Hongyan Li, Huakui Wang, Baojin Xiao

1. Blind separation of noisy mixed speech signals based on wavelettransform 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

2. Outline • Introduction • Model of ICA • Wavelet threshold de-noising • FASTICA • Simulation results • Conclusion

3. 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

4. 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

5. 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 ICA W S A S

6. 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} Rx=E{ xxT}=VΛVT V:The orthogonal matrix of eigenvector of x Λ: the diagonal matrix of its eigen-values

7. Pre-processing • Compute whitening matrix U U= Λ-1/2VT Network architectures for blind separation base on independent component analysis

8. 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

9. Wavelet threshold de-noising algorithm Divide Estimate Calculate Reconstruct Describe of wavelet threshold de-noising algorithm

10. 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:

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

12. Simulation results mixing matrix The mixed speech signals original speech signals

13. Simulation results noisy The noisy mixed speech signals The mixed speech signals

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

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

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

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