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Well-posedness of the permutation problem in sparse filter estimation with lp minimization

Alexis Benichoux 1, 2 Prasad Sudhakar 1 Frédéric Bimbot 1, 2 Rémi Gribonval 1, 2
1 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
2 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : Convolutive source separation is often done in two stages: 1) estimation of the mixing filters and 2) estimation of the sources. Traditional approaches suffer from the ambiguities of arbitrary permutations and scaling in each frequency bin of the estimated filters and/or the sources, and they are usually corrected by taking into account some special properties of the filters/sources. This paper focusses on the filter permutation problem in the absence of scaling, investigating the possible use of the temporal sparsity of the filters as a property enabling permutation correction. Theoretical and experimental results highlight the potential as well as the limits of sparsity as an hypothesis to obtain a well-posed permutation problem.
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Submitted on : Thursday, December 20, 2012 - 11:00:39 PM
Last modification on : Wednesday, June 16, 2021 - 3:41:57 AM
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Alexis Benichoux, Prasad Sudhakar, Frédéric Bimbot, Rémi Gribonval. Well-posedness of the permutation problem in sparse filter estimation with lp minimization. Applied and Computational Harmonic Analysis, Elsevier, 2013, 35 (3), pp.394-406. ⟨10.1016/j.acha.2012.11.001⟩. ⟨hal-00767139⟩

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