Maximum Likelihood Source Separation By the Expectation-Maximization Technique: Deterministic and Stochastic Implementation.

Abstract

This paper deals with the source separation problem which consists in the separation of a mixture of independent sources without a priori knowledge on the mixing matrix. When the source distributions are known in advance, this problem can be solved via the Maximum Likelihood (ML) approach by maximizing the data likelihood function using (i) the ExpectationMaximization (EM) algorithm and (ii) a stochastic version of it, the SEM. Two important features of our algorithm are that (a) the covariance of the additive noise can be estimated as a regular parameter, (b) in the case of discrete sources, it is possible to separate more sources than sensors. The effectiveness of this method is illustrated by numerical simulations. I. Introduction When an array of m sensors samples the fields radiated by n narrow band sources its output is classically modeled as an instantaneous spatial mixture of a random vector made of m one-dimensional components, possibly corrupted by additive noise. The sourc..