Hongyan Li, Huakui Wang, Baojin Xiao College of Information Engineering of Taiyuan University of Technology 8th International Conference on Signal Processing Proceedings,ICSP 2006 B lind separation of noisy mixed speech signals based on wavelet transform and I ndependent C omponent A nalysis Presenter: Jain De,Lee( 李建德 ) Student number:

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 s i (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 S A A W W S S XICA

Pre-processing Centering – 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} R x =E{ xx T }=VΛV T V :The orthogonal matrix of eigenvector of x Λ : the diagonal matrix of its eigen-values

Pre-processing Compute whitening matrix U U= VΛ -1/2 V 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 Calculate Divide Estimate 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(s i )=E[s i 4 ]-3(E[s i 2 ]) 2 fixed-point algorithm can be expressed:

FASTICA 1.Centering 2.Whitening 4.Initial matrix W K=1 4.Initial matrix W K=1 5.Calculate 6. 7.Converged 8.i++ 9.i<number of original signals k++ (5) (4) finish 3.i=1 | w i (k) T w i (k-1) | equal or close 1 Step Chart in FASTICA

mixing matrix Simulation results original speech signals The mixed speech signals The noisy mixed speech signals

Simulation results The wavelet threshold de-noising speech signals The noisy mixed speech signals de-noising

Simulation results The wavelet threshold de-noising speech signals The FASTICA separate de-noising speech signals separate

Simulation results original speech signals The FASTICA separate de-noising speech signals Signal-noise ratio

Conclusion Reduce the affect of noise and improve the signal-noise ratio Renew the original speech signals effectively