1. By: Soroosh Mariooryad Advisor: Dr.Sameti 1 BSS & ICA Speech Recognition - Spring 2008

2.  Observation in 1982:The angular position and the angular velocity of a joint is represented by two nervous signals f 1 (t) and f 2 (t), each one is a linear combination of position and velocity:  At each instant the nervous system knows p(t) and v(t)  p(t) and v(t) must be recoverable form f 1 (t) and f 2 (t) 2 BSS & ICA Speech Recognition - Spring 2008

3.  S i : Original source(assumed to be Independent)  X i : Received (mixed) signals.  Y i : Estimated sources ◦ Goal: Y i =S i 3 BSS & ICA Speech Recognition - Spring 2008

4.  Presented in GRETSI’85, COGNITAVA’85 and Snowbird’86  Choosing m 12 and m 21 correctly results in separation: 4 BSS & ICA Speech Recognition - Spring 2008

5.  Main Idea: Independence (ICA)  The algorithm: 5 BSS & ICA Speech Recognition - Spring 2008

6.  Memory ◦ Instantaneous ◦ Convolutive 6  Linear \ NonLinear  Under\Over determined BSS & ICA Speech Recognition - Spring 2008

7. s1s1 s2s2 x1x1 x2x2 Original sMixed signals a2a2 a1a1 a1a1 7 BSS & ICA Speech Recognition - Spring 2008

8. s1s1 s2s2 x1x1 x2x2 Step1: Sphering Step2: Rotatation Original sMixed signals a2a2 a1a1 a1a1 8 BSS & ICA Speech Recognition - Spring 2008

9. There is one case when rotation doesn’t matter. This case cannot be solved by basic ICA. …when both densities are Gaussian 9 BSS & ICA Speech Recognition - Spring 2008

10.  Combination= 10 BSS & ICA Speech Recognition - Spring 2008

11.  ICA method = Objective function + Optimization algorithm ● Objective Function: ● Mutual Information ● If U i are independent from each other then i (pu)=0 ● Moments and cumulants ● … ● Algorithm : minimizes/maximizes function: ● Gradient-Based ● … 11 BSS & ICA Speech Recognition - Spring 2008

12.  Speech Processing: ◦ Noise Cancelation in car environment ◦ As a preprocess in speech recognition systems ◦ Speech enhancement in Reverberant environment ◦ Cocktail party problem  Other: ◦ Image Denoising ◦ Economic time series ◦ Brain signals (EEG and MEG) 12 BSS & ICA Speech Recognition - Spring 2008

13.  Mixture 1 Mixture 1  Mixture2 Mixture2  Estimated Source 1 Estimated Source 1  Estimated Source 2 Estimated Source 2  Ref: T.-W. Lee, A. J. Bell, and R. Lambert. Blind separation of delayed and convolved sources. In Advances in Neural Information Processing Systems, Volume 9, pages 758- 764. MIT Press, 1997. BSS & ICA Speech Recognition - Spring 200813

14. Questions? 14 BSS & ICA Speech Recognition - Spring 2008