Hongyan Li, Huakui Wang, Baojin Xiao

College of Information Engineering of Taiyuan University of Technology

8th International Conference on Signal Processing Proceedings ,ICSP 2006

Blind separation of noisy mixed speech signals based on wavelet

transform and Independent Component Analysis

Presenter: Jain De ,Lee(李建德 )

Student number: 1099304160

OutlineIntroduction

Model of ICA

Wavelet threshold de-noising

FASTICA

Simulation results

Conclusion

Introduction• Independent component analysis(ICA)– Extracting unknown independent source signals

• Assumptions and status of ICA methods

– Mutual independence of the sources– Perform poorly when noise affects the data Noisy FASTICA algorithm Independent Factor Analysis (IFA) method Wavelet threshold de-noising

Model of ICAICA model is the noiseless one:

x(t)= As(t)

Where A is a unknown matrix, called the mixing matrix

Conditions:

•The components si (t) are statistically independent

•At least as many sensor responses as source signals

•At most one Gaussian source is allowed

Model of ICA (cont.)ICA model is the noising case:

Independent component simply by

x(t)=As(t) + v(t)

v(t): additive noise vector

s(t)=Wx(t)

S A W S

X ICA

Pre-processingCentering– To make x a zero-mean variable

Whitening– To make the components are uncorrelated Using eigen value decomposition compute covariance

matrix of x(t)

x=x-E{x}

Rx=E{ xxT}=VΛVT

V:The orthogonal matrix of eigenvector of xΛ: the diagonal matrix of its eigen-values

Pre-processingCompute whitening matrix U

U= VΛ-1/2VT

)()( tUxtx

Network architectures for blind separation base on independent component analysis

Wavelet threshold de-noising algorithmDe-noising can be performed by

threshold detail coefficientsEach coefficient is thresholded by

comparing against thresholdSelecting of the threshold value– Minimax– Sqtwolog– heursure

Wavelet threshold de-noising algorithm

Calculate

Divide Estimate

Reconstruct

Describe of wavelet threshold de-noising algorithm

FASTICABased on a fixed-point iteration schemekurtosis as the estimation rule of independence

Kurtosis is defined as follows:

Kurt(si)=E[si4]-3(E[si

2])2

fixed-point algorithm can be expressed:

)1(3])ˆ)1((ˆ[)( 3 kwxkwxEkw iiT

iii

FASTICA

1.Centering

2.Whitening

4.Initial matrix W

K=1

5.Calculate

6. )(

)()(

kw

kwkw

i

ii 7.Conver

ged

8.i++9.i<number of original signals

k++

(5)

(4)

finish

3.i=1

|wi(k)Twi(k-1)| equal or close 1

Step Chart in FASTICA

mixing matrix

Simulation results

original speech signals

The mixed speech signalsThe noisy mixed speech signals

Simulation results

The wavelet threshold de-noising speechsignals

The noisy mixed speech signals

de-noising

Simulation results

The wavelet threshold de-noising speechsignals

The FASTICA separate de-noising speech signals

separate

Simulation results

original speech signals The FASTICA separate de-noising speech signalsSignal-noise ratio

Conclusion

Reduce the affect of noise and improve the signal-noise ratio

Renew the original speech signals effectively