 1132 1267 1410 1545

25 CSF [7times7] 628 696 724 765 813 877 9460 1022 1099 1142







Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267

5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716

6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570

7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114

11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667

12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593

13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723

14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649

15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894

16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514

17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484

18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751

19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514

20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606

21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735

22 AWWF 489 614 729 884 997 1111 1221 1369 1415 1524

23 CSF [3times3] 397 604 844 1088 1338 1588 1841 2093 2328 2573

24 CSF [5times5] 648 696 767 861 971 1086 1218 1349 1494 1629

25 CSF [7times7] 890 953 971 1004 1042 1099 1147 1213 1290 1377







Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555

5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216

6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991

7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994

11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899

12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818

13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963

14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953

15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106

16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851

17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764

18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027

19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958

20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953

21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740

22 AWWF 558 663 780 849 1017 1175 1298 1473 1683 1861

23 CSF [3times3] 649 793 879 956 1139 1183 1351 1527 1912 2098

24 CSF [5times5] 941 991 1022 1065 1119 1175 1249 1341 1425 1509

25 CSF [7times7] 1019 1081 1088 1101 1116 1137 1160 1188 1229 1267







Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951

5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419

6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539

7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340

8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621

9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637

10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098

11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503

12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557

13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417

14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458

15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239

16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566

17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613

18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385

19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598

20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557

21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451

22 AWWF 09953 09934 09898 09865 09820 09765 09721 09690 09620 09568

23 CSF [3times3] 09973 09949 09849 09742 09611 09452 09272 09067 08854 08614

24 CSF [5times5] 09938 09924 09900 09866 09822 09771 09710 09640 09555 09469

25 CSF [7times7] 09912 09848 09839 09828 09813 09789 09765 09735 09700 09659







Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163

5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578

6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687

7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460

8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732

9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760

10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261

11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588

12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638

13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488

14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525

15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392

16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665

17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702

18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476

19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689

20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662

21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908

22 AWWF 09974 09960 09941 09912 09888 09852 09791 09745 09700 09656

23 CSF [3times3] 09976 09962 09879 09796 09689 09561 09412 09246 09068 08862

24 CSF [5times5] 09964 09952 09949 09915 09871 09828 09778 09716 09652 09571

25 CSF [7times7] 09925 09913 09906 09895 09889 09861 09838 09810 09785 09766







Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345

5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610

6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669

7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569

8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732

9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734

10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385

11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602

12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628

13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578

14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636

15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501

16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670

17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680

18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565

19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662

20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620

21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339

22 AWWF 09961 09950 09938 09895 09872 09840 09786 09750 09733 09713

23 CSF [3times3] 09979 09961 09940 09843 09762 09666 09550 09418 09282 09126

24 CSF [5times5] 09944 09935 09920 09899 09873 09847 09797 09749 09693 09630

25 CSF [7times7] 09886 09877 09871 09862 09850 09832 09815 09792 09762 09751







Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024

5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227

6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360

7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314

8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398

9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411

10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201

11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395

12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434

13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358

14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396

15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284

16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425

17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469

18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316

19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329

20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312

21 NL-Means 09957 09943 09865 09716 09516 09285 09010 08737 08423 08127

22 AWWF 09943 09918 09893 09836 09748 09690 09614 09568 09492 09453

23 CSF [3times3] 09964 09945 09895 09773 09721 09666 09536 09485 09313 09261

24 CSF [5times5] 09913 09896 09866 09838 09793 09779 09692 09576 09517 09458

25 CSF [7times7] 09834 09818 09799 09783 09779 09752 09717 09659 09600 09534




Sl No

Denoising Images

Filters


1 Mean [3times3] 262 290 410 668

2 Mean [5times5] 443 408 642 946

3 Mean [7times7] 573 520 793 1035

4 Median [3times3] 132 153 252 438

5 Median [5times5] 270 239 443 693

6 Median [7times7] 395 311 499 744

7 ATM [3times3] 262 290 410 668

8 ATM [5times5] 443 408 642 946

9 ATM [7times7] 573 520 793 1035

10 Wiener [3times3] 186 204 318 387

11 Wiener [5times5] 367 351 540 637

12 Wiener [7times7] 464 387 576 668

13 AD 204 237 295 497

14 TV 211 234 334 573

15 Lee [3times3] 00118 109 00336 00583

16 Lee [5times5] 00530 114 01109 02057

17 Lee [7times7] 01315 201 01853 110

18 Bilateral [3times3] 288 308 423 680

19 Bilateral [5times5] 497 433 663 966

20 Bilateral [7times7] 601 545 826 1104

21 NL-Means 117 137 186 211

22 AWWF 183 206 321 387

23 CSF [3times3] 122 142 183 318

24 CSF [5times5] 272 257 402 675

25 CSF [7times7] 4437 390 619 907







1 Mean [3times3] 318 701 1713

2 Mean [5times5] 323 712 1749

3 Mean [7times7] 327 720 1776

4 Median [3times3] 402 742 2445

5 Median [5times5] 409 747 2469

6 Median [7times7] 415 812 2490

7 ATM [3times3] 732 1677 3018

8 ATM [5times5] 809 1723 3056

9 ATM [7times7] 813 1784 3084

10 Wiener [3times3] 787 1559 2806

11 Wiener [5times5] 807 1598 2876

12 Wiener [7times7] 843 1670 3006

13 AD ------ ------- ------

14 TV ------ ------- ------

15 Lee [3times3] 874 1426 3509

16 Lee [5times5] 887 1446 3545

17 Lee [7times7] 968 1579 3779

18 Bilateral [3times3] 536 1100 3265

19 Bilateral [5times5] 583 1353 3520

20 Bilateral [7times7] 588 1359 3639

21 NL-Means 44667 99620 221838

22 AWWF 1181 2417 4546

23 CSF [3times3] 338 706 1866

24 CSF [5times5] 343 717 1898

25 CSF [7times7] 352 729 1930





(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

PS

NR

(d

B)


PS

NR

(d

B)

(a) (b)

σn σn


PS

NR

(d

B)


SN

R (

dB

)

(c) (d)

σn σn





(a) Lena (b) Pepper


RM

SE


RM

SE


(a) (b)

σn σn


RM

SE


RM

SE

(c) (d)

σn σn




(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara


UQ

I


UQ

I

(a) (b)

σn σn

UQ

I

UQ

I


(c) (d)

σn σn



(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)


with AWGN σn = 15







(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k) (l) (m)


AWGN σn = 15







(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

(m)


AWGN σn = 40







(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k)

(l) (m)













(d)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(l)

(m)



34 Conclusion







condition




















image Pepper















others







Chapter 4

Development of

Transform-Domain

Filters



Preview
















4













filtered image











Simulation Results

Conclusion




Filter











bull Mask Selection












= times (41)








2

2

( ) exp2

exp

2

exp2

kxf x A

xA

k

xA

c

σ

σ

= minus

minus =

minus =

(42)



k = a constant






and rests are zeros




INPUT NOISY

IMAGE

7times7

window

DCT

Edge Detection

Percentage of


Selection


FILTERED IMAGE

Masking matrices

IDCT





412 Mask Selection








1 5

2 5 8

3 8 12

4 12 18

5 18 24

6 24 30

7 30

Mask if PEP

Mask if PEP

Mask if PEP

Mask Mask if PEP

Mask if PEP

Mask if PEP

Mask if PEP

le lt le lt le

= lt le lt le

lt le

lt

(43)













In (42) for x = 0 f (0) = A


Hence A = 1
















in Section 44



002 004 006 008 0127

28

29

30

31

Lena

Pepper

Goldhill

Pea

k S

ign

al

to N

ois

e R

ati

o (

dB

)

parameter c

(a)



(a) σn = 20

(b) σn = 30

002 004 006 008 0125

26

27

28

29

Lena

Pepper

Goldhill

Pea

k S

ign

al

to N

ois

e R

ati

o (

dB

)

(b)

parameter c























The Proposed Method






































Step ndash 1



Step ndash 2



Step ndash 3





Step ndash 4




Step ndash 5



Step ndash 6
















Noise level of AWGN

Sl No



Low

(σnle10)

Moderate

(10lt σnle30)

High

(30lt σnle50)



























The Proposed Scheme










as

2

2 2

ˆˆ

ˆk

k k

k n

w yσ

σ σ=

+ (44)

where ˆk

w and k


region of a

particular subband





( )

( )

2

2 2

0(k)

2 2

(k)

arg max P Y(j) |

1max 0 Y j

k

j

n

jM

σσ σ

σ

geisin

isin

=

= minus

prod

sum

N

N

(45)



















shown in Fig 43

Input

DWT

Get a sub-image by




ML Estimation




IDWT

ˆ ( )f x y

Y

Y

( ) ( ) ( )g x y f x y x yη= +

Noisy Image

Output



























performing filters













best performer


















No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148

5 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621

6 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607

7 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815

8 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542

9 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497

10 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131

11 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458

12 LAWML[5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602

13 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638

14 GS-DCT 3376 3313 3188 3098 3001 2911 2746 2706 2689 2611

15 TV-DWT 3465 3376 3229 3056 296 2844 2736 2667 2558 2477

16 RM-DWT 3910 3472 3236 3069 2948 2858 2781 2723 2655 2602







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137

5 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454

6 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505

7 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835

8 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564

9 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451

10 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728

11 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447

12 LAWML[5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560

13 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575

14 GS-DCT 3379 3310 3259 3100 2976 2855 2766 2621 2610 2562

15 TV-DWT 3278 3183 3075 297 2865 2772 2675 2593 2507 2438

16 RM-DWT 3918 3481 3189 3083 2971 2852 2748 2687 2523 2454







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026

5 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462

6 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409

7 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921

8 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724

9 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411

10 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762

11 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361

12 LAWML[5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443

13 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443

14 GS-DCT 3325 3161 3089 2956 2821 2716 2623 2518 2474 2401

15 TV-DWT 2782 2693 2645 2594 254 2488 2434 2379 2327 2277

16 RM-DWT 3812 3331 3076 2922 2800 2719 2635 2555 2497 2442







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989

5 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286

6 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271

7 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044

8 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708

9 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326

10 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739

11 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295

12 LAWML[5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371

13 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378

14 GS-DCT 3376 3195 3085 2995 2808 2649 2544 2439 2416 2321

15 TV-DWT 2712 2693 2645 2594 254 2488 2434 2379 2327 2277

16 RM-DWT 3793 3310 3012 2834 2689 2588 2496 2431 2372 2325







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150

5 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247

6 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267

7 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155

8 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320

9 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438

10 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193

11 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505

12 LAWML[5times5] 299 475 621 747 863 955 1046 1127 1198 1275

13 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223

14 GS-DCT 558 562 649 720 805 893 1080 1131 1153 1261

15 TV-DWT 472 523 619 756 844 965 1092 1183 1341 1472

16 RM-DWT 282 468 614 744 856 949 1037 1109 1199 1275







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177

5 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512

6 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425

7 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083

8 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212

9 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517

10 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487

11 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524

12 LAWML[5times5] 293 472 607 732 852 966 1070 1166 1263 1338

13 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315

14 GS-DCT 521 564 598 718 828 952 1055 1247 1263 1335

15 TV-DWT 585 653 739 834 941 1048 1172 1288 1422 1540

16 RM-DWT 280 463 648 732 833 956 1077 1156 1396 1512







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 174

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474

5 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498

6 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592

7 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792

8 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503

9 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588

10 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353

11 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682

12 LAWML[5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531

13 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531

14 GS-DCT 554 669 727 848 990 1118 1244 1404 1477 1607

15 TV-DWT 1036 1148 1213 1286 1369 1453 1547 1648 175 1853

16 RM-DWT 316 550 738 882 1015 1114 1227 1346 1438 1533







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582

5 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834

6 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866

7 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424

8 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568

9 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752

10 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443

11 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815

12 LAWML[5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663

13 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650

14 GS-DCT 523 644 731 811 1005 1207 1363 1538 1579 1762

15 TV-DWT 1123 1148 1213 1286 1369 1453 1547 1648 1751 1853

16 RM-DWT 323 564 795 976 1153 1295 1440 1552 1661 1754







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178

5 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636

6 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621

7 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021

8 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953

9 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530

10 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661

11 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484

12 LAWML[5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622

13 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649

14 GS-DCT 09944 09937 09911 09896 09856 09813 09740 09720 09626 09578

15 TV-DWT 09968 09938 09925 09877 09843 09788 09724 09652 09570 09481

16 RM-DWT 09985 09954 09917 09878 09844 09808 09766 09692 09654 09596







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289

5 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568

6 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617

7 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400

8 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484

9 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579

10 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022

11 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575

12 LAWML[5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675

13 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689

14 GS-DCT 09971 09960 09954 09921 09883 09822 09754 09721 09689 09635

15 TV-DWT 09953 09932 09908 09878 09839 09797 09741 09684 09613 09544

16 RM-DWT 09991 09971 09885 09868 09853 09833 09798 09752 09708 09639







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328

5 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673

6 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627

7 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926

8 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443

9 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638

10 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541

11 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592

12 LAWML[5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656

13 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658

14 GS-DCT 09958 09949 09939 09913 09881 09845 09789 09756 09703 09648

15 TV-DWT 09976 09954 09935 09902 09873 09841 09779 09768 09718 09654

16 RM-DWT 09992 09961 09926 09889 09859 09788 09759 09698 09659 09599







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138

5 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424

6 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401

7 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005

8 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136

9 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491

10 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233

11 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433

12 LAWML[5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517

13 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521

14 GS-DCT 09945 09933 09913 09867 09823 09764 09701 09645 09532 09512

15 TV-DWT 09801 09783 09755 09724 09685 09643 09593 09537 09478 09413

16 RM-DWT 09989 09951 09898 09859 09807 09759 09700 09647 09573 09511






Filters


1 Mean [3times3]

262 290 410 668

2 Mean [5times5]

443 408 642 946

3 Mean [7times7]

573 520 793 1035

4 VisuShrink

318 423 471 637

5 SureShrink

517 673 770 1007

6 BayesShrink

00232 00273 00194 00190

7 OracleShrink

00285 00267 00242 00238

8 OracleThresh

00285 00267 00242 00238

9 NeighShrink

408times10-10

466times10-10

334times10-10

497times10-10

10 SmoothShrink

660 752 64515 790

11 LAWML [3times3]

408times10-10

466times10-10

334times10-10

497times10-10

12 LAWML[5times5]

408times10-10

466times10-10

334times10-10

497times10-10

13 LAWML [7times7]

408times10-10

466times10-10

334times10-10

497times10-10

14 GS-DCT

05737 072675 067065 07930

15 TV-DWT

201 226 341 479

16 RM-DWT

408times10-10

466times10-10

334times10-10

497times10-10






SYSTEM-1

SYSTEM-2

SYSTEM-3

1 Mean [3times3] 318 701 2313

2 Mean [5times5] 323 712 2349

3 Mean [7times7] 327 720 2376








11 LAWML [3times3] 367 809 2669

12 LAWML[5times5] 370 815 2689

13 LAWML [7times7] 374 823 2715

14 GS-DCT 1381 3038 7025

15 TV-DWT 04261 09375 309

16 RM-DWT 515 1134 3742




PS

NR

(d

B)


PS

NR

(d

B)

PS

NR

(d

B)


PS

NR

(d

B)


(a) (b)

(c) (d)


(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

σn

σn σn

σn




RM

SE

RM

SE


RM

SE


RM

SE

(a) (b)

(c) (d)


(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

σn σn

σn σn



UQ

I


UQ

I

UQ

I


UQ

I


(a) (b)

(c) (d)



(a) Lena (b) Pepper


σn σn

σn σn



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)







(l)

(m)

(n)



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)


σn = 15






(l)

(m)

(n)



(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)







(h) (i) (j)

(m) (k)

(l)

(m) (n)



(a) (b) (c)

(d)

(e) (f) (g) (h)

(i) (j) (k)







(l)

(m) (n)



(a) (b) (c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)






(l)

(m) (n)



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)







(l)

(m) (n)



(a)

(b) (c)

(d) (e)

(g) (h) (i) (j)

(k)







(f)

(m) (n) (l)









(a) (b) (c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m) (n)



45 Conclusion















applications







Chapter 5

Development of

Some Color Image

Denoising Filters



Preview














5















Filter

Simulation Results

Conclusion















(a)

Filter R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

Input

Color Image

(RGB)

Output

Color Image

(RGB)

