The Cosparse Analysis Model and Algorithms

Abstract : After a decade of extensive study of the sparse representation synthesis model, we can safely say that this is a mature and stable field, with clear theoretical foundations, and appealing applications. Alongside this approach, there is an analysis counterpart model, which, despite its similarity to the synthesis alternative, is markedly different. Surprisingly, the analysis model did not get a similar attention, and its understanding today is shallow and partial. In this paper we take a closer look at the analysis approach, better define it as a generative model for signals, and contrast it with the synthesis one. This work proposes effective pursuit methods that aim to solve inverse problems regularized with the analysis-model prior, accompanied by a preliminary theoretical study of their performance. We demonstrate the effectiveness of the analysis model in several experiments.
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Sangnam Nam, Mike E. Davies, Michael Elad, Rémi Gribonval. The Cosparse Analysis Model and Algorithms. Applied and Computational Harmonic Analysis, Elsevier, 2013, 34 (1), pp.30--56. 〈10.1016/j.acha.2012.03.006〉. 〈inria-00602205v2〉

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