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Publications sur convergence rate
Résultat de la recherche dans la liste des publications :
2 Articles de conférence |
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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2 - Smoothing techniques for convex problems. Applications in image processing.
P. Weiss et M. Carlavan et L. Blanc-Féraud et J. Zerubia. Dans Proc. SAMPTA (international conference on Sampling Theory and Applications), Marseille, France, mai 2009.
Mots-clés : nesterov scheme, convergence rate, Dual smoothing.
@INPROCEEDINGS{PWEISS_SAMPTA09,
|
| author |
= |
{Weiss, P. and Carlavan, M. and Blanc-Féraud, L. and Zerubia, J.}, |
| title |
= |
{Smoothing techniques for convex problems. Applications in image processing}, |
| year |
= |
{2009}, |
| month |
= |
{mai}, |
| booktitle |
= |
{Proc. SAMPTA (international conference on Sampling Theory and Applications)}, |
| address |
= |
{Marseille, France}, |
| url |
= |
{http://www.math.univ-toulouse.fr/~weiss/Publis/Conferences/Eusipco09.pdf}, |
| pdf |
= |
{http://www.math.univ-toulouse.fr/~weiss/Publis/Conferences/Sampta09.pdf}, |
| keyword |
= |
{nesterov scheme, convergence rate, Dual smoothing} |
| } |
Abstract :
In this paper, we present two algorithms to solve some inverse problems coming from the field of image processing. The problems we study are convex and can be expressed simply as sums of lp-norms of affine transforms of the image. We propose 2 different techniques. They are - to the best of our knowledge - new in the domain of image processing and one of them is new in the domain of mathematical programming. Both methods converge to the set of minimizers. Additionally, we show that they converge at least as O(1/N) (where N is the iteration counter) which is in some sense an ``optimal'' rate of convergence. Finally, we compare these approaches to some others on a toy problem of image super-resolution with impulse noise. |
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Rapport de recherche et Rapport technique |
1 - Some applications of L infinite norms in image processing.
P. Weiss et G. Aubert et L. Blanc-Féraud. Rapport de Recherche 6115, INRIA, septembre 2006.
Mots-clés : projected subgradient descent, convergence rate, Variation totale, compression bounded noise, meyer G norm, fast l1 minimization.
@TECHREPORT{Some applications of L infinite constraints,
|
| author |
= |
{Weiss, P. and Aubert, G. and Blanc-Féraud, L.}, |
| title |
= |
{Some applications of L infinite norms in image processing}, |
| year |
= |
{2006}, |
| month |
= |
{septembre}, |
| institution |
= |
{INRIA}, |
| type |
= |
{Research Report}, |
| number |
= |
{6115}, |
| url |
= |
{http://www.math.univ-toulouse.fr/~weiss/Publis/RR-6115.pdf}, |
| pdf |
= |
{ftp://ftp-sop.inria.fr/ariana/Articles/2006_Some applications of L infinite constraints.pdf}, |
| keyword |
= |
{projected subgradient descent, convergence rate, Variation totale, compression bounded noise, meyer G norm, fast l1 minimization} |
| } |
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