MAP-based permutation alignment for underdetermined convolutive blind source separation

This paper considers the alignment of permutation for underdetermined blind source separation of convolutively mixed sparse signals in the frequency domain. To resolve the permutation ambiguities between the sources of neighbor frequency bins, a probabilistic approach based on maximizing a posteriori (MAP) is proposed. The prior distribution of the sources is assumed to follow a dependent multivariate super-Gaussian which considers statistical dependence between neighbor frequency bins. It is difficult to obtain the posterior probabilities of all possible permutations which contain a mathematically intractable integration, thus the integrand is approximated as an integrable form, a summation of Dirac delta functions. Given approximated posterior probabilities, the permutation which has the highest posterior probability is selected. It is experimentally shown that the proposed algorithm is better than conventional algorithms in some specific cases in terms of alignment accuracy.