FADILI, Jalal M.; PEYRÉ, Gabriel; VAITER, Samuel; DELEDALLE, Charles-Alban; SALMON, Joseph

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FADILI, Jalal M.
Equipe Image - Laboratoire GREYC - UMR6072

PEYRÉ, Gabriel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

VAITER, Samuel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

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Proc. SampTA'13, Proc. SampTA'13, Proc. SampTA'13, 2013-07, Bremen. 2013p. 113-116

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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.< Réduire

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Stable Recovery with Analysis Decomposable Priors

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