Some uniqueness results in sparse convolutive source separation

Alexis Benichoux 1 Prasad Sudhakar 1 Frédéric Bimbot 1 Rémi Gribonval 1
1 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : The fundamental problems in the traditional frequency do- main approaches to convolutive blind source separation are 1) arbitrary permutations and 2) arbitrary scaling in each frequency bin of the esti- mated filters or sources. These ambiguities are corrected by taking into account some specific properties of the filters or sources, or both. This paper focusses on the filter permutation problem, assuming the absence of the scaling ambiguity, investigating the use of temporal sparsity of the filters as a property to aid permutation correction. Theoretical and ex- perimental results bring out the potential as well as the extent to which sparsity can be used as a hypothesis to formulate a well posed permuta- tion problem.
Keywords : bi-stochastic matrices sparse filters convolutive blind source separation permuta- tion ambiguity lp minimization Hall's Marriage Theorem bi-stochastic matrices.
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Conference papers
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Alexis Benichoux, Prasad Sudhakar, Frédéric Bimbot, Rémi Gribonval. Some uniqueness results in sparse convolutive source separation. International Conference on Latent Variable Analysis and Source Separation, Mar 2012, Tel Aviv, Israel. ⟨hal-00659913⟩

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