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| HAL : hal-00415782, version 2 |
| DOI : 10.1137/090770783 |
| Fiche détaillée |  Récupérer au format |
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| SIAM Journal on Imaging Sciences 3, 3 (2010) 646-669 |
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| Versions disponibles : | v1 (11-09-2009) | v2 (08-07-2010) |
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| Learning the Morphological Diversity |
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| Gabriel Peyré 1Jalal Fadili 2 |
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| (07/2010) |
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| This article proposes a new method for image separation into a linear combination of morphological components. Sparsity in global dictionaries is used to extract the cartoon and oscillating content of the image. Complicated texture patterns are extracted by learning adapted local dictionaries that sparsify patches in the image. These global and local sparsity priors together with the data fidelity define a non-convex energy and the separation is obtained as a stationary point of this energy. This variational optimization is extended to solve more general inverse problems such as inpainting. A new adaptive morphological component analysis algorithm is derived to find a stationary point of the energy. Using adapted dictionaries learned from data allows to circumvent some difficulties faced by fixed dictionaries. Numerical results demonstrate that this adaptivity is indeed crucial to capture complex texture patterns. |
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| 1 : | CEntre de REcherches en MAthématiques de la DEcision (CEREMADE) |
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CNRS : UMR7534 – Université Paris IX - Paris Dauphine |
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| 2 : | Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen (GREYC) |
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CNRS : UMR6072 – Université de Caen – Ecole Nationale Supérieure d'Ingénieurs de Caen |
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| 3 : | Service d'Electronique, des Détecteurs et d'Informatique (SEDI) |
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CEA : DSM/IRFU |
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| Domaine | : | Informatique/Traitement du signal et de l'image Sciences de l'ingénieur/Traitement du signal et de l'image |
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| Adaptive morphological component analysis – sparsity – image separation – inpainting – dictionary learning – cartoon images – texture – wavelets |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00415782, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00415782 | |
| oai:hal.archives-ouvertes.fr:hal-00415782 | |
| Contributeur : Gabriel Peyré | |
| Soumis le : Mercredi 7 Juillet 2010, 22:35:03 | |
| Dernière modification le : Dimanche 2 Janvier 2011, 15:52:36 | |
