Determination of the number of sources in blind source separation

The determination of the number (n) of unobserved sources is an important issue in Blind Source Separation (BSS) of linear and instantaneous mixtures. However BSS is already a difficult task, so we generally assume that this number (n) is known and a priori fixed. In this paper, we address this issue as a Bayesian model selection problem and view the determination of this number (n) as a hypothesis testing problem via comparison of Bayes factors and study the computation of these factors by two numerical approximations: importance sampling from the posterior and simulated annealing sampling. Seeking for a general solution may be tricky to this problem, so we will be interested in blind separation of sparse sources modeled by a double exponential prior “π(.) ∝ exp(−λ|.|)”.