Filter

Filter




Filter R-Channel

G-Channel

RG

B ndash

C

T

ran

sfo

rma

tio

n

C ndash

RG

B

T

ran

sfo

rma

tio

n

B-Channel

(b)

R-Channel

G-Channel

B-Channel Filter

Filter

Input

Color Image

(RGB)

Output Color Image

(RGB)











029900000 058700000 014400000

016873000 033126400 050000000

050000000 041866800 008131200

Y R

Cb G

Cr B


(51)




expression [1]

1

1

1

C R

M G

Y B

= minus

(52)


1

3

1 1

3 3

1 1

3 3

116 16

500

200

n n

n n

YL

Yn

X Ya

X Y

Y Zb

Y Z

= minus

= minus

= minus

(53)





0412 0358 0180

0213 0715 0072

0019 0119 0950

X R G B

Y R G B

Z R G B

= + +

= + +

= + +

(54)




















RGB color space

YCbCr color space

CMY color space

CIE LAB color space





Sl

No

Denoising

Filters

10

25

40

10

25

40

10

25

40

10

25

40

1 M-MF [3times3] 3350 2868 2572 3745 3326 3003 3311 2849 2555 3240 2789 2499

2 M-MF [5times5] 3029 2888 2701 3437 3322 3159 2990 2869 2684 2919 2809 2628

3 M-MF [7times7] 2820 2771 2660 3242 3195 3110 2781 2753 2643 2710 2692 2587

4 M-LAWML [3times3] 3425 2925 2583 3897 3416 3159 3386 2916 2566 3315 2846 2510

5 M-LAWML [5times5] 3455 3011 2712 3857 3341 3008 3416 2993 2695 3345 2932 2639

6 M-LAWML [7times7] 3496 3048 2755 3824 3266 2793 3457 3028 2738 3386 2969 2682

7 MCSF [3times3] 3357 2654 2245 3764 3044 2659 3318 2631 2228 3247 2575 2172

8 MCSF [5times5] 3330 3049 2686 3751 3417 3080 3291 3030 2669 3220 2970 2613

9 MCSF [7times7] 3101 2998 2835 3458 3357 3204 3062 2979 2818 2991 2919 2762

10 MRM-DWT 3502 3011 2765 3987 3388 3149 3463 2992 2748 3392 2932 2692









YC

bC

r

RG

B

CM

Y

CIE

La

b

CP

SN

R (

dB

)

(a)

CM

Y

RG

B

YC

bC

r

CIE

La

b

CP

SN

R (

dB

)

(b)

YC

bC

r

RG

B

CIE

La

b

CM

Y

CP

SN

R (

dB

) (c)











schematic in Fig 53








Input

Color Image

(RGB)

Mean

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

Mean

Filter

Mean

Filter

(a)

Mean

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

Mean

Filter

Mean

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)















Input

Color Image

(RGB)

LAWML

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

LAWML

Filter

LAWML

Filter

(a)

LAWML

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

LAWML

Filter

LAWML

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)
















schematic in Fig 55





Input

Color Image

(RGB)

CSF

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

CSF

Filter

CSF

Filter

(a)

CSF

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

CSF

Filter

CSF

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)







DWT-domain Filter







Fig 56





Input

Color Image

(RGB)

RM-DWT

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

RM-DWT

Filter

RM-DWT

Filter

(a)

RM-DWT

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

RM-DWT

Filter

RM-DWT

Filter

Input

Color Image

(RGB)

Output Color Image

(RGB)

















(30ltσnle50)









highlighted



































analysis






from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 3470 3350 3227 3078 2868 2778 2686 2572 2495 2458

2 M-MF[5times5] 3051 3029 2977 2902 2888 2855 2783 2701 2659 2599

3 M-MF[7times7] 2829 2820 2789 2776 2761 2714 2689 2660 2645 2591

4 M-LAWML [3times3] 3501 3425 3263 3078 2925 2777 2662 2583 2513 2476

5 M-LAWML[5times5] 3513 3455 3336 3161 3011 2893 2769 2712 2682 2623

6 M-LAWML [7times7] 3537 3496 3344 3179 3048 2905 2867 2755 2698 2658

7 MCSF [3times3] 3488 3357 3077 2845 2654 2477 2355 2245 2189 2083

8 MCSF [5times5] 3402 3388 3375 3179 3049 2876 2774 2686 2595 2541

9 MCSF [7times7] 3331 3101 3085 3039 2998 2952 2942 2835 2789 2733

10 MRM-DWT 3587 3502 3373 3175 3046 2908 2876 2765 2698 2661



from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 3346 3176 3087 2942 2831 2725 2629 2538 2458 2388

2 M-MF[5times5] 3271 3097 3065 3009 2956 2894 2835 2776 2713 2673

3 M-MF[7times7] 3162 2914 2916 2859 2834 2812 2773 2737 2734 2682

4 M-LAWML [3times3] 3538 3501 3254 3076 2934 2811 2714 2638 2574 2520

5 M-LAWML[5times5] 3579 3543 3325 3163 3031 2922 2833 2758 2689 2639

6 M-LAWML [7times7] 3593 3545 3327 3170 3049 2939 2849 2777 2703 2657

7 MCSF [3times3] 3443 3346 3039 281 2623 2471 2342 223 2134 2044

8 MCSF [5times5] 3462 3464 3327 3174 3032 2902 2788 269 2597 2517

9 MCSF [7times7] 3432 3313 3278 3131 3078 3012 2948 2879 2817 2783

10 MRM-DWT 3596 3548 3318 3167 3053 2941 2856 2781 2712 2656





to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 469 538 620 737 938 1041 1157 1319 1442 1505

2 M-MF[5times5] 760 779 828 902 917 952 1035 1137 1194 1279

3 M-MF[7times7] 981 992 1028 1067 1049 1120 1153 1192 1213 1291

4 M-LAWML [3times3] 452 494 595 737 879 1042 1190 1303 1412 1474

5 M-LAWML[5times5] 446 477 547 669 796 912 1052 1123 1162 1244

6 M-LAWML [7times7] 434 455 542 656 763 899 939 1069 1141 1195

7 MCSF [3times3] 459 534 737 963 1201 1472 1694 1923 2051 2317

8 MCSF [5times5] 507 551 523 656 762 930 1046 1157 1285 1367

9 MCSF [7times7] 550 717 720 765 808 852 862 975 1028 1096

10 MRM-DWT 412 452 660 692 796 896 930 1056 1141 1191



from 5 to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 541 658 729 862 979 1106 1236 1372 1505 1631

2 M-MF[5times5] 590 721 748 798 848 911 978 1043 1122 1175

3 M-MF[7times7] 669 890 888 948 9762 1001 1047 10915 1095 1162

4 M-LAWML [3times3] 434 452 601 738 870 1002 1120 12233 1316 1401

5 M-LAWML[5times5] 414 431 554 668 778 882 977 10655 1153 1221

6 M-LAWML [7times7] 407 430 553 663 762 865 959 10424 1135 1196

7 MCSF [3times3] 484 541 770 1003 1244 1482 1722 19568 2185 2424

8 MCSF [5times5] 473 472 553 659 777 902 1029 11522 1282 1406

9 MCSF [7times7] 490 631 656 693 737 795 856 92692 995 1035

10 MRM-DWT 406 429 559 665 758 863 951 10376 1123 1198





UQI



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 09954 09936 09906 09863 09811 09746 09677 09593 09502 09392

2 M-MF[5times5] 09871 09853 09842 09826 09806 09784 09751 09715 09682 09628

3 M-MF[7times7] 09768 09755 09749 09741 09733 09717 09699 09675 09652 09617

4 M-LAWML [3times3] 09966 09959 09916 09864 09811 09754 0969 09627 09561 09498

5 M-LAWML[5times5] 09978 09965 09932 09892 09852 09812 09772 09727 09685 09637

6 M-LAWML [7times7] 09977 09966 09932 09898 09861 09827 09788 09747 09709 09665

7 MCSF [3times3] 09972 09963 09863 09756 09625 09466 09286 09081 08868 08628

8 MCSF [5times5] 09945 09939 09934 09899 09861 09828 09725 09655 09572 09484

9 MCSF [7times7] 09912 09903 09855 09844 09829 09805 09789 09751 09716 09675

10 MRM-DWT 09982 09973 09915 09881 09837 09786 09788 09747 09708 09663



UQI



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 09917 09901 09873 09836 09788 09731 09663 09587 09506 09410

2 M-MF[5times5] 09886 09878 09867 09849 09827 09800 09770 09731 09688 09639

3 M-MF[7times7] 09820 09815 09807 09794 09780 09760 09738 09708 09678 09641

4 M-LAWML [3times3] 09980 09950 09912 09867 09816 09758 09702 09639 09576 09505

5 M-LAWML[5times5] 09978 09906 09897 09883 09864 09842 09816 09782 09747 0971

6 M-LAWML [7times7] 09991 09983 09957 09929 09898 09861 09822 09783 09735 09697

7 MCSF [3times3] 09987 09983 099 09817 0971 09582 09433 09267 09089 08883

8 MCSF [5times5] 09979 09971 09968 09934 09898 09847 09797 09735 09671 0959

9 MCSF [7times7] 09921 09913 09906 09895 09889 09862 09838 09810 09785 09766

10 MRM-DWT 09993 09986 09961 09929 09890 09861 09821 09776 09731 09695





from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 3863 3745 3602 3460 3326 3209 3099 3003 2917 2838

2 M-MF[5times5] 3456 3437 3407 3366 3322 3267 3216 3159 3100 3046

3 M-MF[7times7] 3249 3242 3230 3217 3195 3172 3143 3110 3076 3040

4 M-LAWML [3times3] 4173 3897 3683 3537 3416 3323 3236 3159 3088 3019

5 M-LAWML[5times5] 4145 3857 3608 3456 3341 3224 3099 3008 2938 2840

6 M-LAWML [7times7] 4129 3824 3555 3385 3266 3107 2963 2793 2782 2694

7 MCSF [3times3] 4078 3864 3455 3224 3044 2895 2767 2659 2567 2484

8 MCSF [5times5] 3976 3781 3774 3617 3417 3276 3174 3080 2991 2913

9 MCSF [7times7] 3786 3458 3432 3398 3357 3343 3260 3204 3150 3095

10 MRM-DWT 4372 3987 3652 3508 3388 3308 3224 3149 3076 3016




CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 3656 3581 3475 3364 3253 3152 3052 2967 2884 2812

2 M-MF[5times5] 3520 3494 3454 3403 3346 3286 3222 3156 3094 3030

3 M-MF[7times7] 3324 3312 3294 3271 3241 3206 3170 3126 3083 3032

4 M-LAWML [3times3] 4121 3811 3611 3453 3333 3224 3131 3047 2960 2881

5 M-LAWML[5times5] 4105 3781 3575 3390 3261 3127 3028 2929 2835 2760

6 M-LAWML [7times7] 4087 3747 3505 3354 3195 3047 2926 2812 2724 2595

7 MCSF [3times3] 4018 3743 3446 3220 3042 2893 2772 2665 2572 2491

8 MCSF [5times5] 3945 3821 3696 3540 3418 3282 3174 3077 2985 2904

9 MCSF [7times7] 3832 3565 3524 3474 3414 3355 3290 3221 3156 3087

10 MRM-DWT 4212 3895 3676 3535 3402 3314 3212 3130 3050 2974





from 5 to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 298 342 403 474 554 633 719 803 887 971

2 M-MF[5times5] 477 487 504 529 556 592 622 671 718 764

3 M-MF[7times7] 605 610 618 628 644 661 683 710 738 770

4 M-LAWML [3times3] 208 287 367 434 499 555 614 671 728 788

5 M-LAWML[5times5] 215 300 400 477 544 623 719 798 866 969

6 M-LAWML [7times7] 219 312 425 517 593 712 841 1023 1036 1146

7 MCSF [3times3] 232 334 477 623 766 912 1054 1194 1327 1460

8 MCSF [5times5] 262 327 330 391 498 586 659 735 814 891

9 MCSF [7times7] 326 475 490 509 534 543 597 637 678 722

10 MRM-DWT 166 258 389 449 515 565 617 681 738 793




RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 378 413 466 530 602 676 759 837 921 1001

2 M-MF[5times5] 443 456 478 507 541 580 624 673 723 779

3 M-MF[7times7] 555 563 574 590 611 636 663 697 732 777

4 M-LAWML [3times3] 221 316 399 478 549 623 693 763 844 924

5 M-LAWML[5times5] 225 328 415 514 597 696 780 875 975 1063

6 M-LAWML [7times7] 230 341 450 536 644 763 878 1001 1108 1285

7 MCSF [3times3] 249 342 482 625 768 912 1048 1185 1319 1448

8 MCSF [5times5] 271 313 361 433 498 582 659 737 820 900

9 MCSF [7times7] 309 420 441 467 500 535 577 625 673 729

10 MRM-DWT 199 287 370 435 507 561 631 694 761 830





UQI


No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 09926 09903 09865 09813 09747 09671 09579 09475

09366 09245

2 M-MF[5times5] 09807 09799 09784 09764 09739 09704 09667 09623 09570 09515

3 M-MF[7times7] 09686 09681 09673 09663 09646 09627 09601 09572 09540 09504

4

M-LAWML

[3times3] 09977 09945 09910 09870 09834 09796 09751 09705 09656 09598

5

M-

LAWML[5times5] 09975 09939 09894 09848 09803 09739 09659 09577 09506 09384

6

M-LAWML [7times7] 09974 09935 09880 09820 09764 09665 09533 09280 09288 09131

7 MCSF [3times3] 09943 09908 09815 09687 09533 09354 09149 08928 08701 08457

8 MCSF [5times5] 09924 09920 09918 09871 09837 09717 09641 09559 09462 09361

9 MCSF [7times7] 09912 09901 09896 09861 09819 09798 09776 09727 09668 09613

10 MRM-DWT 09982 09953 09873 09832 09789 09788 09744 09699 09644 09596



UQI



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 09917 09901 09873 09836 09787 09731 09661 09588 09501 09411

2 M-MF[5times5] 09886 09879 09866 09849 09827 09802 09769 09731 09689 09640

3 M-MF[7times7] 09820 09815 09806 09795 09780 09760 09739 09710 09680 09641

4 M-LAWML [3times3] 09956 09932 09904 09872 09837 09806 09752 09703 09641 09571

5 M-LAWML[5times5] 09955 09929 09908 09855 09812 09750 09689 09613 09524 09423

6 M-LAWML [7times7] 09954 09925 09884 09843 09783 09704 09607 09501 09385 09177

7 MCSF [3times3] 09960 09931 09865 09774 09661 09528 09380 09213 09035 08850

8 MCSF [5times5] 09950 09943 09922 09888 09849 09801 09744 09681 09605 09526

9 MCSF [7times7] 09903 09897 09886 09872 09853 09831 09804 09769 09732 09686

10 MRM-DWT 09976 09950 09920 09889 09852 09812 09762 09711 09653 09585





Sl

No

Images


1 M-MF [3times3] 265 308

2 M-MF[5times5] 446 425

3 M-MF[7times7] 573 563


456times10-10


456times10-10


456times10-10

7 MCSF [3times3] 124 150

8 MCSF [5times5] 275 270

9 MCSF [7times7] 438 400


456times10-10



Sl

No

Images


1 M-MF [3times3] 265 308

2 M-MF[5times5] 446 425

3 M-MF[7times7] 573 563


456times10-10


456times10-10


456times10-10

7 MCSF [3times3] 124 150

8 MCSF [5times5] 275 270

9 MCSF [7times7] 438 400


456times10-10






Filters


1 M-MF [3times3] 855 1539 4309

2 M-MF[5times5] 8966 1614 4519

3 M-MF[7times7] 945 1701 4762

4 M-LAWML [3times3] 1188 2139 5989

5 M-LAWML[5times5] 1198 2157 6039

6 M-LAWML [7times7] 1245 2242 6277

7 MCSF [3times3] 8711 1568 4390

8 MCSF [5times5] 928 1672 4681

9 MCSF [7times7] 1001 1803 5048

10 MRM-DWT 1307 2353 6588


Sl No Images

Denoising

Filters


1 M-MF [3times3] 1042 1564 4848

2 M-MF[5times5] 1104 1656 5133

3 M-MF[7times7] 1150 1726 5350

4 M-LAWML [3times3] 1624 2436 7551

5 M-LAWML[5times5] 1688 2532 7849

6 M-LAWML [7times7] 1792 2688 8332

7 MCSF [3times3] 1067 1601 4963

8 MCSF [5times5] 1148 1722 5338

9 MCSF [7times7] 1210 1816 5629

10 MRM-DWT 1984 2976 9225






Ex

ecu

tio

n T

ime

in s

econ

ds





CP

SN

R [

dB

]


