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Apprentissage de dictionnaire faiblement cohérent par programmation quadratique mixte

Yuan Liu 1 Stephane Canu 1 Paul Honeine 1 Su Ruan 2
1 DocApp - LITIS - Equipe Apprentissage
LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
2 QuantIF-LITIS - Equipe Quantification en Imagerie Fonctionnelle
LITIS - Laboratoire d'Informatique, de Traitement de l'Information et des Systèmes
Abstract : Sparse representations with dictionary learning has been successfully explored in signal and image processing, as well as in vision and pattern recognition. Several theoretical studies have proven the importance of learning a low-coherence dictionary, i.e., low correlation between its elements. The resulting optimization problem being non-convex and non-smooth, resolution methods rely on constraints relaxation, such as by adding a de-correlation step to each iteration. In this paper, we solve the problem with its explicit constraints. To this end, the sparse coding subproblem is addressed with two strategies, by proximal algorithm or by mixed integer quadratic program (MIQP). The dictionary update is addressed by combining the augmented Lagrangian method (ADMM) and the Extended Proximal Alternative Linearized Minimization (EPALM) method, which is suitable for non-convex problems. We show the relevance of the MIQP+EPALM method in image reconstruction.
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Submitted on : Sunday, July 14, 2019 - 6:08:21 PM
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Yuan Liu, Stephane Canu, Paul Honeine, Su Ruan. Apprentissage de dictionnaire faiblement cohérent par programmation quadratique mixte. 27-ème Colloque GRETSI sur le Traitement du Signal et des Images, Aug 2019, Lille, France. ⟨hal-02183029⟩

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