Beyond coherence: Recovering structured time-frequency representations

Lasse Borup; Rémi Gribonval; Morten Nielsen

doi:10.1016/j.acha.2007.09.002

Beyond coherence: Recovering structured time-frequency representations

Lasse Borup, Rémi Gribonval, Morten Nielsen

Institut for Matematiske Fag

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

11 Citationer (Scopus)

Abstract

Udgivelsesdato: JAN

Originalsprog	Engelsk
Tidsskrift	Applied and Computational Harmonic Analysis
Vol/bind	24
Udgave nummer	1
Sider (fra-til)	120-128
Antal sider	9
ISSN	1063-5203
DOI	https://doi.org/10.1016/j.acha.2007.09.002
Status	Udgivet - 2008

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10.1016/j.acha.2007.09.002

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Citationsformater

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title = "Beyond coherence: Recovering structured time-frequency representations",

abstract = "We consider the problem of recovering a structured sparse representation of a signal in an overcomplete time-frequency dictionary with a particular structure. For infinite dictionaries that are the union of a nice wavelet basis and a Wilson basis, sufficient conditions are given for the basis pursuit and (orthogonal) matching pursuit algorithms to recover a structured representation of an admissible signal. The sufficient conditions take into account the structure of the wavelet/Wilson dictionary and allow very large (even infinite) support sets to be recovered even though the dictionary is highly coherent.",

author = "Lasse Borup and R{\'e}mi Gribonval and Morten Nielsen",

year = "2008",

doi = "10.1016/j.acha.2007.09.002",

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T1 - Beyond coherence: Recovering structured time-frequency representations

AU - Borup, Lasse

AU - Gribonval, Rémi

AU - Nielsen, Morten

PY - 2008

Y1 - 2008

N2 - We consider the problem of recovering a structured sparse representation of a signal in an overcomplete time-frequency dictionary with a particular structure. For infinite dictionaries that are the union of a nice wavelet basis and a Wilson basis, sufficient conditions are given for the basis pursuit and (orthogonal) matching pursuit algorithms to recover a structured representation of an admissible signal. The sufficient conditions take into account the structure of the wavelet/Wilson dictionary and allow very large (even infinite) support sets to be recovered even though the dictionary is highly coherent.

AB - We consider the problem of recovering a structured sparse representation of a signal in an overcomplete time-frequency dictionary with a particular structure. For infinite dictionaries that are the union of a nice wavelet basis and a Wilson basis, sufficient conditions are given for the basis pursuit and (orthogonal) matching pursuit algorithms to recover a structured representation of an admissible signal. The sufficient conditions take into account the structure of the wavelet/Wilson dictionary and allow very large (even infinite) support sets to be recovered even though the dictionary is highly coherent.

U2 - 10.1016/j.acha.2007.09.002

DO - 10.1016/j.acha.2007.09.002

M3 - Journal article

SN - 1063-5203

VL - 24

SP - 120

EP - 128

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

IS - 1

ER -

Beyond coherence: Recovering structured time-frequency representations

Abstract

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