A Maximum Likelihood Approach to Nonlinear Convolutive Blind Source Separation

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.