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

Alexis Benichoux 1 Prasad Sudhakar 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 : A well-known issue in blind convolutive source separation is that the sources and filters are at best identifiable up to an arbitrary scaling and permutation at each frequency bin. We propose to exploit the sparsity of the filters as a consistency measure for correcting such permutations. We show that the permutation is well-posed, up to a global permutation, under appropriate sparsity hypotheses on the filters. A greedy combinatorial algorithm is proposed for permutation recovery. Its empirical performance shows that the time-domain sparsity of the filters allows to recover permutations much beyond theoretical predictions.
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Alexis Benichoux, Prasad Sudhakar, Rémi Gribonval. Well-posedness of the frequency permutation problem in sparse filter estimation with lp minimization. Signal Processing with Adaptive Sparse Structured Representations, Jun 2011, Edinburgh, United Kingdom. ⟨inria-00587789⟩

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