CP

SN

R [

dB

] (a) (b)




(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)


(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image






(a) (b) (c)

(d) (e) (f)








(a) (b) (c)

(d) (e) (f)



(a) Original image






(a)

(b)

(c)

(d)

(e)

(f)


(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image





(a)

(b)

(c)

(d)

(e)

(f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image








(a) Original image




(c)

2

1

3

4

5

6

(a)

2

1

3

4

5

6

(d)

2

1

3

4

5

6

(b)

2

1

3

4

5

6



57 Conclusion



















































Chapter 6

Conclusion



Preview
















6












Conclusion




analyzed here


Images

































σn = 10

σn = 20

σn = 40


Mean 3270 589 09922 2978 826 09849 2696 1142 09700

ATM 3271 589 09922 2983 821 09851 2703 1134 09710

Wiener 3401 507 09943 3019 787 09861 2655 1198 09671

TV 3322 555 09931 3025 782 09864 2585 1298 09633

Lee 3347 540 09936 2974 828 09847 2677 1167 09688

Bilateral 3258 596 09921 2977 826 09849 2671 1175 09686

BayesShrink 3364 527 09938 3020 787 09863 2711 1124 09711

NeighShrink 3445 481 09949 3011 795 09861 2608 1264 09642

Ex

isti

ng

Fil

ters

LAWML 3459 474 09950 3086 729 09882 2732 1086 09721

AWWF 3336 545 09934 3056 754 09865 2688 1152 09690

CSF 3287 578 09949 3031 777 09866 2749 1076 09735

GS-DCT 3310 563 09902 3098 719 09896 2710 1124 09720

TV-DWT 3376 522 09936 3056 754 09855 2667 1180 09652 Pro

po

sed

Fil

ters

RM-DWT 3472 466 09954 3022 785 09815 2734 1083 09725





respectively)


Mean 262 720

ATM 262 1784

Wiener 186 1614

TV 211 -------

Lee 00118 1508

Bilateral 288 1347



Ex

isti

ng

F

ilte

rs

LAWML 408times10-10

809

AWWF 183 2417

CSF 122 729

GS-DCT 05737 3038

TV-DWT 2014 09375

Pro

po

sed

Fil

ters















noise conditions








Images


















space


σn = 10 σn = 20 σn = 40

Denoising

Filters

CPSNR

RMSE

UQI

CPSNR

RMSE

UQI

CPSNR

RMSE

UQI

M-MF [3times3] 3745 342 09903 3460 474 09813 3003 803 09475

M-MF [5times5] 3437 487 09799 3366 529 09764 3159 671 09623

M-MF [7times7] 3242 610 09681 3217 628 09663 3110 710 09572

M-LAWML[3times3] 3897 287 09945 3537 434 09870 3159 671 09705

M-LAWML[5times5] 3857 300 09939 3456 477 09848 3008 798 09577

Ex

isti

ng

F

ilte

rs

M-LAWML[7times7] 3824 312 09935 3385 517 09820 2793 1023 09280

MCSF [3times3] 3864 334 09908 3224 623 09687 2659 1194 08928

MCSF [5times5] 3781 327 09920 3617 391 09871 3080 735 09559

MCSF [7times7] 3458 475 09901 3398 509 09861 3204 637 09727

Pro

po

sed

Fil

ters

MRM-DWT 3987 258 09953 3508 449 09832 3149 681 09699





Denoising Filters

Method Noise

Execution Time

M-MF [3times3] 265 1564

M-MF [5times5] 446 1656

M-MF [7times7] 573 1726


-10

2436


-10 2532

Ex

isti

ng

F

ilte

rs


-10 2688

MCSF [3times3] 12495 1601

MCSF [5times5] 2754 1722

MCSF [7times7] 4386 1816

Pro

po

sed

Fil

ters

MRM-DWT 379times10

-10 2976









62 Conclusion
























conditions

























image denoising







Prentice-Hall 1989


1971













1999


Press 1996







REFERENCES















vol 3 pp 1499-1502 1996









54 no 1 pp 352-358 2005






vol 153 no 4 pp 261-269 2006



919-927 2008

REFERENCES




December 1999












2001






vol 16 no 10 pp 2565-2575 2007



406-421 2008



4281 2006



11 no 6 pp 403-416 2005

REFERENCES







46 2002




Kharagpur 2005






vol14 no 11 2005





2003



vol 24(12) pp 2061-2068 2003








REFERENCES










vol17 no 8 pp 1421-1430 2008






481-488 1995






1296 2007






2301-2311 2008



pp 364-376 2008

REFERENCES




1 no 2 pp 156-167 2007



pp 3-23 2006






29 pp 1136-1141 Dec 1981




vol 1 pp 25-28 1997








pp 1019-1021 1983


370 1984



FL pp 16-22 1987



639 1990

REFERENCES






846 1998





2002








2003





imaging pp 820-823 2004





vol 2 no 3 pp 165-168 1980





REFERENCES














1004 2005






57 no 1 pp 75-78 1995













REFERENCES




12 pp 839-842 2005



4 pp 514-523 2008






pp 117-130 2007



no 2 pp 597-630 2007







1200-1224 1995






no 9 pp 1532-1546 2000




REFERENCES





















vol 54 no 4 pp 1600-1606 2005



1056-1068 2008






2878 2006



2003 vol 1 pp I-101-I-104 2003

REFERENCES






vol 87 no 7 pp 1721-1734 2007



2205 2007



pp349-365 2007





16 no 8 pp 2080-2095 2007



16 no 2 pp 523-533 2007











2675 2006

REFERENCES




pp 1435-1447 2005








vol 15 no 11 pp 3362-3374 2006









3 pp 873-886 2008











REFERENCES




69 2008



15 no 9 pp 2575-2587 2006



1170 2006



vol 17 no 4 pp 482-492 2006



741-744 2005




vol 73 no 12 pp 1832-1835 1983





no 4 pp 550-563 2008



22 no 7 pp 837-845 2003





vol 3 pp 774-777 2000

REFERENCES







pp 479-482 2000















2008

























Punjab







Rourkela



NCNTE-2008 Mumbai


iii






Communication Engg




PO-Kalamati







PUBLICATION





CONTENTS Page No

Certificate

Preface i

Acknowledgement ii


Contents iv

Abstract

vi



xii




15 Image Metrics 19



Preview




Filters

32





28 Conclusion 79

CONTENTS


v


Preview




34 Conclusion 122


Preview


127



Filter

137


45 Conclusion 167


Preview






DWT-domain Filter

183


57 Conclusion 209

6 Conclusion 211

Preview


62 Conclusion 221


References 223



Abstract



(AWGN)










possible





noise in an image












Abstract


vii













execution time




developed














Abstract


viii


of the image




























Abstract


ix




























suppressing AWGN



Abbreviations




4 SN Speckle Noise




8 LL Low-Low

9 LH Low-High

10 HL High-Low

11 HH High-High





16 MED Median








xi



24 HVS

Human Visual System


25 MF Mean Filter








Maximum Likelihood

DEVELOPED FILTERS










Symbols








7 TE Execution Time

8 MN Method Noise

9 2

nσ Noise Variance















xiii

22 ( )hT







28 C Color Space

Chapter 1

Introduction



Preview












Literature Review

Problem Statement

Image Metrics


Conclusion

1




















































( ) ( ) ( )f x y K i x y r x y= (11)


0 ( ) 1r x ylt lt (13)











(b)

(a)

(c)

(d)

Imaging

System

Sampler and

Quantizer

Digital Storage

System

Digital

Computer

Online

Buffer

Display

Device



Object

Transmitter

Recorder








used























etc











































noise are presented
















22

1 Vtn sdotlt











form










noise












( ) ( )AWGN G











f is same or very



represented by SPN



represented as

SPN

with probability 1

( ) 0 2

1 2

f(xy) p d

f x y p d

p d

= minus

= = =

(16)



of density d RVIN


RVIN



f(xy) p df x y

x y p dη

= minus=

=

(17)












( ) ( )tSttnSN

)( η= (18)

( ) ( ) ( ) ( ) SN



digital image SN



















( ) ( ) ( )g x y f x y x yη= + (110)














































































































sense















equations















































projection









































applications















domain






15 Image Metrics













( )1 1

2ˆ ( ) ( )

M N

x y

f x y f x y

M NMSE = =

minus

times

sumsum= (111)

MSERMSE = (112)


( )1 1

ˆ ( ) ( )

M N

x y

f x y f x y

M NMAE = =

minus

times

sumsum= (113)




as






1

10

110 log

3c

c R G B

CPSNR MSE

minus

isin

= sdot

sum dB (115)













is defined by

where

( ) ( )ˆ ˆ

2 2 22

ˆ ˆ

ˆ 22

ˆ

ff f f

f ff f

f fUQI

f f

σ σ σ


++

1 1

1 1

1( )

1ˆ ˆ( )

M N

x y

M N

x y

f f x yM N

f f x yM N

= =

= =

=times

=times

sumsum

sumsum

( )

( )

22

1 1

22

ˆ

1 1

1( )

1

1 ˆ ˆ( )1

M N

f

x y

M N

fx y

f x y fM N

f x y fM N

σ

σ

= =

= =

= minustimes minus

= minustimes minus

sumsum

sumsum

( )( )ˆ

1 1

1 ˆ ˆ( ) ( )1

M N

f fx y

f x y f f x y fM N

σ= =


sumsum

(119)

(120)

(121)

(118)

(117)

(116)












fσ =f

σ




Method Noise





undesirable




1 =1

M

( )x y

x y==

times

sumsumM N

M N

N

N (122)




( )ˆ ( ) ( )f x y T f x y= (124)


Execution Time







access time etc










the filters



Processor









Preview



Literature Review

Problem Statement

Image Metrics


Conclusion


Preview




Bilateral Filter



Simulation Results

Conclusion


Preview



Simulation Results

Conclusion


Preview






Simulation Results

Conclusion


Preview






Simulation Results

Conclusion



Conclusion


17 Conclusion












Chapter 2

Study of Image

Denoising Filters



Preview
















2











Bilateral Filter



Simulation Results

Conclusion









































operation [42]













α lowest and the

2




( )

1ˆ( ) ( )xy

r

s t S


=minus

sum (21)













221 Wiener Filter

















by

( )2

2 2ˆ ( ) ( )

f

f n

f x y g g x y gσ

σ σ= + minus

+ (22)






variance 2

gσ are defined by

1( )

a b

s a t b


= sum sum (23)


and

( )22 1

( )1

a b

g

s a t b

g s t gL

σ= minus = minus




gσ with a priori



nσ from 2

gσ with the














signal processing

222 Lee Filter








where

22 2

2

2 2

1 ( )

0

n

g n

g

g n

k x y

σσ σ

σ

σ σ

minus gt

= le

(26)













sharpening [83-87]










2tg C g= nabla (27)

where t









2

( )[ ( ) ( )]

( )

t


t

C x y t g C g

part= = nabla

part


(28)











2

2( ) exp

sU s

k

= minus

(29)

or

2

1( )

1

U ss

k

=

+

(210)



as given by

[ ]1( ) ( ) ( ) ( ) ( ) ( )nn n


where 1( )ng x y



( )( )N N

C U g x y= nabla

( ) ( 1 ) ( )N






( )( )E E

C U g x y= nabla




+=





















(214)

( ) ( )( )

( ) ( )( )

( )

1

22

22

( ) ( )

( )

( ) ( ) ( )

( )

( ) ( ) ( )

( ) ( )

n n

n

SN

n n n

S E W

n

EW

n n n

E S N

n n

g x y g x y

g x yt


g x y

g x y m g x y g x y

t g x y g x yλ

+ =

nabla∆


nabla


minus ∆ minus



where

( )

( ) min mod( )

sgn sgnmin

2

m a b a b

a ba b

=

+ =

(215)

where

1 0sgn( )

1 0

xx

x

ge=

minus lt (216)


constant


2

tc

h

∆le (217)



+=



24 Bilateral Filter








functions)






122 2

1 1( ) ( )gd g x y g x y = minus (218)


2

1exp

2

g

g

g

dw

σ

= minus

(219)




distance given by

( ) ( )2 2





2

1exp

2

sd

d

dw

σ

= minus

(221)


dw


gw and dw

b g dw w w= (222)



( ) ( )ˆ ( )

( )

a b

b

s a t b

a b

b

s a t b

w s t g x s y t

f x y

w s t

=minus =minus

=minus =minus

+ +

=sum sum

sum sum (223)
















penalized



















( ) [ ]1 1

1 1

( )

ˆ ( ) ( ) ( ) ( ) ( )x y


= = sum (224)

[ ] [ ]1 1

1 1 1 1

( )

0 ( ) ( ) 1 ( ) ( ) 1x y


le le =sum (225)


p

q1

q2










[ ][ ]1 1

1 1 2

( ) ( )1( ) ( ) exp

p

d x y x yw x y x y

Z h

= minus

(226)

[ ]

1 1

1 1

2( )

( ) ( )expp

x y

d x y x yZ

hforall

= minus

sum (227)




[ ] ( )( ) ( )( )1 1

2

1 1 ( ) ( )

sim

x y x yR

























respectively [8889]








segmentation [97]


















(DWT)






Forward

WT


WT

Input

Image

Output

Image



























(a) decomposition

(b) reconstruction

f(n)

d1(n) H0 darr2

G0 darr2

H0 darr2

G0 darr2

a1(n)

d2(n)

a2(n)

(a)

f(n)

d1(n)

H1

darr2 G1

darr2

a1(n)

d2(n)

a2(n)

H1

darr2 G1

darr2

(b)



LL2 HL2

HL1

LH2 HH2

LH1 HH1


Transform


Image




















263 VisuShrink




where 2


image













264 SureShrink









( )22 2

1

1( ) 2 min

L

h n n i h i h

i

SURE T Y i Y T Y TL

σ σ=


sum (232)

where 2





265 BayesShrink





2ˆ

ˆn

B

F

Tσ

σ= (233)




ˆF



( )

1ˆ

06745

ij

n ij






Yσ can be found

empirically by

2 2

2 1

1ˆ

n

Y i j

i j

Yn

σ=

= sum (236)

In case 2 2ˆ ˆn Y

σ σge ˆF



( )maxB ijT Y=







( )2

1

arg min ( )h

h

n

OS T ij ijT

i j

T Y Fξ=

= minussum (237)



( )2

1

arg min ( )h

h

n

OT T ij ijT

i j

T Y Fζ=

= minussum (238)




as


and

( ) T

x x x Tζ = gt1 (240)


267 NeighShrink










2

21 U

ij

ij

T

S+

Γ = minus

(241)




1 12 2

1 1

j i

ij m n

n j m i

S Y+ +

= minus = minus

= sum sum (242)







counterpart ijY as


268 SmoothShrink










Step-1



d1

d2

d3

d4




Step-2



1 23 4nn d ijd Y Y n∆ = minus = (244)


th direction

Step-3


( )arg mindn

nY

d= ∆K (245)

Step-4



îjF =K (246)



269 LAWML








( )2

2 2

0( )

2 2

( )

ˆ ( ) arg max ( )

1max 0 ( )

j N k

n

j N k

k P Y j

Y jL

σσ σ

σ

geisin

isin

=

= minus

prod

sum (247)




nσ σ+ L is






by

2

2 2

ˆ ( )ˆ ( ) ( )ˆ ( ) n

kF k Y k

k

σ

σ σ= sdot

+ (248)



























performance




















Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094

5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382

6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496

7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322

8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586

9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613

10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186

11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469

12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534

13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393

14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412

15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268

16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534

17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595

18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368

19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573

20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519

21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636

22 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148

23 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621

24 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607

25 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815

26 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542

27 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497

28 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131

29 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458

30 LAWML [5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602

31 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638







Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102

5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419

6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562

7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312

8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632

9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687

10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185

11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460

12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526

13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361

14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376

15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271

16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547

17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609

18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348

19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592

20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552

21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651

22 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137

23 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454

24 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505

25 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835

26 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564

27 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451

28 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728

29 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447

30 LAWML [5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560

31 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575







Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102

5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343

6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420

7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162

11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368

12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407

13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340

14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378

15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258

16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451

17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469

18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325

19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451

20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400

21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668

22 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026

23 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462

24 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409

25 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921

26 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724

27 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411

28 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762

29 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361

30 LAWML [5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443

31 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443







Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998

5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121

6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214

7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3657 3167 2865 2921 2750 2606 2489 2390 2297 2213

