Sparse decomposition of stereo signals with Matching Pursuit and application to blind separation of more than two sources from a stereo mixture

We develop a method of sparse decomposition of stereo audio signals, and test its application to blind separation of more than two sources from only two linear mixtures. The decomposition is done in a stereo dictionary which we can define based on any standard time-frequency or time-scale dictionary, such as the multiscale Gabor dictionary. A decomposition of a stereo mixture in the dictionary is computed with a Matching Pursuit type algorithm called Stereo Matching Pursuit. We experiment an application to blind source separation with three (mono) sources mixed on two channels. We cluster the parameters of the stereo atoms of the decomposition to estimate the mixing parameters, and recover estimates. of the sources by a partial reconstruction using only the appropriate atoms of the decomposition. The method outperforms the best achievable linear demixing by 3 dB to more than 7 dB on our preliminary experiments, and its performance should increase as we let the number of iterations of the pursuit increase. Sample sound files can be found here: http://www.irisa.fr/metiss/gribonva/