Partly Smooth Regularization of Inverse Problems
Peyré, Gabriel; Vaiter, Samuel; Fadili, Jalal (2014), Partly Smooth Regularization of Inverse Problems. https://basepub.dauphine.fr/handle/123456789/13272
Type
Document de travail / Working paperDate
2014Series title
Université Paris-DauphinePublished in
Paris
Pages
21
Metadata
Show full item recordAuthor(s)
Peyré, GabrielCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Vaiter, Samuel

Fadili, Jalal
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
This article studies the regularization of inverse problems with a con- vex prior promoting some notion of low-complexity. This low-complexity is obtained by using regularizers that are partly smooth functions. Such functions force the solution of variational problems to live in a low-dimension manifold which is stable under small perturbations of the functional. This property is crucial to make the underlying low-complexity model robust to small noise. We show that a simple criterion implies the stability of the active manifold to small noise perturbations of the observation when the regularization parameter is tuned proportionally to the noise level. This unifies and generalizes several previous works, where this theorem is known to hold for sparse, group sparse, total variation and low-rank regularizations.Subjects / Keywords
Inverse problem; convexity; low-rank; partial smoothness; sensitivity analysis; sparsityRelated items
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