Blind separation of sparse sources using variational EM

In this paper, we tackle the general linear instantaneous model (possibly underdetermined and noisy) using the assumption of sparsity of the sources on a given dictionary. We model the sparsity of expansion coefficients with a Student t prior. The conjugate-exponential characterisation of the t distribution as an infinite mixture of scaled Gaussians enables us to derive an efficient variational expectation maximisation algorithm (V-EM). The resulting deterministic algorithm has superior properties in terms of computation time and achieves a separation performance comparable in quality to alternative methods based on Markov Chain Monte Carlo (MCMC).