Maximum Likelihood Source SeparationBy the Expectation-Maximization Technique : Deterministic and Stochastic Implementation

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 Expectation-Maximization (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 eeectiveness of this method is illustrated by numerical simulations.