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 correspondence is to generalize a result by Donoho and Huo and Elad and Bruckstein on sparse representations of signals in a union of two orthonormal bases for R^N. We consider general (redundant) dictionaries for R^N, and derive sufficient conditions for having unique sparse representations of signals in such dictionaries. The special case where the dictionary is given by the union of L \ge 2 orthonormal bases for R^N is studied in more detail. In particular, it is proved that the result of Donoho and Huo, concerning the replacement of the \ell^0 optimization problem with a linear programming problem when searching for sparse representations, has an analog for dictionaries that may be highly redundant.
Type de document :
Article dans une revue
IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2003, 49 (12), pp.3320--3325. 〈10.1109/TIT.2003.820031〉
Liste complète des métadonnées

Littérature citée [6 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00570057
Contributeur : Rémi Gribonval <>
Soumis le : samedi 26 février 2011 - 21:10:06
Dernière modification le : mercredi 16 mai 2018 - 11:23:03
Document(s) archivé(s) le : mardi 6 novembre 2012 - 15:06:25

Fichier

MultiONB-final-copyrighted.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Citation

Rémi Gribonval, Morten Nielsen. Sparse representations in unions of bases. IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2003, 49 (12), pp.3320--3325. 〈10.1109/TIT.2003.820031〉. 〈inria-00570057〉

Partager

Métriques

Consultations de la notice

327

Téléchargements de fichiers

525