Paper
20 September 2007 Learning adapted dictionaries for geometry and texture separation
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Abstract
This article proposes a new method for image separation into a linear combination of morphological components. This method is applied to decompose an image into meaningful cartoon and textural layers and is used to solve more general inverse problems such as image inpainting. For each of these components, a dictionary is learned from a set of exemplar images. Each layer is characterized by a sparse expansion in the corresponding dictionary. The separation inverse problem is formalized within a variational framework as the optimization of an energy functional. The morphological component analysis algorithm allows to solve iteratively this optimization problem under sparsity-promoting penalties. 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.
© (2007) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Gabriel Peyré, Jalal Fadili, and Jean-Luc Starck "Learning adapted dictionaries for geometry and texture separation", Proc. SPIE 6701, Wavelets XII, 67011T (20 September 2007); https://doi.org/10.1117/12.731244
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CITATIONS
Cited by 26 scholarly publications and 1 patent.
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KEYWORDS
Associative arrays

Wavelets

Inverse problems

Optimization (mathematics)

Image restoration

Image processing

Transform theory

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