Thumbnail

Stable Recovery with Analysis Decomposable Priors

Salmon, Joseph; Deledalle, Charles-Alban; Vaiter, Samuel; Peyré, Gabriel; Fadili, Jalal (2013), Stable Recovery with Analysis Decomposable Priors, Proceedings SampTA 2013, EURASIP, p. 113-116

View/Open
Type
Communication / Conférence
Date
2013
Conference title
SampTA 2013
Conference date
2013-07
Conference city
Bremen
Conference country
Allemagne
Book title
Proceedings SampTA 2013
Publisher
EURASIP
Pages
113-116
Metadata
Show full item record
Author(s)
Salmon, Joseph cc
Laboratoire Traitement et Communication de l'Information [LTCI]
Deledalle, Charles-Alban

Vaiter, Samuel cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Peyré, Gabriel
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Fadili, Jalal
Groupe de Recherche en Informatique, Image et Instrumentation de Caen [GREYC]
Abstract (EN)
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.
Subjects / Keywords
inverse problems; analysis regularization