Image restoration is a well-known ill-posed inverse problem whose aim is to recover a sharp clean image from the corresponding blur- and noise-corrupted observation. Variational methods penalize solutions deemed undesirable by incorporating regularization techniques. A popular strategy relies on using sparsity promoting regularizers; it is well known that, in general, nonconvex regularizers hold the potential for promoting sparsity more effectively than convex regularizers. Recently a new class of convex non-convex (CNC) variational models has been proposed which includes a general parametric nonconvex nonseparable regularizer. However, the performance of this approach depends critically on the regularization parameter. In this paper we propose to use a parametric CNC variational restoration model within a bilevel framework, where the parameter is tuned by minimizing a measure of the restoration residual whiteness. Some preliminary numerical experiments are shown which indicate the effectiveness of the proposal.

Automatic Parameter Selection Based on Residual Whiteness for Convex Non-convex Variational Restoration

Lanza A.
Primo
Membro del Collaboration Group
;
Morigi S.
Secondo
Membro del Collaboration Group
;
Sgallari F.
Ultimo
Membro del Collaboration Group
2021

Abstract

Image restoration is a well-known ill-posed inverse problem whose aim is to recover a sharp clean image from the corresponding blur- and noise-corrupted observation. Variational methods penalize solutions deemed undesirable by incorporating regularization techniques. A popular strategy relies on using sparsity promoting regularizers; it is well known that, in general, nonconvex regularizers hold the potential for promoting sparsity more effectively than convex regularizers. Recently a new class of convex non-convex (CNC) variational models has been proposed which includes a general parametric nonconvex nonseparable regularizer. However, the performance of this approach depends critically on the regularization parameter. In this paper we propose to use a parametric CNC variational restoration model within a bilevel framework, where the parameter is tuned by minimizing a measure of the restoration residual whiteness. Some preliminary numerical experiments are shown which indicate the effectiveness of the proposal.
Springer Proceedings in Mathematics and Statistics
95
111
Lanza A.; Morigi S.; Sgallari F.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11585/843977
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