hal-00716593, version 2

## Greedy-Like Algorithms for the Cosparse Analysis Model

Raja Giryes a1, Sangnam Nam () b2, Michael Elad () 1, Rémi Gribonval (, ) 2, Mike E. Davies () 3

Résumé : The cosparse analysis model has been introduced recently as an interesting alternative to the standard sparse synthesis approach. A prominent question brought up by this new construction is the analysis pursuit problem -- the need to find a signal belonging to this model, given a set of corrupted measurements of it. Several pursuit methods have already been proposed based on $\ell_1$ relaxation and a greedy approach. In this work we pursue this question further, and propose a new family of pursuit algorithms for the cosparse analysis model, mimicking the greedy-like methods -- compressive sampling matching pursuit (CoSaMP), subspace pursuit (SP), iterative hard thresholding (IHT) and hard thresholding pursuit (HTP). Assuming the availability of a near optimal projection scheme that finds the nearest cosparse subspace to any vector, we provide performance guarantees for these algorithms. Our theoretical study relies on a restricted isometry property adapted to the context of the cosparse analysis model. We explore empirically the performance of these algorithms by adopting a plain thresholding projection, demonstrating their good performance.

• Domaine : Informatique/Traitement du signal et de l'image
Sciences de l'ingénieur/Traitement du signal et de l'image
Mathématiques/Analyse fonctionnelle
• Mots-clés : Sparse representations – Compressed sensing – Synthesis – Analysis – CoSaMP – Subspace-pursuit – Iterative hard threshodling – Hard thresholding pursuit.
• Commentaire : partially funded by the ERC – PLEASE project – ERC-2011-StG-277906
• Versions disponibles :  v1 (10-07-2012) v2 (18-01-2013)

• hal-00716593, version 2
• oai:hal.inria.fr:hal-00716593
• Contributeur :
• Soumis le : Vendredi 18 Janvier 2013, 11:01:29
• Dernière modification le : Mardi 7 Mai 2013, 16:39:53