
Publications about convergence rate
Result of the query in the list of publications :
2 Conference articles 
1  A proximal method for inverse problems in image processing. P. Weiss and L. BlancFéraud. In Proc. European Signal Processing Conference (EUSIPCO), Glasgow, Scotland, August 2009. Keywords : Extragradient method, proximal method, Image decomposition, Meyer's model, convergence rate.
@INPROCEEDINGS{PWEISS_Eusipco,

author 
= 
{Weiss, P. and BlancFéraud, L.}, 
title 
= 
{A proximal method for inverse problems in image processing}, 
year 
= 
{2009}, 
month 
= 
{August}, 
booktitle 
= 
{Proc. European Signal Processing Conference (EUSIPCO)}, 
address 
= 
{Glasgow, Scotland}, 
url 
= 
{http://www.math.univtoulouse.fr/~weiss/Publis/Conferences/Eusipco09.pdf}, 
pdf 
= 
{http://www.math.univtoulouse.fr/~weiss/Publis/Conferences/Eusipco09.pdf}, 
keyword 
= 
{Extragradient method, proximal method, Image decomposition, 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. 

2  Smoothing techniques for convex problems. Applications in image processing. P. Weiss and M. Carlavan and L. BlancFéraud and J. Zerubia. In Proc. SAMPTA (international conference on Sampling Theory and Applications), Marseille, France, May 2009. Keywords : nesterov scheme, convergence rate, Dual smoothing.
@INPROCEEDINGS{PWEISS_SAMPTA09,

author 
= 
{Weiss, P. and Carlavan, M. and BlancFéraud, L. and Zerubia, J.}, 
title 
= 
{Smoothing techniques for convex problems. Applications in image processing}, 
year 
= 
{2009}, 
month 
= 
{May}, 
booktitle 
= 
{Proc. SAMPTA (international conference on Sampling Theory and Applications)}, 
address 
= 
{Marseille, France}, 
url 
= 
{http://www.math.univtoulouse.fr/~weiss/Publis/Conferences/Eusipco09.pdf}, 
pdf 
= 
{http://www.math.univtoulouse.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 lpnorms 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 superresolution with impulse noise. 

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Technical and Research Report 
1  Some applications of L infinite norms in image processing. P. Weiss and G. Aubert and L. BlancFéraud. Research Report 6115, INRIA, September 2006. Keywords : projected subgradient descent, convergence rate, Total variation, compression bounded noise, meyer G norm, fast l1 minimization.
@TECHREPORT{Some applications of L infinite constraints,

author 
= 
{Weiss, P. and Aubert, G. and BlancFéraud, L.}, 
title 
= 
{Some applications of L infinite norms in image processing}, 
year 
= 
{2006}, 
month 
= 
{September}, 
institution 
= 
{INRIA}, 
type 
= 
{Research Report}, 
number 
= 
{6115}, 
url 
= 
{http://www.math.univtoulouse.fr/~weiss/Publis/RR6115.pdf}, 
pdf 
= 
{ftp://ftpsop.inria.fr/ariana/Articles/2006_Some applications of L infinite constraints.pdf}, 
keyword 
= 
{projected subgradient descent, convergence rate, Total variation, compression bounded noise, meyer G norm, fast l1 minimization} 
} 

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