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

A method for blind separation of instantaneous mixture of colored sources, based on the minimization a Gaussian mutual information criterion, is proposed. It amounts to jointly approximately diagonalizing a set of estimated spectral density matrices. Separation is shown to be achievable (up to a scaling and a permutation) if no pair of sources can have proportional spectral densities. An effcient algorithm for the joint approximate diagonalization of positive matrix is described. Theoretical results on the asymptotic performance of the procedure are given and some simulations are performed showing good agreement with the theory. It is seen that nearly optimal performance can be attained by jointly diagonalizing only a few spectral matrices.