Bayesian space-frequency separation of wide-band sound sources by a hierarchical approach

This paper proposes an efficient solution to the separation of uncorrelated wide-band sound sources which overlap each other in both space and frequency domains. The space-frequency separation is solved in a hierarchical way by (1) expanding the sound sources onto a set of spatial basis functions whose coefficients become the unknowns of the problem (backpropagation step) and (2) blindly demixing the coefficients of the spatial basis into uncorrelated components relating to sources of distinct physical origins (separation step). The backpropagation and separation steps are both investigated from a Bayesian perspective. In particular, Markov Chain Monte Carlo sampling is advocated to obtain Bayesian estimates of the separated sources. Separation is guaranteed for sound sources having different power spectra and sufficiently smooth spatial modes with respect to frequency. The validity and efficiency of the proposed separation procedure are demonstrated on laboratory experiments.