11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255

12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293

13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226

14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231

15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166

16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277

17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319

18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199

19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229

20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231

21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667

22 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989

23 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286

24 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271

25 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044

26 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708

27 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326

28 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739

29 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295

30 LAWML [5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371

31 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378







Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287

5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642

6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438

7 ATM [3times3] 511 589 696 821 9639 1106 1267 1428 1593 1759

8 ATM [5times5] 828 844 869 910 9562 1004 1071 1134 1208 1298

9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257

10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057

11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484

12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377

13 AD 470 688 772 874 989 1109 1236 1369 1491 1621

14 TV 428 555 663 782 902 1032 1167 1298 1445 1586

15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871

16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377

17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285

18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667

19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318

20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402

21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876

22 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150

23 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247

24 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267

25 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155

26 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320

27 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438

28 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193

29 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505

30 LAWML [5times5] 299 474 621 747 863 955 1046 1127 1198 1275

31 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223







Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267

5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573

6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333

7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779

8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231

9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155

10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060

11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499

12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389

13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680

14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652

15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864

16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356

17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264

18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706

19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287

20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349

21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809

22 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177

23 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512

24 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425

25 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083

26 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212

27 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517

28 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487

29 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524

30 LAWML [5times5] 293 472 607 732 852 966 1070 1166 1263 1338

31 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315







Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267

5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716

6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570

7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114

11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667

12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593

13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723

14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649

15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894

16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514

17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484

18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751

19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514

20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606

21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735

22 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474

23 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498

24 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592

25 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792

26 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503

27 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588

28 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353

29 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682

30 LAWML [5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531

31 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531







Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555

5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216

6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991

7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994

11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899

12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818

13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963

14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953

15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106

16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851

17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764

18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027

19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958

20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953

21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740

22 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582

23 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834

24 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866

25 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424

26 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568

27 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752

28 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443

29 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815

30 LAWML [5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663

31 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650







Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951

5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419

6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539

7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340

8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621

9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637

10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098

11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503

12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557

13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417

14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458

15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239

16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566

17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613

18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385

19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598

20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557

21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451

22 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178

23 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636

24 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621

25 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021

26 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953

27 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530

28 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661

29 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484

30 LAWML [5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622

31 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649







Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163

5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578

6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687

7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460

8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732

9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760

10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261

11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588

12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638

13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488

14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525

15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392

16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665

17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702

18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476

19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689

20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662

21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908

22 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289

23 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568

24 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617

25 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400

26 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484

27 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579

28 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022

29 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575

30 LAWML [5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675

31 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689







Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345

5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610

6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669

7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569

8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732

9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734

10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385

11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602

12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628

13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578

14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636

15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501

16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670

17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680

18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565

19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662

20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620

21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339

22 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328

23 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673

24 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627

25 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926

26 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443

27 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638

28 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541

29 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592

30 LAWML [5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656

31 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658







Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024

5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227

6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360

7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314

8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398

9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411

10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201

11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395

12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434

13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358

14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396

15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284

16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425

17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469

18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316

19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329

20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312

21 NL-Means 09957 09943 098 65

09716 09516 09285 09010 08737 08423 08127

22 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138

23 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424

24 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401

25 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005

26 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136

27 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491

28 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233

29 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433

30 LAWML [5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517

31 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521




Sl No

Denoising Images

Filters


1 Mean [3times3] 262 290 410 668

2 Mean [5times5] 443 408 642 946

3 Mean [7times7] 573 520 793 1035

4 Median [3times3] 132 153 252 438

5 Median [5times5] 270 239 443 693

6 Median [7times7] 395 311 499 744

7 ATM [3times3] 262 290 410 668

8 ATM [5times5] 443 408 642 946

9 ATM [7times7] 573 520 793 1035

10 Wiener [3times3] 186 204 318 387

11 Wiener [5times5] 367 351 540 637

12 Wiener [7times7] 464 387 576 668

13 AD 204 237 295 497

14 TV 211 234 334 573

15 Lee [3times3] 00118 109 00336 00583

16 Lee [5times5] 00530 114 01109 02057

17 Lee [7times7] 01315 201 01853 110

18 Bilateral [3times3] 288 308 423 680

19 Bilateral [5times5] 497 433 663 966

20 Bilateral [7times7] 601 545 826 1104

21 NL-Means 117 137 186 211

22 VisuShrink 318 423 471 637

23 SureShrink 517 673 770 1007

24 BayesShrink 00232 00273 00194 00190

25 OracleShrink 00285 00267 00242 00238

26 OracleThresh 00285 00267 00242 00238


466times10-10

334times10-10

497times10-10

28 SmoothShrink 660 752 645 790


466times10-10

334times10-10

497times10-10


466times10-10

334times10-10

497times10-10


466times10-10

334times10-10

497times10-10






1 Mean [3times3] 318 701 1713

2 Mean [5times5] 323 712 1749

3 Mean [7times7] 327 720 1776

4 Median [3times3] 402 742 2445

5 Median [5times5] 409 747 2469

6 Median [7times7] 415 812 2490

7 ATM [3times3] 732 1677 3018

8 ATM [5times5] 809 1723 3056

9 ATM [7times7] 813 1784 3084

10 Wiener [3times3] 787 1559 2806

11 Wiener [5times5] 807 1598 2876

12 Wiener [7times7] 843 1670 3006

13 AD ------ ------- ------

14 TV ------ ------- ------

15 Lee [3times3] 874 1426 3509

16 Lee [5times5] 887 1446 3545

17 Lee [7times7] 968 1579 3779

18 Bilateral [3times3] 536 1100 3265

19 Bilateral [5times5] 583 1353 3520

20 Bilateral [7times7] 588 1359 3639

21 NL-Means 44667 99620 221838

22 VisuShrink 0540 119 392







29 LAWML [3times3] 367 809 2669

30 LAWML [5times5] 370 815 2689

31 LAWML [7times7] 374 823 2715





(a) Lena


(d) Barbara

σn

PS

NR

(d

B)


PS

NR

(d

B)


SN

R (

dB

)


PS

NR

(d

B)

(a) (b)

(c) (d)

σn

σn σn




(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

RM

SE


RM

SE


(a) (b)

RM

SE


RM

SE

(c) (d)


σn σn

σn σn





(a) Lena (b) Pepper


UQ


UQ

I


QI


UQ

I


(a) (b)

(c) (d)

σn σn

σn σn



(b)

(f)

(j)

(n)

(a)

(e)

(i)

(m)

(q)

(r)

(c)

(d)

(g)

(h)

(k)

(l)

(o)

(p)

(s)









(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)


AWGN σn = 15








(a) (b) (c) (d) (e) (f) (g)

(h) (i) (j) (k) (l)

(m)

(l) (m) (n)

(o) (p) (q) (r) (s)









(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m) (n) (o) (p)

(q) (r) (s)








(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)









(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)


AWGN σn = 40








(a)

(b) (c)

(d)

(f) (g)

(h)

(i)

(e)

(j) (k) (l) (m) (n)

(o) (p) (q) (r) (s)









(d)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k)

(l)

(m)

(n)

(o)

(p)

(q)

(r)

(s)









28 Conclusion
























domain filters












research work

Chapter 3

Development of


Image Filters



Preview















3












Simulation Results

Conclusion













power








much


The AWWF Theory

The AWWF Algorithm

Window Selection



311 The AWWF Theory







































Step-1



Step-2




Step-3







medium



Step-4


shown in Fig 34


sub-section






Sobel operator


Blurred Image

Edge Image

p

q






q

p

Wiener

Filtering

p1 OR q1









homogenous regions





pixels




used is 5times5















Simulation Results

Conclusion


















( ) ( )2 2



max

1 sd

dw

d= minus (32)









( )1

2 2 2

1 1| ( ) |gd g x y g x y = minus (33)


by

2

2exp

2

g

g

g

dw

σ

minus=

(34)





gw as




( )( ) ( )

ˆ

( )

a b

s a t b

a b

s a t b

w s t g x s y t

f x y

w s t

= minus = minus

= minus = minus

+ +

=

sum sum

sum sum (36)










(a) (b)








Experiment 1








Experiment 2








be taken as 1











(a) Lena image

(b) Goldhill image

0 1 2 3 4 515

20

25

30

σ = 30

σ = 40

σ = 50n

n

n

gσ

PS

NR

(d

B)

(a)

0 1 2 3 4 516

18

20

22

24

26

28

σ = 30

σ = 40

σ = 50

n

n

n

PS

NR

(d

B)

gσ

(b)



0 1 2 3 4 507

075

08

085

09

095

1

σ = 30

σ = 40

σ = 50

n

n

n

UQ

I

gσ

(a)

gσ

UQ

I

0 1 2 3 4 508

085

09

095

1

σ = 30

σ = 40

σ = 50

n

n

n

(b)


(a) Lena image

(b) Goldhill image































NL-Means filter








analysis











Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 Median [3times3] 3498 3216 2985 2794 2636 2498 2377 2277 2175 2094

5 Median [5times5] 3170 3074 2978 2875 2781 2684 2608 2526 2453 2382

6 Median [7times7] 2960 2917 2865 2813 2758 2699 2644 2601 2545 2496

7 ATM [3times3] 3396 3271 3126 2983 2844 2724 2607 2503 2408 2322

8 ATM [5times5] 2977 2959 2932 2893 2850 2807 2752 2703 2647 2586

9 ATM [7times7] 2788 2759 2752 2741 2728 2713 2689 2666 2641 2613

10 Wiener [3times3] 3788 3401 3137 2915 2738 259 2462 2356 2267 2186

11 Wiener [5times5] 3657 3294 3147 3019 2900 2796 2699 2613 2543 2469

12 Wiener [7times7] 3578 3154 3046 2944 2857 2778 2715 2655 2593 2534

13 AD 3468 3137 3037 2927 2821 2722 2628 2540 2465 2393

14 TV 3549 3322 3170 3025 2901 2785 2677 2585 2492 2412

15 Lee [3times3] 3787 3345 3077 2878 2734 2604 2497 2411 2331 2268

16 Lee [5times5] 3755 3347 3129 2974 2866 2770 2707 2641 2578 2534

17 Lee [7times7] 3712 3304 3091 2952 2857 2784 2728 2677 2630 2595

18 Bilateral [3times3] 3370 3258 3120 2977 2848 2727 2621 2531 2447 2368

19 Bilateral [5times5] 3276 2914 2888 2855 2813 2772 2727 2671 2622 2573

20 Bilateral [7times7] 3109 2662 2655 2643 2630 2613 2589 2573 2547 2519

21 NL-Means 3787 3443 2943 2553 2291 2097 1947 1828 1729 1636

22 AWWF 3488 3336 3178 3056 2929 2813 2741 2688 2601 2585

23 CSF [3times3] 3719 3287 2971 2735 2551 2397 2269 2155 2060 1970

24 CSF [5times5] 3371 3280 3158 3031 2911 2796 2688 2598 2507 2432

25 CSF [7times7] 3015 2987 2962 2932 2896 2847 2801 2749 2699 2646






Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 Median [3times3] 3555 3257 3010 2813 2648 2510 2388 2279 2184 2102

5 Median [5times5] 3423 3276 3130 2996 2872 2764 2665 2568 2493 2419

6 Median [7times7] 3319 3162 3075 2987 2900 2823 2748 2678 2620 2562

7 ATM [3times3] 3233 3174 3058 2932 2810 2694 2582 2483 2398 2312

8 ATM [5times5] 3112 3067 3038 2993 2940 2885 2818 2757 2688 2632

9 ATM [7times7] 2901 2876 2869 2858 2841 2819 2782 2756 2724 2687

10 Wiener [3times3] 3811 3445 3177 2944 2756 2599 2467 2356 2267 2185

11 Wiener [5times5] 3767 3382 3216 3074 2941 2818 2714 2619 2534 2460

12 Wiener [7times7] 3598 3252 3125 3008 2906 2815 2736 2658 2590 2526

13 AD 3348 3068 2979 2881 2782 2685 2597 2511 2436 2361

14 TV 3358 3121 3013 2908 2803 2710 2613 2531 2445 2376

15 Lee [3times3] 3789 3369 3105 2903 2740 2608 2502 2412 2334 2271

16 Lee [5times5] 3777 3391 3177 3028 2902 2805 2727 2656 2594 2547

17 Lee [7times7] 3728 3345 3138 3003 2903 2821 2757 2702 2651 2609

18 Bilateral [3times3] 3176 3107 3006 2897 2785 2683 2584 2497 2420 2348

19 Bilateral [5times5] 3088 2981 2950 2910 2863 2811 2756 2697 2641 2592

20 Bilateral [7times7] 2996 2736 2724 2712 2692 2672 2640 2616 2590 2552

21 NL-Means 3796 3462 2958 2568 2302 2114 1963 1843 1736 1651

22 AWWF 3516 3396 3258 3101 3011 2891 2821 2743 2710 2638

23 CSF [3times3] 3680 3275 2968 2739 2552 2400 2271 2159 2063 1973

24 CSF [5times5] 3499 3381 3235 3084 2949 2819 2705 2607 2514 2434

25 CSF [7times7] 3217 3126 3091 3044 2991 2925 2861 2792 2730 2696






Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 Median [3times3] 3376 3044 2878 2722 2590 2467 2361 2265 2177 2102

5 Median [5times5] 3077 2860 2796 2732 2663 2595 2532 2466 2401 2343

6 Median [7times7] 2934 2729 2695 2662 2619 2578 2543 2499 2467 2420

7 ATM [3times3] 3188 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2912 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2702 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3663 3235 3041 2859 2696 2562 2441 2332 2247 2162

11 Wiener [5times5] 3488 3043 2956 2867 2776 2688 2600 2517 2445 2368

12 Wiener [7times7] 3299 2887 2831 2767 2708 2651 2589 2526 2471 2407

13 AD 3307 2988 2913 2827 2738 2650 2565 2483 2406 2340

14 TV 3311 3130 3019 2913 2809 2716 2627 2541 2462 2378

15 Lee [3times3] 3660 3238 3003 2831 2696 2586 2485 2398 2321 2258

16 Lee [5times5] 3629 3200 2995 2859 2765 2687 2612 2549 2493 2451

17 Lee [7times7] 3598 3156 2948 2822 2732 2662 2605 2559 2515 2469

18 Bilateral [3times3] 3144 3073 2977 2867 2763 2663 2567 2483 2399 2325

19 Bilateral [5times5] 3017 2772 2749 2720 2683 2639 2597 2550 2498 2451

20 Bilateral [7times7] 2913 2575 2564 2550 2532 2512 2485 2462 2427 2400

21 NL-Means 3659 3293 2892 2561 2310 2126 1980 1860 1759 1668

22 AWWF 3434 3234 3087 2918 2815 2720 2638 2539 2510 2446

23 CSF [3times3] 3615 3250 2960 2738 2559 2411 2282 2171 2079 1992

24 CSF [5times5] 3189 3127 3041 2940 2838 2741 2641 2552 2464 2389

25 CSF [7times7] 2914 2854 2836 2809 2776 2730 2692 2644 2590 2534






Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 Median [3times3] 2766 2585 2509 2431 2352 2276 2202 2133 2062 1998

