Gaussian Mixture Model-Based Bayesian Analysis for Underdetermined Blind Source Separation

Abstract

This paper proposes a Gaussian mixture model-based Bayesian analysis for blind source separation of an underdetermined model that has more sources than sensors. The proposed algorithm follows a hierarchical learning procedure and alternative estimations for sources and the mixing matrix. The independent sources are estimated from their posterior means, and the mixing matrix is estimated by the maximum likelihood method. Because each source is conditionally correlated with others in its Markov blanket, the correlations between them are approximated by using linear response theory; this is based on the factorized approximation to the sources' true posteriors. In this framework, each source is modeled as a mixture of Gaussians to fit its actual distribution. Given enough Gaussians, the mixture model can learn any distribution. The algorithm provides a good identification of the mixing system, and its flexibility speeds up the convergence. The iterative learning for Gaussians leads to a parametric density estimation for all hidden sources as well as their recovery in the end. The major advantages of this algorithm are its flexibility and its fast convergence. Simulations using synthetic data validate the effectiveness of the algorithm.