Learning adapted dictionaries for geometry and texture separation

Gabriel Peyré; Jalal Fadili; Jean-Luc Starck

doi:10.1117/12.731244

20 September 2007 Learning adapted dictionaries for geometry and texture separation

Gabriel Peyré, Jalal Fadili, Jean-Luc Starck

Author Affiliations +

Proceedings Volume 6701, Wavelets XII; 67011T (2007) https://doi.org/10.1117/12.731244
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

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.

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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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