Blind separation of instantaneous mixture of sources via the Gaussian mutual information criterion

Abstract

A method for blind separation of an instantaneous mixture of colored sources is proposed. It is based on the minimization of the Gaussian mutual information criterion, leading to a second-order procedure, which amounts to jointly approximately diagonalizing a set of estimated spectral density matrices. An efficient algorithm for this purpose is described. It is shown that separation is achievable (up to a scaling and a permutation) if there is no pair of sources with proportional spectral densities. Results on the asymptotic performance of the procedure are derived and some simulation are performed for finite samples, showing good agreement with the theoretical findings. It is seen that nearly optimal performance can be attained by jointly approximately diagonalizing only a few spectral matrices.