Coherence-based Partial Exact Recovery Condition for OMP/OLS

Abstract : We address the exact recovery of the support of a k-sparse vector with Orthogonal Matching Pursuit (OMP) and Orthogonal Least Squares (OLS) in a noiseless setting. We consider the scenario where OMP/OLS have selected good atoms during the first l iterations (l < k) and derive a new sufficient and worst-case necessary condition for their success in k steps. Our result is based on the coherence of the dictionary and relaxes Tropp's well-known condition < 1=(2k 1) to the case where OMP/OLS have a partial knowledge of the support.
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Pré-publication, Document de travail
IRIS, SBS. A revised version of this preprint appeared in the IEEE Trans. on Information Theory, vol 59, nr .. 2012
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Contributeur : Cedric Herzet <>
Soumis le : vendredi 30 novembre 2012 - 15:57:06
Dernière modification le : jeudi 11 janvier 2018 - 06:24:14
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  • HAL Id : hal-00759433, version 1

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Cedric Herzet, Charles Soussen, Jérôme Idier, Rémi Gribonval. Coherence-based Partial Exact Recovery Condition for OMP/OLS. IRIS, SBS. A revised version of this preprint appeared in the IEEE Trans. on Information Theory, vol 59, nr .. 2012. 〈hal-00759433〉

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