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Sparse Representations in Unions of Bases

Rémi Gribonval 1 Morten Nielsen 2
1 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : The purpose of this paper is to generalize a result by Donoho, Huo, Elad and Bruckstein on sparse representations of signals in a union of two orthonormal bases. We consider general (redundant) dictionaries in finite dimension, and derive sufficient conditions on a signal for having unique sparse representations in such dictionaries. The special case where the dictionary is given by a union of several orthonormal bases is studied in more detail. In particular, it is proved that the result of Donoho and Huo, concerning the replacement of a combinatorial optimization problem with a linear programming problem when searching for sparse representations, has an analog for dictionaries that may be highly redundant.
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https://hal.inria.fr/inria-00071943
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Submitted on : Tuesday, May 23, 2006 - 7:19:23 PM
Last modification on : Friday, February 4, 2022 - 3:22:20 AM
Long-term archiving on: : Sunday, April 4, 2010 - 10:45:39 PM

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  • HAL Id : inria-00071943, version 1

Citation

Rémi Gribonval, Morten Nielsen. Sparse Representations in Unions of Bases. [Research Report] RR-4642, INRIA. 2002. ⟨inria-00071943⟩

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