Gaussian Mixture Model for Underdetermined Source Separation

Abstract

This paper proposes a Bayesian method for underdetermined blind source separation based on the Gaussian mixture model. The proposed algorithm follows a hierarchical learning and alternative estimations for sources and mixing matrix. The independent sources are estimated from their a posteriori means and the mixing matrix is estimated by maximum likelihood (ML). Both estimations require the a posteriori correlations of sources which exist in the underdetermined model with full row rank in general. Under this framework, each source prior is modeled as a mixture of Gaussians. This mixture model provides us an advantage that it can deal with the hybrid mixtures of both sparse and non-sparse sources, the iterative learning for Gaussians leads to parametric density estimation for each hidden source as well as their recovery in the end. Simulations by using synthetic data validate the effectiveness of the learning algorithm