Binary Sparse Coding of Convolutive Mixtures for Sound Localization and Separation via Spatialization

We propose a sparse coding approach to address the problem of source-sensor localization and speech reconstruction. This approach relies on designing a dictionary of spatialized signals by projecting the microphone array recordings into the array manifolds characterized for different locations in a reverberant enclosure using the image model. Sparse representation over this dictionary enables identifying the subspace of the actual recordings and its correspondence to the source and sensor locations. The speech signal is reconstructed by inverse filtering the acoustic channels associated to the array manifolds. We provide rigorous analysis on the optimality of speech reconstruction by elucidating the links between inverse filtering and source separation followed by deconvolution. This procedure is evaluated for localization, reconstruction and recognition of simultaneous speech sources using real data recordings. The results demonstrate the effectiveness of the proposed approach and compare favorably against beamforming and independent component analysis techniques.