Wavelets in compressive sensing

天津大学精仪学院闫超 1014202037

Wavelets in compressive sensing-introduction

Compressive sensing (CS), compressived sensing or compressived sample

Compressed sensing is a mathematical tool that creates hi-res data sets from lo-res samples. It can be used to resurrect old musical recordings, find enemy radio signals, and generate MRIs much more quickly.

Wavelets in compressive sensing-history

History:Embryo-@2000-A PHD thesisTheory improvement-@2004- 陶哲轩 , Emmanuel Candes, Donoho

L1-minimization

Wavelets in compressive sensing-application

MRI image

Wavelets in compressive sensing-experiments

Compressive sensing of optical imaging

@2008-IEEE SIGNAL PROCESSING MAGAZINE-Single-pixel imaging via compressive sampling

Wavelets in compressive sensing-experiments

Compressive sensing of optical imaging

@2008-IEEE SIGNAL PROCESSING MAGAZINE-Single-pixel imaging via compressive sampling

Wavelets in compressive sensing-experiments

Compressive sensing of optical imaging

@2012- 光学 精密工程 - 应用压缩传感理论的单像素相机成像系统

Wavelets in compressive sensing-experiments

Compressive sensing of terahertz imaging

@2008-APL-A single-pixel terahertz imaging system based on compressed sensing

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Wavelets in compressive sensing-experiments

Compressive sensing of terahertz imaging

@2011- J Infrared Milli Terahz Waves -A Fast Spatial-domain Terahertz Imaging Using Block-based Compressed Sensing

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Wavelets in compressive sensing-experiments

Compressive sensing of terahertz imaging

@2008-OL-Terahertz imaging with compressed sensing and phase retrieval

Wavelets in compressive sensing-mathematica

Theory

sparse: 1. DCT (Discrete cosine transform) 2. WT (Wavelet transform)

Wavelets in compressive sensing-simulation

DCT: 30.21739s 21.75909dB

WT: 9.71886s 38.97849dB

DCT: 81.32332s 22.74607dB

WT: 64.06961s 25.94528dB

Wavelets in compressive sensing-simulation

H1-PSNR-DCT vs WT H1-elapsed time-DCT vs WT

Lena-PSNR-DCT vs WT Lena-elapsed time-DCT vs WT

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Wavelets in compressive sensing-simulation

db8: 19.23621s 24.7816dB

sym8: 18.66266s 25.8342dB

coif4: 18.63087s 16.1393dB

bior4.4: 19.37384s 22.4711dB

rbior4.4: 19.45398s 19.9363dB

Wavelets in compressive sensing-simulation

db4: 19.24032s 24.9472dB

db8: 19.23621s 24.7816dB

sym4: 18.93414s 25.7825dB

sym8: 18.66266s 25.8342dB

Thank you