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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
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