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B lind S ource S eparation & I ndependent C omponent A nalysis

B lind S ource S eparation & I ndependent C omponent A nalysis. By: Soroosh Mariooryad Advisor: Dr.Sameti. History.

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B lind S ource S eparation & I ndependent C omponent A nalysis

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  1. Blind Source Separation &Independent Component Analysis By: Soroosh Mariooryad Advisor: Dr.Sameti BSS & ICA Speech Recognition - Spring 2008

  2. History • Observation in 1982:The angular position and the angular velocity of a joint is represented by two nervous signals f1(t) and f2(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 f1(t) and f2(t) BSS & ICA Speech Recognition - Spring 2008

  3. Blind Source Separation • Si: Original source(assumed to be Independent) • Xi: Received (mixed) signals. • Yi: Estimated sources • Goal: Yi=Si BSS & ICA Speech Recognition - Spring 2008

  4. Herault and Jutten (HJ) Algorithm • Presented in GRETSI’85, COGNITAVA’85 and Snowbird’86 • Choosing m12 and m21 correctly results in separation: BSS & ICA Speech Recognition - Spring 2008

  5. Herault and Jutten (HJ) Algorithm • Main Idea: Independence (ICA) • The algorithm: BSS & ICA Speech Recognition - Spring 2008

  6. Types of Mixtures • Memory • Instantaneous • Convolutive • Linear \ NonLinear • Under\Over determined BSS & ICA Speech Recognition - Spring 2008

  7. Illustration of ICA with 2 signals (Geometric Method) a1 s2 x2 a2 a1 s1 x1 Original s Mixed signals BSS & ICA Speech Recognition - Spring 2008

  8. Illustration of ICA with 2 signals (Geometric Method) a1 s2 x2 a2 a1 s1 x1 Original s Mixed signals Step2: Rotatation Step1: Sphering BSS & ICA Speech Recognition - Spring 2008

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

  10. Geometric Method • Combination= BSS & ICA Speech Recognition - Spring 2008

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

  12. Applications • 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) BSS & ICA Speech Recognition - Spring 2008

  13. Example of Separation • Mixture 1 • Mixture2 • Estimated Source 1 • 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 2008

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

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