Blind separation of noisy mixed speech signals
based on wavelet transform and
Independent Component Analysis
Hongyan Li, Huakui Wang, Baojin Xiao
College of Information Engineering of Taiyuan University of Technology
8th International Conference on Signal Processing Proceedings ,ICSP 2006
Presenter: Jain De ,Lee(李建德)
Student number: 1099304160
Outline
 Introduction
 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 ICA
 ICA 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:
x(t)=As(t) + v(t)
v(t): additive noise vector
 Independent component simply by
s(t)=Wx(t)
X
S
A
ICA
W
S
Pre-processing
 Centering
– To make x a zero-mean variable
x=x-E{x}
 Whitening
– To make the components are uncorrelated
 Using eigen value decomposition compute covariance matrix of x(t)
Rx=E{ xxT}=VΛVT
V:The orthogonal matrix of eigenvector of x
Λ: the diagonal matrix of its eigen-values
Pre-processing
 Compute whitening matrix U
U= VΛ-1/2VT

x (t )  Ux(t )
Network architectures for blind separation base on
independent component analysis
Wavelet threshold de-noising algorithm
 De-noising can be performed by threshold detail
coefficients
 Each coefficient is thresholded by comparing
against threshold
 Selecting of the threshold value
– Minimax
– Sqtwolog
– heursure
Wavelet threshold de-noising algorithm
Divide
Estimate
Calculate
Reconstruct
Describe of wavelet threshold de-noising algorithm
FASTICA
 Based on a fixed-point iteration scheme
 kurtosis as the estimation rule of independence
Kurtosis is defined as follows:
Kurt(si)=E[si4]-3(E[si2])2
fixed-point algorithm can be expressed:
wi (k )  E[ xˆi (wi (k 1)T xˆi )3 ]  3wi (k 1)
FASTICA
2.Whitening
1.Centering
3.i=1
4.Initial matrix W
K=1
k++
(5)
7.Converged
8.i++
6.wi (k ) 
wi (k )
wi (k )
9.i<number of
original signals
5.Calculate
(4)
finish
|wi(k)Twi(k-1)| equal or close 1
Step Chart in FASTICA
Simulation results
mixing matrix
original speech signals
The noisy mixed speech signals
The mixed speech signals
Simulation results
de-noising
The noisy mixed speech signals
The wavelet threshold de-noising speech
signals
Simulation results
separate
The wavelet threshold de-noising speech
signals
The FASTICA separate de-noising speech
signals
Simulation results
original speech signals
FASTICA separate de-noising speech signals
Signal-noiseThe
ratio
Conclusion
 Reduce the affect of noise and improve the signal-noise ratio
 Renew the original speech signals effectively