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Stable Recovery with Analysis Decomposable Priors

Abstract : In this paper, we investigate in a unified way the structural properties of solutions to inverse problems. These solutions are regularized by the generic class of semi-norms defined as a decomposable norm composed with a linear operator, the so-called analysis type decomposable prior. This encompasses several well-known analysis-type regularizations such as the discrete total variation (in any dimension), analysis group-Lasso or the nuclear norm. Our main results establish sufficient conditions under which uniqueness and stability to a bounded noise of the regularized solution are guaranteed. Along the way, we also provide a strong sufficient uniqueness result that is of independent interest and goes beyond the case of decomposable norms.
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https://hal.archives-ouvertes.fr/hal-00926732
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Submitted on : Friday, January 10, 2014 - 10:39:24 AM
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  • HAL Id : hal-00926732, version 1

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Jalal M. Fadili, Gabriel Peyré, Samuel Vaiter, Charles-Alban Deledalle, Joseph Salmon. Stable Recovery with Analysis Decomposable Priors. Proc. SampTA'13, Jul 2013, Bremen, Germany. pp.113-116. ⟨hal-00926732⟩

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