A variational Bayesian approach to number of sources estimation for multichannel blind deconvolution

Abstract

Most traditional multichannel blind deconvolution algorithms rely on some assumptions on the mixing model, e.g. the number of sources is known a priori; and the mixing environment is noise-free. Unfortunately, these assumptions are not necessarily true in practice. In this paper, we will relax the assumption placed on the number of sources by studying a state space mixing model where the number of sources is assumed to be unknown but not greater than the number of sensors. Based on this mixing model, we will formulate the estimation of the number of sources problem as a model order selection problem. Model comparison, as a common method of model order selection, usually involves the evaluation of multi-variable integrals which is computationally intractable. A variational Bayesian method is therefore used to overcome this multi-variable integral issue. The problem is solved by approximating the true, complicated posteriors with a set of independent, simple, tractable posteriors. To realize the objective of optimal approximation, we maximize an objective function called negative free energy. We will derive a variational Bayesian algorithm, in which the number of sources will be estimated through two approaches: automatic relevance determination and comparison of the optimized negative free energy. The proposed variational Bayesian algorithm will be evaluated on both artificially generated examples, and practical signals.