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Learning the Morphological Diversity

Starck, Jean-Luc; Fadili, Jalal; Peyré, Gabriel (2010), Learning the Morphological Diversity, SIAM Journal on Imaging Sciences, 3, 3, p. 646-669. http://dx.doi.org/10.1137/090770783

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00415782/fr/
Date
2010
Journal name
SIAM Journal on Imaging Sciences
Volume
3
Number
3
Publisher
SIAM
Pages
646-669
Publication identifier
http://dx.doi.org/10.1137/090770783
Metadata
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Author(s)
Starck, Jean-Luc
Fadili, Jalal
Peyré, Gabriel
Abstract (EN)
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.
Subjects / Keywords
Adaptive morphological component analysis; sparsity; image separation; inpainting; dictionary learning; cartoon images; texture; wavelets

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