Sparse decompositions in 'incoherent' dictionaries

R. Gribonval; Morten Nielsen

doi:10.1109/ICIP.2003.1246891

Sparse decompositions in 'incoherent' dictionaries

R. Gribonval, Morten Nielsen

Institut for Matematiske Fag

Publikation: Bidrag til bog/antologi/rapport/konference proceeding › Konferenceartikel i proceeding › Forskning

12 Citationer (Scopus)

Abstrakt

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 be 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.

Originalsprog	Engelsk
Titel	Proceedings of the 2003 International Conference on Image Processing
Vol/bind	1
Forlag	Kluwer Academic Publishers
Publikationsdato	2003
Sider	33-36
ISBN (Elektronisk)	0-7803-7750-8
DOI	https://doi.org/10.1109/ICIP.2003.1246891
Status	Udgivet - 2003
Begivenhed	2003 International Conference on Image Processing - Varighed: 14 sep. 2003 → 17 sep. 2003

Konference

Konference	2003 International Conference on Image Processing
Periode	14/09/2003 → 17/09/2003

Bibliografisk note

ISSN ; 1522-4880

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10.1109/ICIP.2003.1246891

Citationsformater

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title = "Sparse decompositions in 'incoherent' dictionaries",

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 be 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.",

author = "R. Gribonval and Morten Nielsen",

note = "ISSN ; 1522-4880; null ; Conference date: 14-09-2003 Through 17-09-2003",

year = "2003",

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language = "English",

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AU - Gribonval, R.

AU - Nielsen, Morten

N1 - ISSN ; 1522-4880

PY - 2003

Y1 - 2003

N2 - 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 be 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.

AB - 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 be 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.

U2 - 10.1109/ICIP.2003.1246891

DO - 10.1109/ICIP.2003.1246891

M3 - Article in proceeding

VL - 1

SP - 33

EP - 36

BT - Proceedings of the 2003 International Conference on Image Processing

PB - Kluwer Academic Publishers

Y2 - 14 September 2003 through 17 September 2003

ER -

Sparse decompositions in 'incoherent' dictionaries

Abstrakt

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