Sparse Decompositions in ``incoherent'' dictionaries

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/images in a union of two orthonormal bases. We consider general (redundant) dictionaries in finite dimension, and derive sufficient conditions on a signal/image for having a unique sparse representation in such a dictionary. 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 he highly redundant. The special case where the dictionary is given by a union of several orthonormal bases is studied in more detail and some examples are given.
Type de document :
Communication dans un congrès
Proc. IEEE Intl. Conf. Image Proc. (ICIP'03), Sep 2003, Barcelona, Spain. IEEE, 1, pp.I-33 -- I-36, 2003, 〈10.1109/ICIP.2003.1246891〉
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https://hal.inria.fr/inria-00570099
Contributeur : Rémi Gribonval <>
Soumis le : samedi 26 février 2011 - 18:33:35
Dernière modification le : mardi 24 avril 2018 - 16:16:02
Document(s) archivé(s) le : vendredi 27 mai 2011 - 02:37:26

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Rémi Gribonval, Morten Nielsen. Sparse Decompositions in ``incoherent'' dictionaries. Proc. IEEE Intl. Conf. Image Proc. (ICIP'03), Sep 2003, Barcelona, Spain. IEEE, 1, pp.I-33 -- I-36, 2003, 〈10.1109/ICIP.2003.1246891〉. 〈inria-00570099〉

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