Stable Recovery with Analysis Decomposable Priors

Abstract : In this paper, we investigate in a unified way the structural properties of solutions to inverse problems regularized by the generic class of semi-norms defined as a decomposable norm composed with a linear operator, the so-called analysis decomposable prior. This encompasses several well-known analysis-type regularizations such as the discrete total variation, 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.
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Jalal M. Fadili, Gabriel Peyré, Samuel Vaiter, Charles-Alban Deledalle, Joseph Salmon. Stable Recovery with Analysis Decomposable Priors. SPARS 2013, Jul 2013, Lausanne, Switzerland. 1 pp. ⟨hal-00926727⟩

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