5 Median [5times5] 2476 2326 2314 2296 2277 2249 2219 2190 2157 2121

6 Median [7times7] 2411 2354 2344 2331 2317 2298 2275 2258 2235 2214

7 ATM [3times3] 3199 3081 2980 2869 2760 2655 2556 2462 2377 2298

8 ATM [5times5] 2906 2803 2782 2757 2721 2685 2648 2605 2557 2515

9 ATM [7times7] 2734 2645 2638 2629 2616 2603 2586 2568 2546 2521

10 Wiener [3times3] 3657 3167 2865 2821 2750 2606 2489 2390 2297 2213

11 Wiener [5times5] 3478 2831 2743 2653 2570 2499 2432 2366 2309 2255

12 Wiener [7times7] 3319 2738 2673 2604 2545 2489 2434 2384 2337 2293

13 AD 2859 2606 2575 2535 2488 2437 2386 2330 2278 2226

14 TV 2749 2647 2599 2548 2494 2442 2388 2333 2281 2231

15 Lee [3times3] 3654 3159 2890 2705 2568 2462 2369 2291 2223 2166

16 Lee [5times5] 3621 3156 2896 2732 2613 2517 2436 2378 2326 2277

17 Lee [7times7] 3609 3130 2880 2722 2610 2528 2464 2406 2358 2319

18 Bilateral [3times3] 2622 2601 2567 2524 2474 2420 2365 2308 2253 2199

19 Bilateral [5times5] 2603 2369 2361 2351 2337 2320 2300 2279 2257 2229

20 Bilateral [7times7] 2558 2317 2314 2308 2301 2293 2280 2267 2252 2231

21 NL-Means 3688 3259 2868 2540 2301 2124 1974 1858 1752 1667

22 AWWF 3319 3169 3028 2954 2798 2671 2585 2475 2360 2273

23 CSF [3times3] 3188 3013 2922 2851 2698 2666 2551 2445 2249 2169

24 CSF [5times5] 2865 2820 2792 2756 2714 2671 2618 2557 2504 2455

25 CSF [7times7] 2796 2744 2739 2729 2716 2701 2683 2662 2633 2607






Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 Median [3times3] 454 627 818 1020 1224 1435 1649 1851 2083 2287

5 Median [5times5] 663 7395 826 930 1035 1157 1264 1389 1512 1642

6 Median [7times7] 844 884 940 999 1063 1139 1213 1275 1359 1438

7 ATM [3times3] 511 589 696 821 963 1106 1267 1428 1593 1759

8 ATM [5times5] 828 844 869 910 956 1004 1071 1134 1208 1298

9 ATM [7times7] 1029 1063 1071 1086 1101 1122 1152 1183 1218 1257

10 Wiener [3times3] 325 507 688 887 1088 1290 1496 1690 1874 2057

11 Wiener [5times5] 378 573 678 787 902 1017 1139 1257 1364 1484

12 Wiener [7times7] 414 673 762 859 948 1040 1119 1198 1287 1377

13 AD 470 688 772 874 989 1109 1236 1369 1491 1621

14 TV 428 555 663 782 902 1032 1167 1298 1445 1586

15 Lee [3times3] 325 540 736 925 1094 1269 1438 1588 1741 1871

16 Lee [5times5] 338 540 693 828 938 1050 1129 1218 1310 1377

17 Lee [7times7] 355 566 724 851 948 1032 1101 1167 1234 1285

18 Bilateral [3times3] 526 596 701 826 958 1104 1247 1382 1522 1667

19 Bilateral [5times5] 586 889 915 951 999 1048 1104 1175 1244 1318

20 Bilateral [7times7] 711 1188 1198 1213 1234 1257 1292 1300 1356 1402

21 NL-Means 325 481 859 1349 1823 2279 2708 3108 3483 3876

22 AWWF 459 545 655 754 874 999 1086 1152 1275 1295

23 CSF [3times3] 352 578 831 1094 1351 1614 1869 2131 2379 2639

24 CSF [5times5] 526 583 670 777 892 1017 1152 1280 1420 1550

25 CSF [7times7] 792 818 841 869 907 961 1012 1076 1139 1211






Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 Median [3times3] 425 599 795 999 1208 1415 1629 1848 2063 2267

5 Median [5times5] 495 586 693 808 933 1055 1185 1326 14433 1573

6 Median [7times7] 558 668 739 818 902 986 1076 1167 1247 1333

7 ATM [3times3] 616 657 752 869 1002 1145 1303 1461 16116 1779

8 ATM [5times5] 708 744 770 810 861 918 991 1065 1152 1231

9 ATM [7times7] 903 928 935 948 966 991 1035 1065 1106 1155

10 Wiener [3times3] 316 481 655 859 1065 1275 1489 1690 18743 2060

11 Wiener [5times5] 333 517 627 739 861 991 1119 1249 1377 1499

12 Wiener [7times7] 405 601 696 798 897 997 1091 1193 12903 1389

13 AD 540 744 823 923 1035 1157 1280 1415 15428 1680

14 TV 534 701 793 895 1009 1124 1257 1382 15275 1652

15 Lee [3times3] 325 525 714 900 1086 1264 1430 1586 1734 1864

16 Lee [5times5] 329 512 655 780 902 1007 1104 1195 12852 1356

17 Lee [7times7] 348 540 685 803 900 989 1065 1134 12036 1264

18 Bilateral [3times3] 658 711 800 907 1032 1160 1300 1438 15708 1706

19 Bilateral [5times5] 728 823 851 892 943 1002 1065 1142 12189 1287

20 Bilateral [7times7] 810 1091 1106 1122 1149 1175 1220 1254 12903 1349

21 NL-Means 322 471 846 1326 1800 2236 2659 3054 34553 3809

22 AWWF 445 510 596 716 795 912 989 1083 1124 1221

23 CSF [3times3] 368 586 836 1088 1349 1606 1864 2121 2371 2629

24 CSF [5times5] 453 517 614 731 854 991 1132 1267 1410 1545

25 CSF [7times7] 628 696 724 765 813 877 9460 1022 1099 1142







Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 1740

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 Median [3times3] 523 765 925 1109 1290 1489 1680 1879 2078 2267

5 Median [5times5] 737 946 1017 1096 1188 1285 1382 1489 1606 1716

6 Median [7times7] 870 1101 1145 1188 1249 1310 1364 1433 1489 1570

7 ATM [3times3] 649 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 892 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1136 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 375 614 767 946 1142 1333 1532 1739 1917 2114

11 Wiener [5times5] 459 765 846 938 1042 1152 1277 1405 1527 1667

12 Wiener [7times7] 571 918 979 1053 1127 1203 1292 1389 1481 1593

13 AD 566 816 889 981 1088 1206 1328 1461 1596 1723

14 TV 563 693 787 889 1004 1116 1236 1366 1496 1649

15 Lee [3times3] 377 612 803 979 1142 1298 1458 1611 1762 1894

16 Lee [5times5] 390 640 810 946 1055 1155 1259 1354 1443 1514

17 Lee [7times7] 405 673 854 989 1096 1188 1269 1338 1407 1484

18 Bilateral [3times3] 683 739 826 938 1058 1188 1326 1461 1609 1751

19 Bilateral [5times5] 790 1048 1076 1111 1160 1221 1280 1351 1435 1514

20 Bilateral [7times7] 891 1313 1331 1351 1382 1414 1458 1496 1558 1606

21 NL-Means 377 573 892 1336 1782 2203 2601 2993 3363 3735

22 AWWF 489 614 729 884 997 1111 1221 1369 1415 1524

23 CSF [3times3] 397 604 844 1088 1338 1588 1841 2093 2328 2573

24 CSF [5times5] 648 696 767 861 971 1086 1218 1349 1494 1629

25 CSF [7times7] 890 953 971 1004 1042 1099 1147 1213 1290 1377







Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 Median [3times3] 1055 1298 1417 1550 1698 1853 2019 2187 2374 2555

5 Median [5times5] 1474 1751 1774 1813 1851 1912 1981 2047 2126 2216

6 Median [7times7] 1588 1695 1713 1741 1769 1807 1856 1894 1943 1991

7 ATM [3times3] 641 734 823 935 1060 1198 1343 1496 1649 1807

8 ATM [5times5] 898 1009 1035 1065 1111 1157 1208 1269 1341 1407

9 ATM [7times7] 1095 1211 1221 1234 1254 1272 1298 1326 1359 1397

10 Wiener [3times3] 378 527 940 882 1073 1267 1450 1626 1810 1994

11 Wiener [5times5] 465 979 1083 1201 1320 1433 1550 1672 1785 1899

12 Wiener [7times7] 558 1088 1173 1269 1359 1450 1545 1637 1728 1818

13 AD 948 1267 1313 1377 1453 1540 1634 1741 1851 1963

14 TV 1076 1208 1277 1356 1443 1532 1629 1736 1843 1953

15 Lee [3times3] 379 670 912 1132 1326 1496 1665 1823 1971 2106

16 Lee [5times5] 394 673 907 1096 1257 1405 1542 1649 1751 1851

17 Lee [7times7] 399 693 925 1109 1262 1387 1494 1596 1688 1764

18 Bilateral [3times3] 1246 1275 1326 1394 1476 1570 1672 1787 1904 2027

19 Bilateral [5times5] 1273 1665 1680 1700 1728 1762 1802 1848 1894 1958

20 Bilateral [7times7] 1341 1769 1774 1787 1802 1818 1846 1874 1907 1953

21 NL-Means 365 596 938 1369 1802 2208 2626 3001 3391 3740

22 AWWF 558 663 780 849 1017 1175 1298 1473 1683 1861

23 CSF [3times3] 649 793 879 956 1139 1183 1351 1527 1912 2098

24 CSF [5times5] 941 991 1022 1065 1119 1175 1249 1341 1425 1509

25 CSF [7times7] 1019 1081 1088 1101 1116 1137 1160 1188 1229 1267







Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 Median [3times3] 09955 09913 09853 09773 09676 09559 09425 09286 09117 08951

5 Median [5times5] 09903 09878 09848 09808 09762 09703 09648 09577 09503 09419

6 Median [7times7] 09841 09824 09801 09775 09745 09709 09669 09636 09585 09539

7 ATM [3times3] 09939 09922 09892 09851 09795 09731 09649 09558 09454 09340

8 ATM [5times5] 09878 09838 09828 09812 09792 09772 09740 09710 09671 09621

9 ATM [7times7] 09812 09739 09734 09728 09720 09710 09694 09678 09659 09637

10 Wiener [3times3] 09977 09943 09896 09827 09742 0964 09517 09386 09249 09098

11 Wiener [5times5] 09958 09926 09897 09861 09818 09768 09709 09646 09581 09503

12 Wiener [7times7] 09907 09897 09868 09833 09797 09755 09715 09671 09617 09557

13 AD 09951 09895 09867 09830 09784 09728 09663 09586 09506 09417

14 TV 09959 09931 09902 09864 09820 09765 09701 09633 09547 09458

15 Lee [3times3] 09977 09936 09881 09813 09740 09650 09554 09456 09346 09239

16 Lee [5times5] 09955 09936 09893 09847 09805 09755 09715 09666 09610 09566

17 Lee [7times7] 09936 09929 09884 09839 09799 09761 09725 09688 09648 09613

18 Bilateral [3times3] 09939 09921 09891 09849 09797 09731 09658 09578 09487 09385

19 Bilateral [5times5] 09916 09828 09816 09802 09781 09757 09728 09686 09646 09598

20 Bilateral [7times7] 09879 09706 09702 09693 09682 09664 09642 09623 09592 09557

21 NL-Means 09977 09947 09840 09616 09318 08971 08601 08230 07861 07451

22 AWWF 09953 09934 09898 09865 09820 09765 09721 09690 09620 09568

23 CSF [3times3] 09973 09949 09849 09742 09611 09452 09272 09067 08854 08614

24 CSF [5times5] 09938 09924 09900 09866 09822 09771 09710 09640 09555 09469

25 CSF [7times7] 09912 09848 09839 09828 09813 09789 09765 09735 09700 09659







Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 Median [3times3] 09969 09938 09890 09828 09750 09659 09552 09431 09298 09163

5 Median [5times5] 09957 09940 09916 09885 09848 09805 09756 09696 09641 09578

6 Median [7times7] 09938 09921 09903 09882 09855 09827 09795 09759 09725 09687

7 ATM [3times3] 09929 09924 09901 09868 09824 09772 09706 09631 09553 09460

8 ATM [5times5] 09911 09901 09894 09883 09868 09850 09825 09798 09764 09732

9 ATM [7times7] 09886 09844 09842 09838 09832 09823 09807 09796 09780 09760

10 Wiener [3times3] 09978 09959 09925 09871 09802 09715 09614 09503 09389 09261

11 Wiener [5times5] 09955 09953 09930 09903 09868 09824 09775 09718 09655 09588

12 Wiener [7times7] 09941 09935 09913 09886 09855 09820 09782 09738 09692 09638

13 AD 09949 09901 09879 09848 09809 09761 09707 09641 09571 09488

14 TV 09950 09913 09889 09859 09820 09778 09722 09665 09594 09525

15 Lee [3times3] 09982 09952 09912 09859 09795 09722 09645 09563 09475 09392

16 Lee [5times5] 09960 09954 09925 09893 09857 09820 09784 09742 09701 09665

17 Lee [7times7] 09954 09949 09917 09886 09856 09825 09796 09766 09734 09702

18 Bilateral [3times3] 09925 09912 09888 09855 09813 09762 09700 09632 09559 09476

19 Bilateral [5times5] 09913 09885 09876 09862 09843 09821 09795 09761 09726 09689

20 Bilateral [7times7] 09879 09807 09799 09791 09778 09763 09742 09721 09697 09662

21 NL-Means 09978 09961 09877 09702 09462 09191 08885 08572 08224 07908

22 AWWF 09974 09960 09941 09912 09888 09852 09791 09745 09700 09656

23 CSF [3times3] 09976 09962 09879 09796 09689 09561 09412 09246 09068 08862

24 CSF [5times5] 09964 09952 09949 09915 09871 09828 09778 09716 09652 09571

25 CSF [7times7] 09925 09913 09906 09895 09889 09861 09838 09810 09785 09766







Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 Median [3times3] 09945 09922 09886 09838 09781 09710 09631 09542 09444 09345

5 Median [5times5] 09916 09880 09861 09839 09812 09780 09746 09705 09658 09610

6 Median [7times7] 09878 09838 09824 09810 09790 09769 09749 09723 09702 09669

7 ATM [3times3] 09946 09928 09909 09883 09850 09809 09760 09703 09639 09569

8 ATM [5times5] 09923 09862 09855 09847 09833 09819 09802 09782 09757 09732

9 ATM [7times7] 09883 09800 09797 09792 09786 09780 09771 09761 09749 09734

10 Wiener [3times3] 09971 09950 09921 09880 09824 09760 09682 09589 09497 09385

11 Wiener [5times5] 09942 09921 09903 09880 09852 09816 09773 09724 09670 09602

12 Wiener [7times7] 09917 09886 09870 09848 09824 09798 09764 09725 09684 09628

13 AD 09957 09910 09893 09869 09838 09801 09755 09702 09641 09578

14 TV 09958 09936 09917 09894 09865 09833 09795 09750 09700 09636

15 Lee [3times3] 09981 09950 09914 09872 09824 09773 09711 09645 09572 09501

16 Lee [5times5] 09956 09946 09912 09879 09848 09817 09780 09743 09704 09670

17 Lee [7times7] 09947 09940 09902 09868 09836 09805 09775 09747 09716 09680

18 Bilateral [3times3] 09938 09927 09908 09881 09848 09807 09757 09703 09636 09565

19 Bilateral [5times5] 09916 09853 09844 09832 09815 09793 09770 09740 09703 09662

20 Bilateral [7times7] 09810 08936 09764 09754 09742 09725 09704 09683 09649 09620

21 NL-Means 09967 09956 09891 09767 09590 09381 09147 08896 08631 08339

22 AWWF 09961 09950 09938 09895 09872 09840 09786 09750 09733 09713

23 CSF [3times3] 09979 09961 09940 09843 09762 09666 09550 09418 09282 09126

24 CSF [5times5] 09944 09935 09920 09899 09873 09847 09797 09749 09693 09630

25 CSF [7times7] 09886 09877 09871 09862 09850 09832 09815 09792 09762 09751







Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 Median [3times3] 09818 09733 09683 09622 09549 09466 09371 09268 09145 09024

