Underdetermined blind separation of delayed sound sources in the frequency domain

This paper focuses on the blind separation of n sources from m mixtures when the underlying system is underdetermined (i.e., when m < n), as applied to mixtures with only attenuations and delays (i.e., no reverberation). The separation is realized in the frequency domain where, at least for speech and music signals, the representation is sparse. The procedure is organized in three stages. First, the matrix of relative attenuations is inferred by angular clustering of the magnitude of the input, yielding a coarse partition of the data into their nearest sources. Second, for each partition, the differential delay is inferred by shifting the sensor channels and scattering the real and imaginary components until the cluster reappears. And third, given the attenuation and delay matrices, the sources are inferred at each frequency bin by assuming that the magnitude of the spectral coefficients is Laplacian distributed, which leads to the minimization of the sum of magnitudes, subject to the mixing equations. The resulting problem is an instance of second-order cone programming. The approach is experimentally illustrated for m = 2 sensors and n up to six speech and music sources, using synthetic mixtures simulating real acoustic scenarios without reverberation. (C) 2002 Elsevier B.V. All rights reserved.