A Gaussian mixture model for underdetermined independent component analysis

This paper proposes a Bayesian Independent Component Analysis based on the Gaussian mixture model for underdetermined blind source separation. 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. The correlations are approximated with the help of linear response theory and factorized approximation to the true posterior. Under this framework, each source prior is modeled as a mixture of Gaussians. This mixture model provides us a flexibility that it can deal with the hybrid mixtures of both sparse and non-sparse sources, while most algorithms for underdetermined model only assume sparse prior for the sources. Simulations by using synthetic data validate the effectiveness of the learning algorithm.