5 Median [5times5] 09807 09508 09495 09475 09450 09416 09374 09335 09286 09227

6 Median [7times7] 09766 09536 09524 09508 09491 09469 09440 09420 09390 09360

7 ATM [3times3] 09786 09740 09717 09686 09647 09600 09538 09474 09401 09314

8 ATM [5times5] 09769 09555 09548 09538 09524 09504 09481 09458 09430 09398

9 ATM [7times7] 09716 09523 09522 09516 09512 09501 09490 09476 09432 09411

10 Wiener [3times3] 09933 09904 09861 09803 09734 09651 09552 09447 09331 09201

11 Wiener [5times5] 09919 09847 09812 09767 09718 09665 09607 09538 09470 09395

12 Wiener [7times7] 09898 09808 09776 09737 09696 09652 09603 09550 09495 09434

13 AD 09857 09741 09722 09694 09659 09614 09564 09503 09436 09358

14 TV 09816 09766 09738 09707 09668 09626 09576 09520 09461 09396

15 Lee [3times3] 09978 09930 09870 09800 09724 09646 09559 09470 09377 09284

16 Lee [5times5] 09949 09929 09871 09810 09748 09682 09613 09554 09490 09425

17 Lee [7times7] 09932 09925 09865 09805 09744 09688 09634 09576 09519 09469

18 Bilateral [3times3] 09751 09738 09716 09686 09646 09597 09542 09475 09400 09316

19 Bilateral [5times5] 09734 09543 09534 09520 09501 09478 09447 09414 09378 09329

20 Bilateral [7times7] 09688 09483 09477 09466 09453 09436 09414 09386 09357 09312

21 NL-Means 09957 09943 09865 09716 09516 09285 09010 08737 08423 08127

22 AWWF 09943 09918 09893 09836 09748 09690 09614 09568 09492 09453

23 CSF [3times3] 09964 09945 09895 09773 09721 09666 09536 09485 09313 09261

24 CSF [5times5] 09913 09896 09866 09838 09793 09779 09692 09576 09517 09458

25 CSF [7times7] 09834 09818 09799 09783 09779 09752 09717 09659 09600 09534




Sl No

Denoising Images

Filters


1 Mean [3times3] 262 290 410 668

2 Mean [5times5] 443 408 642 946

3 Mean [7times7] 573 520 793 1035

4 Median [3times3] 132 153 252 438

5 Median [5times5] 270 239 443 693

6 Median [7times7] 395 311 499 744

7 ATM [3times3] 262 290 410 668

8 ATM [5times5] 443 408 642 946

9 ATM [7times7] 573 520 793 1035

10 Wiener [3times3] 186 204 318 387

11 Wiener [5times5] 367 351 540 637

12 Wiener [7times7] 464 387 576 668

13 AD 204 237 295 497

14 TV 211 234 334 573

15 Lee [3times3] 00118 109 00336 00583

16 Lee [5times5] 00530 114 01109 02057

17 Lee [7times7] 01315 201 01853 110

18 Bilateral [3times3] 288 308 423 680

19 Bilateral [5times5] 497 433 663 966

20 Bilateral [7times7] 601 545 826 1104

21 NL-Means 117 137 186 211

22 AWWF 183 206 321 387

23 CSF [3times3] 122 142 183 318

24 CSF [5times5] 272 257 402 675

25 CSF [7times7] 4437 390 619 907







1 Mean [3times3] 318 701 1713

2 Mean [5times5] 323 712 1749

3 Mean [7times7] 327 720 1776

4 Median [3times3] 402 742 2445

5 Median [5times5] 409 747 2469

6 Median [7times7] 415 812 2490

7 ATM [3times3] 732 1677 3018

8 ATM [5times5] 809 1723 3056

9 ATM [7times7] 813 1784 3084

10 Wiener [3times3] 787 1559 2806

11 Wiener [5times5] 807 1598 2876

12 Wiener [7times7] 843 1670 3006

13 AD ------ ------- ------

14 TV ------ ------- ------

15 Lee [3times3] 874 1426 3509

16 Lee [5times5] 887 1446 3545

17 Lee [7times7] 968 1579 3779

18 Bilateral [3times3] 536 1100 3265

19 Bilateral [5times5] 583 1353 3520

20 Bilateral [7times7] 588 1359 3639

21 NL-Means 44667 99620 221838

22 AWWF 1181 2417 4546

23 CSF [3times3] 338 706 1866

24 CSF [5times5] 343 717 1898

25 CSF [7times7] 352 729 1930





(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

PS

NR

(d

B)


PS

NR

(d

B)

(a) (b)

σn σn


PS

NR

(d

B)


SN

R (

dB

)

(c) (d)

σn σn





(a) Lena (b) Pepper


RM

SE


RM

SE


(a) (b)

σn σn


RM

SE


RM

SE

(c) (d)

σn σn




(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara


UQ

I


UQ

I

(a) (b)

σn σn

UQ

I

UQ

I


(c) (d)

σn σn



(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m)


with AWGN σn = 15







(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k) (l) (m)


AWGN σn = 15







(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(m)








(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

(j) (k) (l)

(m)


AWGN σn = 40







(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)

(k)

(l) (m)













(d)

(a) (b) (c) (d)

(e) (f) (g) (h)

(i) (j) (k) (l)

(l)

(m)



34 Conclusion







condition




















image Pepper















others







Chapter 4

Development of

Transform-Domain

Filters



Preview
















4













filtered image











Simulation Results

Conclusion




Filter











bull Mask Selection












= times (41)








2

2

( ) exp2

exp

2

exp2

kxf x A

xA

k

xA

c

σ

σ

= minus

minus =

minus =

(42)



k = a constant






and rests are zeros




INPUT NOISY

IMAGE

7times7

window

DCT

Edge Detection

Percentage of


Selection


FILTERED IMAGE

Masking matrices

IDCT





412 Mask Selection








1 5

2 5 8

3 8 12

4 12 18

5 18 24

6 24 30

7 30

Mask if PEP

Mask if PEP

Mask if PEP

Mask Mask if PEP

Mask if PEP

Mask if PEP

Mask if PEP

le lt le lt le

= lt le lt le

lt le

lt

(43)













In (42) for x = 0 f (0) = A


Hence A = 1
















in Section 44



002 004 006 008 0127

28

29

30

31

Lena

Pepper

Goldhill

Pea

k S

ign

al

to N

ois

e R

ati

o (

dB

)

parameter c

(a)



(a) σn = 20

(b) σn = 30

002 004 006 008 0125

26

27

28

29

Lena

Pepper

Goldhill

Pea

k S

ign

al

to N

ois

e R

ati

o (

dB

)

(b)

parameter c























The Proposed Method






































Step ndash 1



Step ndash 2



Step ndash 3





Step ndash 4




Step ndash 5



Step ndash 6
















Noise level of AWGN

Sl No



Low

(σnle10)

Moderate

(10lt σnle30)

High

(30lt σnle50)



























The Proposed Scheme










as

2

2 2

ˆˆ

ˆk

k k

k n

w yσ

σ σ=

+ (44)

where ˆk

w and k


region of a

particular subband





( )

( )

2

2 2

0(k)

2 2

(k)

arg max P Y(j) |

1max 0 Y j

k

j

n

jM

σσ σ

σ

geisin

isin

=

= minus

prod

sum

N

N

(45)



















shown in Fig 43

Input

DWT

Get a sub-image by




ML Estimation




IDWT

ˆ ( )f x y

Y

Y

( ) ( ) ( )g x y f x y x yη= +

Noisy Image

Output



























performing filters













best performer


















No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 3388 3270 3127 2978 2848 2728 2626 2530 2445 2362

2 Mean [5times5] 2977 2959 2931 2892 2848 2805 2748 2696 2649 2593

3 Mean [7times7] 2766 2760 2750 2737 2721 2701 2677 2649 2623 2589

4 VisuShrink 3165 3056 2960 2875 2791 2678 2541 2395 2257 2148

5 SureShrink 2980 2961 2928 2882 2839 2793 2745 2701 2664 2621

6 BayesShrink 3747 3364 3158 3020 2918 2840 2777 2711 2664 2607

7 OracleShrink 3613 3170 2880 2651 2452 2290 2148 2021 1910 1815

8 OracleThresh 3534 2997 2645 2385 2183 2013 1865 1741 1631 1542

9 NeighShrink 3870 3445 3197 3011 2880 2769 2676 2608 2542 2497

10 SmoothShrink 3234 3041 2893 2743 2606 2488 2381 2289 2203 2131

11 LAWML [3times3] 3839 3413 3161 2978 2847 2741 2648 2572 2508 2458

12 LAWML[5times5] 3860 3459 3226 3066 2941 2853 2774 2709 2656 2602

13 LAWML [7times7] 3853 3458 3234 3086 2969 2884 2800 2741 2689 2638

14 GS-DCT 3376 3313 3188 3098 3001 2911 2746 2706 2689 2611

15 TV-DWT 3465 3376 3229 3056 296 2844 2736 2667 2558 2477

16 RM-DWT 3910 3472 3236 3069 2948 2858 2781 2723 2655 2602







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 3190 3116 3015 2899 2788 2682 2586 2495 2415 2345

2 Mean [5times5] 3061 3039 3001 2955 2902 2840 2781 2722 2656 2601

3 Mean [7times7] 2862 2855 2841 2818 2793 2771 2732 2696 2658 2618

4 VisuShrink 2794 2740 2667 2587 2534 2475 2401 2321 2233 2137

5 SureShrink 2671 2667 2658 2642 2625 2596 2564 2529 2496 2454

6 BayesShrink 3743 3369 3145 2990 2898 2824 2745 2669 2598 2505

7 OracleShrink 3648 3200 2895 2666 2474 2307 2163 2040 1930 1835

8 OracleThresh 3532 3017 2694 2450 2236 2044 1889 1762 1654 1564

9 NeighShrink 3829 3437 3194 3017 2868 2755 2652 2578 2509 2451

10 SmoothShrink 2672 2588 2452 2319 2190 2079 1974 1882 1803 1728

11 LAWML [3times3] 3837 3428 3181 3003 2861 2738 2641 2565 2501 2447

12 LAWML[5times5] 3877 3464 3246 3084 2952 2843 2754 2679 2610 2560

13 LAWML [7times7] 3842 3463 3245 3088 2967 2857 2767 2695 2621 2575

14 GS-DCT 3379 3310 3259 3100 2976 2855 2766 2621 2610 2562

15 TV-DWT 3278 3183 3075 297 2865 2772 2675 2593 2507 2438

16 RM-DWT 3918 3481 3189 3083 2971 2852 2748 2687 2523 2454







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 3154 3082 2983 2877 2769 2666 2573 2483 2401 2332

2 Mean [5times5] 2815 2802 2779 2748 2713 2669 2625 2574 2525 2477

3 Mean [7times7] 2648 2644 2634 262 2607 2583 2556 2525 2495 2453

4 VisuShrink 2971 2864 2778 2693 2591 2484 2370 2247 2135 2026

5 SureShrink 2744 2738 2718 2690 2660 2623 2589 2545 2512 2462

6 BayesShrink 3648 3234 3020 2868 2750 2654 2582 2517 2458 2409

7 OracleShrink 3302 2945 2707 2547 2416 2293 2182 2087 2000 1921

8 OracleThresh 3371 2914 2656 2455 2293 2158 2030 1919 1818 1724

9 NeighShrink 3737 3305 3063 2902 2779 2675 2595 2527 2465 2411

10 SmoothShrink 2813 2681 2522 2372 2237 2119 2013 1916 1837 1762

11 LAWML [3times3] 3655 3278 3037 2877 2742 2644 2558 2477 2420 2361

12 LAWML[5times5] 3722 3302 3078 2920 2803 2710 2629 2556 2492 2443

13 LAWML [7times7] 3689 3302 3078 2927 2811 2724 2640 2573 2511 2443

14 GS-DCT 3325 3161 3089 2956 2821 2716 2623 2518 2474 2401

15 TV-DWT 2782 2693 2645 2594 254 2488 2434 2379 2327 2277

16 RM-DWT 3812 3331 3076 2922 2800 2719 2635 2555 2497 2442







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 2652 2602 2568 2525 2475 2419 2364 2306 2250 2195

2 Mean [5times5] 2381 2376 2368 2357 2343 2325 2304 2284 2256 2231

3 Mean [7times7] 2353 2351 2347 2341 2332 2321 2307 2292 2275 2253

4 VisuShrink 2661 2572 2475 2391 2325 2261 2199 2135 2074 1989

5 SureShrink 2434 2430 2423 2412 2397 2380 2358 2333 2312 2286

6 BayesShrink 3591 3138 2904 2748 2634 2539 2453 2368 2311 2271

7 OracleShrink 3101 2628 2507 2442 2384 2325 2256 2188 2115 2044

8 OracleThresh 3403 2743 2519 2376 2229 2095 1983 1880 1787 1708

9 NeighShrink 3750 3292 3033 2857 2725 2611 2527 2455 2385 2326

10 SmoothShrink 2767 2587 2453 2319 2197 2084 1982 1892 1809 1739

11 LAWML [3times3] 3713 3257 3002 2821 2687 2581 2491 2419 2352 2295

12 LAWML[5times5] 3727 3278 3030 2865 2742 2642 2560 2483 2421 2371

13 LAWML [7times7] 3716 3276 3029 2865 2744 2647 2566 2494 2433 2378

14 GS-DCT 3376 3195 3085 2995 2808 2649 2544 2439 2416 2321

15 TV-DWT 2712 2693 2645 2594 254 2488 2434 2379 2327 2277

16 RM-DWT 3793 3310 3012 2834 2689 2588 2496 2431 2372 2325







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 515 590 696 827 960 1102 1240 1385 1527 1680

2 Mean [5times5] 828 845 873 913 960 1009 1077 1144 1207 1288

3 Mean [7times7] 1055 1063 1075 1091 1111 1137 1169 1207 1244 1294

4 VisuShrink 666 756 844 931 1025 1168 1367 1618 1896 2150

5 SureShrink 825 843 876 923 970 1023 1081 1137 1187 1247

6 BayesShrink 341 530 672 788 886 969 1042 1124 1187 1267

7 OracleShrink 398 663 925 1205 1515 1826 2150 2489 2828 3155

8 OracleThresh 436 809 1213 1637 2065 2512 2978 3435 3899 4320

9 NeighShrink 296 483 642 796 925 1052 1171 1266 1366 1438

10 SmoothShrink 615 769 912 1084 1269 1453 1644 1828 2018 2193

11 LAWML [3times3] 306 501 669 827 961 1086 1209 1319 1420 1505

12 LAWML[5times5] 299 475 621 747 863 955 1046 1127 1198 1275

13 LAWML [7times7] 302 475 615 730 835 921 1015 1086 1153 1223

14 GS-DCT 558 562 649 720 805 893 1080 1131 1153 1261

15 TV-DWT 472 523 619 756 844 965 1092 1183 1341 1472

16 RM-DWT 282 468 614 744 856 949 1037 1109 1199 1275







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 647 705 792 905 1029 1162 1298 1442 1581 1714

2 Mean [5times5] 751 770 805 849 902 969 1037 1110 1198 1276

3 Mean [7times7] 945 952 968 994 1023 1049 1097 1144 1195 1251

4 VisuShrink 1022 1088 1183 1297 1378 1475 1607 1762 1951 2177

5 SureShrink 1177 1183 1195 1217 1241 1283 1332 1386 1440 1512

6 BayesShrink 342 527 682 815 906 987 1081 1180 1281 1425

7 OracleShrink 382 640 910 1184 1477 1790 2113 2435 2764 3083

8 OracleThresh 437 790 1146 1518 1943 2424 2897 3353 3797 4212

9 NeighShrink 310 487 644 790 938 1069 1203 1310 1419 1517

10 SmoothShrink 1174 1295 1515 1766 2049 2328 2627 2921 3199 3487

11 LAWML [3times3] 307 492 654 803 946 1090 1219 1330 1432 1524

12 LAWML[5times5] 293 472 607 732 852 966 1070 1166 1263 1338

13 LAWML [7times7] 305 473 608 728 837 950 1054 1145 1247 1315

14 GS-DCT 521 564 598 718 828 952 1055 1247 1263 1335

15 TV-DWT 585 653 739 834 941 1048 1172 1288 1422 1540

16 RM-DWT 280 463 648 732 833 956 1077 1156 1396 1512







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 675 733 822 929 1052 1184 1318 1462 1607 174

2 Mean [5times5] 997 1012 1041 1077 1122 1180 1241 1316 1393 1472

3 Mean [7times7] 1209 1214 1229 1248 1267 1303 1344 1393 1442 1513

4 VisuShrink 833 943 1041 1148 1291 1460 1665 1918 2182 2474

5 SureShrink 1082 1090 1115 1152 1192 1244 1294 1361 1414 1498

6 BayesShrink 382 615 788 938 1075 1201 1304 1406 1505 1592

7 OracleShrink 569 859 1129 1358 1579 1819 2068 2307 255 2792

8 OracleThresh 526 890 1198 1510 1819 2125 2463 2799 3144 3503

9 NeighShrink 345 567 749 902 1041 1172 1285 1390 1492 1588

10 SmoothShrink 1000 1164 1398 1661 1941 2223 2512 2808 3076 3353

11 LAWML [3times3] 379 585 772 929 1085 1214 1341 1472 1572 1682

12 LAWML[5times5] 351 569 737 884 1011 1126 1236 1344 1447 1531

13 LAWML [7times7] 364 569 737 877 1002 1108 1220 1318 1415 1531

14 GS-DCT 554 669 727 848 990 1118 1244 1404 1477 1607

15 TV-DWT 1036 1148 1213 1286 1369 1453 1547 1648 175 1853

16 RM-DWT 316 550 738 882 1015 1114 1227 1346 1438 1533







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 1203 1275 1326 1393 1475 1574 1677 1792 1912 2037

