Greedy-like algorithms for the cosparse analysis model

R. Giryes, M. Elad, S. Nam, R. Gribonval, M.E. Davies

Research output: Contribution to journalArticlepeer-review


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 ℓ 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.
Original languageEnglish
Pages (from-to)22-60
JournalLinear algebra and its applications
Publication statusPublished - 1 Jan 2014


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