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| HAL : hal-00637003, version 2 |
| DOI : 10.1109/TIT.2013.2238606 |
| Fiche détaillée |  Récupérer au format |
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| IEEE Transactions on Information Theory 59, 5 (2013) 3158-3174 |
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| Versions disponibles : | v1 (02-11-2011) | v2 (13-11-2012) |
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| Joint k-step analysis of Orthogonal Matching Pursuit and Orthogonal Least Squares |
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| Charles Soussen 1Rémi Gribonval 2 |
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| (05/2013) |
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| Tropp's analysis of Orthogonal Matching Pursuit (OMP) using the Exact Recovery Condition (ERC) is extended to a first exact recovery analysis of Orthogonal Least Squares (OLS). We show that when the ERC is met, OLS is guaranteed to exactly recover the unknown support in at most k iterations where k denotes the support cardinality. Moreover, we provide a closer look at the analysis of both OMP and OLS when the ERC is not fulfilled. The existence of dictionaries for which some subsets are never recovered by OMP is proved. This phenomenon also appears with basis pursuit where support recovery depends on the sign patterns, but it does not occur for OLS. Finally, numerical experiments show that none of the considered algorithms is uniformly better than the other but for correlated dictionaries, guaranteed exact recovery may be obtained after fewer iterations for OLS than for OMP. |
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| 1 : | Centre de recherche en automatique de Nancy (CRAN) |
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CNRS : UMR7039 – Université Henri Poincaré - Nancy I – Institut National Polytechnique de Lorraine (INPL) |
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| 2 : | METISS (INRIA - IRISA) |
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CNRS : UMR6074 – INRIA – Institut National des Sciences Appliquées (INSA) - Rennes – Université de Rennes 1 |
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| 3 : | Institut de Recherche en Communications et en Cybernétique de Nantes (IRCCyN) |
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CNRS : UMR6597 – PRES Université Nantes Angers Le Mans [UNAM] – École Centrale de Nantes – École Nationale Supérieure des Mines - Nantes – Ecole Polytechnique de l'Université de Nantes |
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| 4 : | FLUMINANCE (INRIA - CEMAGREF) |
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INRIA – CEMAGREF |
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| Domaine | : | Sciences de l'ingénieur/Automatique / Robotique |
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| Exact recovery condition (ERC) – forward selection – Orthogonal Matching Pursuit (OMP) – Orthogonal Least Squares (OLS) – Order Recursive Matching Pursuit (ORMP) – Optimized Orthogonal Matching Pursuit (OOMP). |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00637003, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00637003 | |
| oai:hal.archives-ouvertes.fr:hal-00637003 | |
| Contributeur : Charles Soussen | |
| Soumis le : Mardi 13 Novembre 2012, 16:19:57 | |
| Dernière modification le : Mercredi 24 Avril 2013, 18:00:37 | |
