1 - A proximal method for inverse problems in image processing.
P. Weiss et L. Blanc-Féraud. Dans Proc. European Signal Processing Conference (EUSIPCO), Glasgow, Scotland, août 2009.
Mots-clés : Extragradient method, proximal method, Decomposition d'images, Meyer's model, convergence rate.
@INPROCEEDINGS{PWEISS_Eusipco,
|
| author |
= |
{Weiss, P. and Blanc-Féraud, L.}, |
| title |
= |
{A proximal method for inverse problems in image processing}, |
| year |
= |
{2009}, |
| month |
= |
{août}, |
| booktitle |
= |
{Proc. European Signal Processing Conference (EUSIPCO)}, |
| address |
= |
{Glasgow, Scotland}, |
| url |
= |
{http://www.math.univ-toulouse.fr/~weiss/Publis/Conferences/Eusipco09.pdf}, |
| pdf |
= |
{http://www.math.univ-toulouse.fr/~weiss/Publis/Conferences/Eusipco09.pdf}, |
| keyword |
= |
{Extragradient method, proximal method, Decomposition d'images, Meyer's model, convergence rate} |
| } |
Abstract :
In this paper, we present a new algorithm to solve some inverse problems coming from the field of image processing. The models we study consist in minimizing a regularizing, convex criterion under a convex and compact set. The main idea of our scheme consists in solving the underlying variational inequality with a proximal method rather than the initial convex problem. Using recent results of A. Nemirovski [13], we show that the scheme converges at least as O(1/k) (where k is the iteration counter). This is in some sense an optimal rate of convergence. Finally, we compare this approach to some others on a problem of image cartoon+texture decomposition. |
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