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hal-00716593, version 1

## Greedy-Like Algorithms for the Cosparse Analysis Model

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

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.

• a –  Technion
• b –  INRIA
• 1:  Department of Computer Science [Haifa]
• University of Haifa
• 2:  METISS (INRIA - IRISA)
• CNRS : UMR6074 – INRIA – Institut National des Sciences Appliquées (INSA) - Rennes – Université de Rennes 1
• 3:  Institute for Digital Communication Joint Research Institute for Signal & Image Processing School of Engineering and Electronics - University of Edinburgh
• University of Edinburgh
• Domain : Computer Science/Signal and Image Processing
Engineering Sciences/Signal and Image processing
Mathematics/Functional Analysis
• Keywords : Sparse representations – Compressed sensing – Synthesis – Analysis – CoSaMP – Subspace-pursuit – Iterative hard threshodling – Hard thresholding pursuit.
• Available versions :  v1 (2012-07-10) v2 (2013-01-18)

• hal-00716593, version 1
• oai:hal.inria.fr:hal-00716593
• From:
• Submitted on: Tuesday, 10 July 2012 20:31:49
• Updated on: Tuesday, 10 July 2012 21:56:55