A maximum likelihood approach to nonlinear convolutive blind source separation

Authors:
Jingyi Zhang;Li Chin Khor;Wai Lok Woo;Satnam Singh Dlay
Affiliations:
School of Electrical, Electronic and Computer Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, United Kindom;School of Electrical, Electronic and Computer Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, United Kindom;School of Electrical, Electronic and Computer Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, United Kindom;School of Electrical, Electronic and Computer Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne, United Kindom
Venue:
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Year:
2006

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Abstract

A novel learning algorithm for blind source separation of post-nonlinear convolutive mixtures with non-stationary sources is proposed in this paper. The proposed mixture model characterizes both convolutive mixture and post-nonlinear distortions of the sources. A novel iterative technique based on Maximum Likelihood (ML) approach is developed where the Expectation-Maximization (EM) algorithm is generalized to estimate the parameters in the proposed model. The post-nonlinear distortion is estimated by using a set of polynomials. The sufficient statistics associated with the source signals are estimated in the E-step while in the M-step, the parameters are optimized by using these statistics. In general, the nonlinear maximization in the M-step is difficult to be formulated in a closed form. However, the use of polynomial as the nonlinearity estimator facilitates the M-step tractable and can be solved via linear equations.