We cast the under-determined convolutive speech separation as sparse approximation of the spatial spectra of the mixing sources. In this framework we compare and contrast the major practical algorithms for structured sparse recovery of speech signal. Specific attention is paid to characterization of the measurement matrix. We first propose how it can be identified using the Image model of multipath effect where the acoustic parameters are estimated by localizing a speaker and its images in a free space model. We further study the circumstances in which the coherence of the projections induced by microphone array design tend to affect the recovery performance.
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