# Greedy-Like Algorithms for the Cosparse Analysis Model

2 PANAMA - Parcimonie et Nouveaux Algorithmes pour le Signal et la Modélisation Audio
Inria Rennes – Bretagne Atlantique , IRISA-D5 - SIGNAUX ET IMAGES NUMÉRIQUES, ROBOTIQUE
Abstract : 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.
Keywords :
Document type :
Journal articles
Domain :

https://hal.inria.fr/hal-00716593
Contributor : Rémi Gribonval <>
Submitted on : Friday, January 18, 2013 - 11:01:29 AM
Last modification on : Friday, November 16, 2018 - 1:39:11 AM
Document(s) archivé(s) le : Saturday, April 1, 2017 - 6:56:13 AM

### Files

analysis_greedy_like.pdf
Files produced by the author(s)

### Citation

Raja Giryes, Sangnam Nam, Michael Elad, Rémi Gribonval, Mike E. Davies. Greedy-Like Algorithms for the Cosparse Analysis Model. Linear Algebra and its Applications, Elsevier, 2014, Special Issue on Sparse Approximate Solution of Linear Systems, 441, pp.22--60. ⟨10.1016/j.laa.2013.03.004⟩. ⟨hal-00716593v2⟩

Record views