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Cosparse Analysis Modeling - Uniqueness and Algorithms

Sangnam Nam 1 Michael Davies 2 Michael Elad 3 Rémi Gribonval 1
1 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : In the past decade there has been a great interest in a synthesis-based model for signals, based on sparse and redundant representations. Such a model assumes that the signal of interest can be composed as a linear combination of few columns from a given matrix (the dictionary). An alternative analysis-based model can be envisioned, where an analysis operator multiplies the signal, leading to a cosparse outcome. In this paper, we consider this analysis model, in the context of a generic missing data problem (e.g., compressed sensing, inpainting, source separation, etc.). Our work proposes a uniqueness result for the solution of this problem, based on properties of the analysis operator and the measurement matrix. This paper also considers two pursuit algorithms for solving the missing data problem, an L1-based and a new greedy method. Our simulations demonstrate the appeal of the analysis model, and the success of the pursuit techniques presented.
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Submitted on : Tuesday, February 22, 2011 - 6:33:41 PM
Last modification on : Wednesday, June 16, 2021 - 3:41:31 AM
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Sangnam Nam, Michael Davies, Michael Elad, Rémi Gribonval. Cosparse Analysis Modeling - Uniqueness and Algorithms. Acoustics, Speech and Signal Processing, IEEE International Conference on (ICASSP 2011), May 2011, Prague, Czech Republic. ⟨10.1109/ICASSP.2011.5947680⟩. ⟨inria-00557933⟩

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