2 Mean [5times5] 1644 1654 1669 1690 1718 1754 1797 1838 1899 1954

3 Mean [7times7] 1698 1702 1710 1722 1741 1762 1790 1822 1858 1905

4 VisuShrink 1191 1319 1475 1625 1754 1888 2027 2182 2341 2582

5 SureShrink 1547 1554 1566 1586 1614 1646 1688 1738 1780 1834

6 BayesShrink 408 687 900 1077 1229 1371 1513 1669 1782 1866

7 OracleShrink 717 1237 1422 1533 1638 1754 1899 2053 2233 2424

8 OracleThresh 507 1084 1402 1654 1959 2285 2600 2927 3258 3568

9 NeighShrink 340 576 776 950 1106 1261 1390 1510 1637 1752

10 SmoothShrink 1054 1297 1513 1766 2032 2314 2603 2887 3177 3443

11 LAWML [3times3] 354 599 804 990 1156 1306 1448 1574 1700 1815

12 LAWML[5times5] 349 585 779 941 1085 1217 1338 1462 1570 1663

13 LAWML [7times7] 353 586 779 941 1082 1210 1329 1443 1549 1650

14 GS-DCT 523 644 731 811 1005 1207 1363 1538 1579 1762

15 TV-DWT 1123 1148 1213 1286 1369 1453 1547 1648 1751 1853

16 RM-DWT 323 564 795 976 1153 1295 1440 1552 1661 1754







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 Mean [3times3] 09941 09922 09892 09849 09797 09732 09663 09579 09488 09376

2 Mean [5times5] 09845 09838 09827 09811 09791 09769 09736 09700 09665 09613

3 Mean [7times7] 09743 09739 09733 09725 09714 09701 09683 09659 09636 09601

4 VisuShrink 09902 09874 09843 09809 09769 09704 09607 09473 09321 09178

5 SureShrink 09848 09841 09828 09808 09788 09764 09734 09704 09675 09636

6 BayesShrink 09943 09938 09900 09863 09826 09790 09755 09711 09675 09621

7 OracleShrink 09965 09903 09811 09680 09500 09283 09018 08712 08372 08021

8 OracleThresh 09959 09858 09685 09439 09133 08759 08329 07873 07399 06953

9 NeighShrink 09981 09949 09910 09861 09812 09757 09698 09642 09582 09530

10 SmoothShrink 09729 09658 09521 09336 09118 08867 08687 08284 07984 07661

11 LAWML [3times3] 09979 09945 09902 09850 09797 09740 09676 09613 09547 09484

12 LAWML[5times5] 09980 09950 09915 09877 09835 09797 09755 09712 09670 09622

13 LAWML [7times7] 09980 09951 09916 09882 09845 09811 09773 09731 09693 09649

14 GS-DCT 09944 09937 09911 09896 09856 09813 09740 09720 09626 09578

15 TV-DWT 09968 09938 09925 09877 09843 09788 09724 09652 09570 09481

16 RM-DWT 09985 09954 09917 09878 09844 09808 09766 09692 09654 09596







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 Mean [3times3] 09927 09912 09889 09856 09814 09762 09702 09631 09557 09476

2 Mean [5times5] 09900 09894 09884 09871 09853 09831 09805 09776 09737 09699

3 Mean [7times7] 09839 09836 09830 09821 09809 09799 09779 09758 09734 09706

4 VisuShrink 09817 09793 09756 09710 09676 09634 09575 09502 09408 09289

5 SureShrink 09751 09749 09743 09732 09720 09700 09675 09645 09613 09568

6 BayesShrink 09980 09952 09919 09883 09855 09826 09789 09745 09696 09617

7 OracleShrink 09975 09928 09855 09753 09617 09437 09222 08974 08697 08400

8 OracleThresh 09967 09893 09775 09610 09372 09049 08683 08294 07885 07484

9 NeighShrink 09983 09959 09928 09891 09845 09798 09743 09692 09636 09579

10 SmoothShrink 09734 09693 09583 09439 09257 09054 08817 08561 08305 08022

11 LAWML [3times3] 09984 09958 09925 09887 09843 09791 09736 09683 09630 09575

12 LAWML[5times5] 09987 09885 09876 09862 09843 09821 09795 09761 09713 09675

13 LAWML [7times7] 09988 09961 09935 09907 09876 09838 09800 09761 09726 09689

14 GS-DCT 09971 09960 09954 09921 09883 09822 09754 09721 09689 09635

15 TV-DWT 09953 09932 09908 09878 09839 09797 09741 09684 09613 09544

16 RM-DWT 09991 09971 09885 09868 09853 09833 09798 09752 09708 09639







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Goldhill

1 Mean [3times3] 09939 09928 09909 09884 09850 09809 09762 09705 0964 09575

2 Mean [5times5] 09866 09861 09853 09841 09827 09807 09784 09754 09722 09687

3 Mean [7times7] 09801 09799 09793 09785 09777 09762 09744 09722 09699 09665

4 VisuShrink 09908 09882 09856 09826 09784 09730 09659 09562 09454 09328

5 SureShrink 09843 09840 09831 09819 09804 09785 09765 09736 09712 09673

6 BayesShrink 09981 09950 09917 09881 09842 09801 09761 09719 09673 09627

7 OracleShrink 09957 09901 09828 09750 09660 09546 09412 09266 09105 08926

8 OracleThresh 09964 09895 09810 09699 09563 09404 09206 08981 08732 08443

9 NeighShrink 09984 09957 09925 09891 09854 09813 09773 09731 09684 09638

10 SmoothShrink 09878 09816 09736 09627 09494 09340 09162 08959 08760 08541

11 LAWML [3times3] 09982 09955 09921 09884 09841 09798 09751 09696 09648 09592

12 LAWML[5times5] 09984 09956 09927 09895 09861 09826 09787 09744 09699 09656

13 LAWML [7times7] 09986 09957 09928 09896 09863 09831 09791 09754 09711 09658

14 GS-DCT 09958 09949 09939 09913 09881 09845 09789 09756 09703 09648

15 TV-DWT 09976 09954 09935 09902 09873 09841 09779 09768 09718 09654

16 RM-DWT 09992 09961 09926 09889 09859 09788 09759 09698 09659 09599







No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Barbara

1 Mean [3times3] 09753 09739 09718 09688 09649 09601 09545 09478 09403 09318

2 Mean [5times5] 09560 09554 09545 09532 09515 09491 09462 09433 0939 09346

3 Mean [7times7] 09525 09521 09516 09507 09494 0948 09458 09433 09407 09371

4 VisuShrink 09777 09726 09661 09596 09540 09479 09417 09342 09261 09138

5 SureShrink 09613 09609 09602 09590 09573 09552 09526 09493 09463 09424

6 BayesShrink 09974 09927 09874 09817 09759 09696 09624 09534 09461 09401

7 OracleShrink 09919 09756 09674 09618 09560 09492 09400 09294 09158 09005

8 OracleThresh 09960 09817 09690 09569 09398 09188 08961 08702 08422 08136

9 NeighShrink 09982 09949 09907 09859 09808 09747 09691 09631 09560 09491

10 SmoothShrink 09813 09726 09630 09501 09344 09159 08949 08721 08477 08233

11 LAWML [3times3] 09974 09944 09900 09846 09789 09728 09663 09598 09524 09433

12 LAWML[5times5] 09976 09946 09904 09860 09813 09763 09710 09650 09589 09517

13 LAWML [7times7] 09981 09947 09905 09861 09814 09765 09713 09656 09598 09521

14 GS-DCT 09945 09933 09913 09867 09823 09764 09701 09645 09532 09512

15 TV-DWT 09801 09783 09755 09724 09685 09643 09593 09537 09478 09413

16 RM-DWT 09989 09951 09898 09859 09807 09759 09700 09647 09573 09511






Filters


1 Mean [3times3]

262 290 410 668

2 Mean [5times5]

443 408 642 946

3 Mean [7times7]

573 520 793 1035

4 VisuShrink

318 423 471 637

5 SureShrink

517 673 770 1007

6 BayesShrink

00232 00273 00194 00190

7 OracleShrink

00285 00267 00242 00238

8 OracleThresh

00285 00267 00242 00238

9 NeighShrink

408times10-10

466times10-10

334times10-10

497times10-10

10 SmoothShrink

660 752 64515 790

11 LAWML [3times3]

408times10-10

466times10-10

334times10-10

497times10-10

12 LAWML[5times5]

408times10-10

466times10-10

334times10-10

497times10-10

13 LAWML [7times7]

408times10-10

466times10-10

334times10-10

497times10-10

14 GS-DCT

05737 072675 067065 07930

15 TV-DWT

201 226 341 479

16 RM-DWT

408times10-10

466times10-10

334times10-10

497times10-10






SYSTEM-1

SYSTEM-2

SYSTEM-3

1 Mean [3times3] 318 701 2313

2 Mean [5times5] 323 712 2349

3 Mean [7times7] 327 720 2376








11 LAWML [3times3] 367 809 2669

12 LAWML[5times5] 370 815 2689

13 LAWML [7times7] 374 823 2715

14 GS-DCT 1381 3038 7025

15 TV-DWT 04261 09375 309

16 RM-DWT 515 1134 3742




PS

NR

(d

B)


PS

NR

(d

B)

PS

NR

(d

B)


PS

NR

(d

B)


(a) (b)

(c) (d)


(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

σn

σn σn

σn




RM

SE

RM

SE


RM

SE


RM

SE

(a) (b)

(c) (d)


(a) Lena

(b) Pepper

(c) Goldhill

(d) Barbara

σn σn

σn σn



UQ

I


UQ

I

UQ

I


UQ

I


(a) (b)

(c) (d)



(a) Lena (b) Pepper


σn σn

σn σn



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)







(l)

(m)

(n)



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)


σn = 15






(l)

(m)

(n)



(a) (b) (c) (d) (e)

(f) (g) (h) (i) (j)







(h) (i) (j)

(m) (k)

(l)

(m) (n)



(a) (b) (c)

(d)

(e) (f) (g) (h)

(i) (j) (k)







(l)

(m) (n)



(a) (b) (c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)






(l)

(m) (n)



(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)







(l)

(m) (n)



(a)

(b) (c)

(d) (e)

(g) (h) (i) (j)

(k)







(f)

(m) (n) (l)









(a) (b) (c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

(m) (n)



45 Conclusion















applications







Chapter 5

Development of

Some Color Image

Denoising Filters



Preview














5















Filter

Simulation Results

Conclusion















(a)

Filter R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

Input

Color Image

(RGB)

Output

Color Image

(RGB)

Filter

Filter




Filter R-Channel

G-Channel

RG

B ndash

C

T

ran

sfo

rma

tio

n

C ndash

RG

B

T

ran

sfo

rma

tio

n

B-Channel

(b)

R-Channel

G-Channel

B-Channel Filter

Filter

Input

Color Image

(RGB)

Output Color Image

(RGB)











029900000 058700000 014400000

016873000 033126400 050000000

050000000 041866800 008131200

Y R

Cb G

Cr B


(51)




expression [1]

1

1

1

C R

M G

Y B

= minus

(52)


1

3

1 1

3 3

1 1

3 3

116 16

500

200

n n

n n

YL

Yn

X Ya

X Y

Y Zb

Y Z

= minus

= minus

= minus

(53)





0412 0358 0180

0213 0715 0072

0019 0119 0950

X R G B

Y R G B

Z R G B

= + +

= + +

= + +

(54)




















RGB color space

YCbCr color space

CMY color space

CIE LAB color space





Sl

No

Denoising

Filters

10

25

40

10

25

40

10

25

40

10

25

40

1 M-MF [3times3] 3350 2868 2572 3745 3326 3003 3311 2849 2555 3240 2789 2499

2 M-MF [5times5] 3029 2888 2701 3437 3322 3159 2990 2869 2684 2919 2809 2628

3 M-MF [7times7] 2820 2771 2660 3242 3195 3110 2781 2753 2643 2710 2692 2587

4 M-LAWML [3times3] 3425 2925 2583 3897 3416 3159 3386 2916 2566 3315 2846 2510

5 M-LAWML [5times5] 3455 3011 2712 3857 3341 3008 3416 2993 2695 3345 2932 2639

6 M-LAWML [7times7] 3496 3048 2755 3824 3266 2793 3457 3028 2738 3386 2969 2682

7 MCSF [3times3] 3357 2654 2245 3764 3044 2659 3318 2631 2228 3247 2575 2172

8 MCSF [5times5] 3330 3049 2686 3751 3417 3080 3291 3030 2669 3220 2970 2613

9 MCSF [7times7] 3101 2998 2835 3458 3357 3204 3062 2979 2818 2991 2919 2762

10 MRM-DWT 3502 3011 2765 3987 3388 3149 3463 2992 2748 3392 2932 2692









YC

bC

r

RG

B

CM

Y

CIE

La

b

CP

SN

R (

dB

)

(a)

CM

Y

RG

B

YC

bC

r

CIE

La

b

CP

SN

R (

dB

)

(b)

YC

bC

r

RG

B

CIE

La

b

CM

Y

CP

SN

R (

dB

) (c)











schematic in Fig 53








Input

Color Image

(RGB)

Mean

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

Mean

Filter

Mean

Filter

(a)

Mean

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

Mean

Filter

Mean

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)















Input

Color Image

(RGB)

LAWML

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

LAWML

Filter

LAWML

Filter

(a)

LAWML

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

LAWML

Filter

LAWML

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)
















schematic in Fig 55





Input

Color Image

(RGB)

CSF

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output

Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

CSF

Filter

CSF

Filter

(a)

CSF

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

CSF

Filter

CSF

Filter

Input Color Image

(RGB)

Output Color Image

(RGB)







DWT-domain Filter







Fig 56





Input

Color Image

(RGB)

RM-DWT

Filter R-Channel

G-Channel

RG

B ndash

YC

bC

r

T

ran

sfo

rma

tio

n

YC

bC

r ndash

RG

B

T

ran

sfo

rma

tio

n

Output Color Image

(RGB)

B-Channel

(b)

R-Channel

G-Channel

B-Channel

Y

Cb

Cr

Y

Cb

Cr

RM-DWT

Filter

RM-DWT

Filter

(a)

RM-DWT

Filter

R-Channel

G-Channel

B-Channel

R-Channel

G-Channel

B-Channel

RM-DWT

Filter

RM-DWT

Filter

Input

Color Image

(RGB)

Output Color Image

(RGB)

















(30ltσnle50)









highlighted



































analysis






from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 3470 3350 3227 3078 2868 2778 2686 2572 2495 2458

2 M-MF[5times5] 3051 3029 2977 2902 2888 2855 2783 2701 2659 2599

3 M-MF[7times7] 2829 2820 2789 2776 2761 2714 2689 2660 2645 2591

4 M-LAWML [3times3] 3501 3425 3263 3078 2925 2777 2662 2583 2513 2476

5 M-LAWML[5times5] 3513 3455 3336 3161 3011 2893 2769 2712 2682 2623

6 M-LAWML [7times7] 3537 3496 3344 3179 3048 2905 2867 2755 2698 2658

7 MCSF [3times3] 3488 3357 3077 2845 2654 2477 2355 2245 2189 2083

8 MCSF [5times5] 3402 3388 3375 3179 3049 2876 2774 2686 2595 2541

9 MCSF [7times7] 3331 3101 3085 3039 2998 2952 2942 2835 2789 2733

10 MRM-DWT 3587 3502 3373 3175 3046 2908 2876 2765 2698 2661



from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 3346 3176 3087 2942 2831 2725 2629 2538 2458 2388

2 M-MF[5times5] 3271 3097 3065 3009 2956 2894 2835 2776 2713 2673

3 M-MF[7times7] 3162 2914 2916 2859 2834 2812 2773 2737 2734 2682

4 M-LAWML [3times3] 3538 3501 3254 3076 2934 2811 2714 2638 2574 2520

5 M-LAWML[5times5] 3579 3543 3325 3163 3031 2922 2833 2758 2689 2639

6 M-LAWML [7times7] 3593 3545 3327 3170 3049 2939 2849 2777 2703 2657

7 MCSF [3times3] 3443 3346 3039 281 2623 2471 2342 223 2134 2044

8 MCSF [5times5] 3462 3464 3327 3174 3032 2902 2788 269 2597 2517

9 MCSF [7times7] 3432 3313 3278 3131 3078 3012 2948 2879 2817 2783

10 MRM-DWT 3596 3548 3318 3167 3053 2941 2856 2781 2712 2656





to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 469 538 620 737 938 1041 1157 1319 1442 1505

2 M-MF[5times5] 760 779 828 902 917 952 1035 1137 1194 1279

3 M-MF[7times7] 981 992 1028 1067 1049 1120 1153 1192 1213 1291

4 M-LAWML [3times3] 452 494 595 737 879 1042 1190 1303 1412 1474

5 M-LAWML[5times5] 446 477 547 669 796 912 1052 1123 1162 1244

6 M-LAWML [7times7] 434 455 542 656 763 899 939 1069 1141 1195

7 MCSF [3times3] 459 534 737 963 1201 1472 1694 1923 2051 2317

8 MCSF [5times5] 507 551 523 656 762 930 1046 1157 1285 1367

9 MCSF [7times7] 550 717 720 765 808 852 862 975 1028 1096

10 MRM-DWT 412 452 660 692 796 896 930 1056 1141 1191



from 5 to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 541 658 729 862 979 1106 1236 1372 1505 1631

2 M-MF[5times5] 590 721 748 798 848 911 978 1043 1122 1175

3 M-MF[7times7] 669 890 888 948 9762 1001 1047 10915 1095 1162

4 M-LAWML [3times3] 434 452 601 738 870 1002 1120 12233 1316 1401

5 M-LAWML[5times5] 414 431 554 668 778 882 977 10655 1153 1221

6 M-LAWML [7times7] 407 430 553 663 762 865 959 10424 1135 1196

7 MCSF [3times3] 484 541 770 1003 1244 1482 1722 19568 2185 2424

8 MCSF [5times5] 473 472 553 659 777 902 1029 11522 1282 1406

9 MCSF [7times7] 490 631 656 693 737 795 856 92692 995 1035

10 MRM-DWT 406 429 559 665 758 863 951 10376 1123 1198





UQI



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 09954 09936 09906 09863 09811 09746 09677 09593 09502 09392

2 M-MF[5times5] 09871 09853 09842 09826 09806 09784 09751 09715 09682 09628

3 M-MF[7times7] 09768 09755 09749 09741 09733 09717 09699 09675 09652 09617

4 M-LAWML [3times3] 09966 09959 09916 09864 09811 09754 0969 09627 09561 09498

5 M-LAWML[5times5] 09978 09965 09932 09892 09852 09812 09772 09727 09685 09637

6 M-LAWML [7times7] 09977 09966 09932 09898 09861 09827 09788 09747 09709 09665

7 MCSF [3times3] 09972 09963 09863 09756 09625 09466 09286 09081 08868 08628

8 MCSF [5times5] 09945 09939 09934 09899 09861 09828 09725 09655 09572 09484

9 MCSF [7times7] 09912 09903 09855 09844 09829 09805 09789 09751 09716 09675

10 MRM-DWT 09982 09973 09915 09881 09837 09786 09788 09747 09708 09663



UQI



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 09917 09901 09873 09836 09788 09731 09663 09587 09506 09410

2 M-MF[5times5] 09886 09878 09867 09849 09827 09800 09770 09731 09688 09639

3 M-MF[7times7] 09820 09815 09807 09794 09780 09760 09738 09708 09678 09641

4 M-LAWML [3times3] 09980 09950 09912 09867 09816 09758 09702 09639 09576 09505

5 M-LAWML[5times5] 09978 09906 09897 09883 09864 09842 09816 09782 09747 0971

6 M-LAWML [7times7] 09991 09983 09957 09929 09898 09861 09822 09783 09735 09697

7 MCSF [3times3] 09987 09983 099 09817 0971 09582 09433 09267 09089 08883

8 MCSF [5times5] 09979 09971 09968 09934 09898 09847 09797 09735 09671 0959

9 MCSF [7times7] 09921 09913 09906 09895 09889 09862 09838 09810 09785 09766

10 MRM-DWT 09993 09986 09961 09929 09890 09861 09821 09776 09731 09695





from 5 to 50)

CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 3863 3745 3602 3460 3326 3209 3099 3003 2917 2838

2 M-MF[5times5] 3456 3437 3407 3366 3322 3267 3216 3159 3100 3046

3 M-MF[7times7] 3249 3242 3230 3217 3195 3172 3143 3110 3076 3040

4 M-LAWML [3times3] 4173 3897 3683 3537 3416 3323 3236 3159 3088 3019

5 M-LAWML[5times5] 4145 3857 3608 3456 3341 3224 3099 3008 2938 2840

6 M-LAWML [7times7] 4129 3824 3555 3385 3266 3107 2963 2793 2782 2694

7 MCSF [3times3] 4078 3864 3455 3224 3044 2895 2767 2659 2567 2484

8 MCSF [5times5] 3976 3781 3774 3617 3417 3276 3174 3080 2991 2913

9 MCSF [7times7] 3786 3458 3432 3398 3357 3343 3260 3204 3150 3095

10 MRM-DWT 4372 3987 3652 3508 3388 3308 3224 3149 3076 3016




CPSNR (dB)



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 3656 3581 3475 3364 3253 3152 3052 2967 2884 2812

2 M-MF[5times5] 3520 3494 3454 3403 3346 3286 3222 3156 3094 3030

3 M-MF[7times7] 3324 3312 3294 3271 3241 3206 3170 3126 3083 3032

4 M-LAWML [3times3] 4121 3811 3611 3453 3333 3224 3131 3047 2960 2881

5 M-LAWML[5times5] 4105 3781 3575 3390 3261 3127 3028 2929 2835 2760

6 M-LAWML [7times7] 4087 3747 3505 3354 3195 3047 2926 2812 2724 2595

7 MCSF [3times3] 4018 3743 3446 3220 3042 2893 2772 2665 2572 2491

8 MCSF [5times5] 3945 3821 3696 3540 3418 3282 3174 3077 2985 2904

9 MCSF [7times7] 3832 3565 3524 3474 3414 3355 3290 3221 3156 3087

10 MRM-DWT 4212 3895 3676 3535 3402 3314 3212 3130 3050 2974





from 5 to 50)

RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 298 342 403 474 554 633 719 803 887 971

2 M-MF[5times5] 477 487 504 529 556 592 622 671 718 764

3 M-MF[7times7] 605 610 618 628 644 661 683 710 738 770

4 M-LAWML [3times3] 208 287 367 434 499 555 614 671 728 788

5 M-LAWML[5times5] 215 300 400 477 544 623 719 798 866 969

6 M-LAWML [7times7] 219 312 425 517 593 712 841 1023 1036 1146

7 MCSF [3times3] 232 334 477 623 766 912 1054 1194 1327 1460

8 MCSF [5times5] 262 327 330 391 498 586 659 735 814 891

9 MCSF [7times7] 326 475 490 509 534 543 597 637 678 722

10 MRM-DWT 166 258 389 449 515 565 617 681 738 793




RMSE



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 378 413 466 530 602 676 759 837 921 1001

2 M-MF[5times5] 443 456 478 507 541 580 624 673 723 779

3 M-MF[7times7] 555 563 574 590 611 636 663 697 732 777

4 M-LAWML [3times3] 221 316 399 478 549 623 693 763 844 924

5 M-LAWML[5times5] 225 328 415 514 597 696 780 875 975 1063

6 M-LAWML [7times7] 230 341 450 536 644 763 878 1001 1108 1285

7 MCSF [3times3] 249 342 482 625 768 912 1048 1185 1319 1448

8 MCSF [5times5] 271 313 361 433 498 582 659 737 820 900

9 MCSF [7times7] 309 420 441 467 500 535 577 625 673 729

10 MRM-DWT 199 287 370 435 507 561 631 694 761 830





UQI


No

Denoising

Filters

5 10 15 20 25 30 35 40 45 50

Test Image Lena

1 M-MF [3times3] 09926 09903 09865 09813 09747 09671 09579 09475

09366 09245

2 M-MF[5times5] 09807 09799 09784 09764 09739 09704 09667 09623 09570 09515

3 M-MF[7times7] 09686 09681 09673 09663 09646 09627 09601 09572 09540 09504

4

M-LAWML

[3times3] 09977 09945 09910 09870 09834 09796 09751 09705 09656 09598

5

M-

LAWML[5times5] 09975 09939 09894 09848 09803 09739 09659 09577 09506 09384

6

M-LAWML [7times7] 09974 09935 09880 09820 09764 09665 09533 09280 09288 09131

7 MCSF [3times3] 09943 09908 09815 09687 09533 09354 09149 08928 08701 08457

8 MCSF [5times5] 09924 09920 09918 09871 09837 09717 09641 09559 09462 09361

9 MCSF [7times7] 09912 09901 09896 09861 09819 09798 09776 09727 09668 09613

10 MRM-DWT 09982 09953 09873 09832 09789 09788 09744 09699 09644 09596



UQI



5 10 15 20 25 30 35 40 45 50

Test Image Pepper

1 M-MF [3times3] 09917 09901 09873 09836 09787 09731 09661 09588 09501 09411

2 M-MF[5times5] 09886 09879 09866 09849 09827 09802 09769 09731 09689 09640

3 M-MF[7times7] 09820 09815 09806 09795 09780 09760 09739 09710 09680 09641

4 M-LAWML [3times3] 09956 09932 09904 09872 09837 09806 09752 09703 09641 09571

5 M-LAWML[5times5] 09955 09929 09908 09855 09812 09750 09689 09613 09524 09423

6 M-LAWML [7times7] 09954 09925 09884 09843 09783 09704 09607 09501 09385 09177

7 MCSF [3times3] 09960 09931 09865 09774 09661 09528 09380 09213 09035 08850

8 MCSF [5times5] 09950 09943 09922 09888 09849 09801 09744 09681 09605 09526

9 MCSF [7times7] 09903 09897 09886 09872 09853 09831 09804 09769 09732 09686

10 MRM-DWT 09976 09950 09920 09889 09852 09812 09762 09711 09653 09585





Sl

No

Images


1 M-MF [3times3] 265 308

2 M-MF[5times5] 446 425

3 M-MF[7times7] 573 563


456times10-10


456times10-10


456times10-10

7 MCSF [3times3] 124 150

8 MCSF [5times5] 275 270

9 MCSF [7times7] 438 400


456times10-10



Sl

No

Images


1 M-MF [3times3] 265 308

2 M-MF[5times5] 446 425

3 M-MF[7times7] 573 563


456times10-10


456times10-10


456times10-10

7 MCSF [3times3] 124 150

8 MCSF [5times5] 275 270

9 MCSF [7times7] 438 400


456times10-10






Filters


1 M-MF [3times3] 855 1539 4309

2 M-MF[5times5] 8966 1614 4519

3 M-MF[7times7] 945 1701 4762

4 M-LAWML [3times3] 1188 2139 5989

5 M-LAWML[5times5] 1198 2157 6039

6 M-LAWML [7times7] 1245 2242 6277

7 MCSF [3times3] 8711 1568 4390

8 MCSF [5times5] 928 1672 4681

9 MCSF [7times7] 1001 1803 5048

10 MRM-DWT 1307 2353 6588


Sl No Images

Denoising

Filters


1 M-MF [3times3] 1042 1564 4848

2 M-MF[5times5] 1104 1656 5133

3 M-MF[7times7] 1150 1726 5350

4 M-LAWML [3times3] 1624 2436 7551

5 M-LAWML[5times5] 1688 2532 7849

6 M-LAWML [7times7] 1792 2688 8332

7 MCSF [3times3] 1067 1601 4963

8 MCSF [5times5] 1148 1722 5338

9 MCSF [7times7] 1210 1816 5629

10 MRM-DWT 1984 2976 9225






Ex

ecu

tio

n T

ime

in s

econ

ds





CP

SN

R [

dB

]


CP

SN

R [

dB

] (a) (b)




(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)


(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image






(a) (b) (c)

(d) (e) (f)








(a) (b) (c)

(d) (e) (f)



(a) Original image






(a)

(b)

(c)

(d)

(e)

(f)


(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image

(b) Noisy image





(a)

(b)

(c)

(d)

(e)

(f)



(a) Original image

(b) Noisy image







(a) (b) (c)

(d) (e) (f)



(a) Original image








(a) Original image




(c)

2

1

3

4

5

6

(a)

2

1

3

4

5

6

(d)

2

1

3

4

5

6

(b)

2

1

3

4

5

6



57 Conclusion



















































Chapter 6

Conclusion



Preview
















6












Conclusion




analyzed here


Images

































σn = 10

σn = 20

σn = 40


Mean 3270 589 09922 2978 826 09849 2696 1142 09700

ATM 3271 589 09922 2983 821 09851 2703 1134 09710

Wiener 3401 507 09943 3019 787 09861 2655 1198 09671

TV 3322 555 09931 3025 782 09864 2585 1298 09633

Lee 3347 540 09936 2974 828 09847 2677 1167 09688

Bilateral 3258 596 09921 2977 826 09849 2671 1175 09686

BayesShrink 3364 527 09938 3020 787 09863 2711 1124 09711

NeighShrink 3445 481 09949 3011 795 09861 2608 1264 09642

Ex

isti

ng

Fil

ters

LAWML 3459 474 09950 3086 729 09882 2732 1086 09721

AWWF 3336 545 09934 3056 754 09865 2688 1152 09690

CSF 3287 578 09949 3031 777 09866 2749 1076 09735

GS-DCT 3310 563 09902 3098 719 09896 2710 1124 09720

TV-DWT 3376 522 09936 3056 754 09855 2667 1180 09652 Pro

po

sed

Fil

ters

RM-DWT 3472 466 09954 3022 785 09815 2734 1083 09725





respectively)


Mean 262 720

ATM 262 1784

Wiener 186 1614

TV 211 -------

Lee 00118 1508

Bilateral 288 1347



Ex

isti

ng

F

ilte

rs

LAWML 408times10-10

809

AWWF 183 2417

CSF 122 729

GS-DCT 05737 3038

TV-DWT 2014 09375

Pro

po

sed

Fil

ters















noise conditions








Images


















space


σn = 10 σn = 20 σn = 40

Denoising

Filters

CPSNR

RMSE

UQI

CPSNR

RMSE

UQI

CPSNR

RMSE

UQI

M-MF [3times3] 3745 342 09903 3460 474 09813 3003 803 09475

M-MF [5times5] 3437 487 09799 3366 529 09764 3159 671 09623

M-MF [7times7] 3242 610 09681 3217 628 09663 3110 710 09572

M-LAWML[3times3] 3897 287 09945 3537 434 09870 3159 671 09705

M-LAWML[5times5] 3857 300 09939 3456 477 09848 3008 798 09577

Ex

isti

ng

F

ilte

rs

M-LAWML[7times7] 3824 312 09935 3385 517 09820 2793 1023 09280

MCSF [3times3] 3864 334 09908 3224 623 09687 2659 1194 08928

MCSF [5times5] 3781 327 09920 3617 391 09871 3080 735 09559

MCSF [7times7] 3458 475 09901 3398 509 09861 3204 637 09727

Pro

po

sed

Fil

ters

MRM-DWT 3987 258 09953 3508 449 09832 3149 681 09699





Denoising Filters

Method Noise

Execution Time

M-MF [3times3] 265 1564

M-MF [5times5] 446 1656

M-MF [7times7] 573 1726


-10

2436


-10 2532

Ex

isti

ng

F

ilte

rs


-10 2688

MCSF [3times3] 12495 1601

MCSF [5times5] 2754 1722

MCSF [7times7] 4386 1816

Pro

po

sed

Fil

ters

MRM-DWT 379times10

-10 2976









62 Conclusion
























conditions

























image denoising







Prentice-Hall 1989


1971













1999


Press 1996







REFERENCES















vol 3 pp 1499-1502 1996









54 no 1 pp 352-358 2005






vol 153 no 4 pp 261-269 2006



919-927 2008

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2008

























Punjab







Rourkela



NCNTE-2008 Mumbai

Documents

Development of Some Novel Spatial-Domain and Transform - ethesis