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Publications sur discrepancy principle
Résultat de la recherche dans la liste des publications :
3 Articles de conférence |
1 - Two constrained formulations for deblurring Poisson noisy images.
M. Carlavan et L. Blanc-Féraud. Dans Proc. IEEE International Conference on Image Processing (ICIP), Brussels, Belgium, septembre 2011.
Mots-clés : Poisson deconvolution, discrepancy principle, constrained convex optimization.
@INPROCEEDINGS{ICIP2011_Carlavan,
|
| author |
= |
{Carlavan, M. and Blanc-Féraud, L.}, |
| title |
= |
{Two constrained formulations for deblurring Poisson noisy images}, |
| year |
= |
{2011}, |
| month |
= |
{septembre}, |
| booktitle |
= |
{Proc. IEEE International Conference on Image Processing (ICIP)}, |
| address |
= |
{Brussels, Belgium}, |
| url |
= |
{http://hal.inria.fr/inria-00591035/fr/}, |
| keyword |
= |
{Poisson deconvolution, discrepancy principle, constrained convex optimization} |
| } |
Abstract :
Deblurring noisy Poisson images has recently been subject of an increasingly amount of works in many areas such as astronomy or biological imaging. Several methods have promoted explicit prior on the solution to regularize the ill-posed inverse problem and to improve the quality of the image. In each of these methods, a regularizing parameter is introduced to control the weight of the prior. Unfortunately, this regularizing parameter has to be manually set such that it gives the best qualitative results. To tackle this issue, we present in this paper two constrained formulations for the Poisson deconvolution problem, derived from recent advances in regularizing parameter estimation for Poisson noise. We first show how to improve the accuracy of these estimators and how to link these estimators to constrained formulations. We then propose an algorithm to solve the resulting optimization problems and detail how to perform the projections on the constraints. Results on real and synthetic data are presented. |
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2 - Formulation contrainte pour la déconvolution de bruit de Poisson.
M. Carlavan et L. Blanc-Féraud. Dans Proc. GRETSI Symposium on Signal and Image Processing, Bordeaux, France, septembre 2011.
Mots-clés : 3D confocal microscopy, constrained convex optimization, discrepancy principle, Poisson noise.
@INPROCEEDINGS{CarlavanGRETSI11,
|
| author |
= |
{Carlavan, M. and Blanc-Féraud, L.}, |
| title |
= |
{Formulation contrainte pour la déconvolution de bruit de Poisson}, |
| year |
= |
{2011}, |
| month |
= |
{septembre}, |
| booktitle |
= |
{Proc. GRETSI Symposium on Signal and Image Processing}, |
| address |
= |
{Bordeaux, France}, |
| url |
= |
{http://hal.inria.fr/inria-00602015/fr/}, |
| keyword |
= |
{3D confocal microscopy, constrained convex optimization, discrepancy principle, Poisson noise} |
| } |
Résumé :
Nous considérons le problème de la restauration d’image floue et bruitée par du bruit de Poisson. De nombreux travaux ont proposé de traiter ce problème comme la minimisation d’une énergie convexe composée d’un terme d’attache aux données et d’un terme de régularisation choisi selon l’a priori dont on dispose sur l’image à restaurer. Un des problèmes récurrents dans ce type d’approche est le choix du paramètre de régularisation qui contrôle le compromis entre l’attache aux données et la régularisation. Une approche est de choisir ce paramètre de régularisation en procédant à plusieurs minimisations pour plusieurs valeurs du paramètre et en ne gardant que celle qui donne une image restaurée vérifiant un certain critère (qu’il soit qualitatif ou quantitatif). Cette technique est évidemment très couteuse lorsque les données traitées sont de grande dimension, comme c’est le cas en microscopie 3D par exemple. Nous proposons ici de formuler le problème de restauration
d’image floue et bruitée par du bruit de Poisson comme un problème contraint sur l’antilog de la vraisemblance poissonienne et proposons une
estimation de la borne à partir des travaux de Bertero et al. sur le principe de discrepancy pour l’estimation du paramètre de régularisation en présence de bruit de Poisson. Nous montrons des résultats sur des images synthétiques et réelles et comparons avec l'écriture non-contrainte utilisant une approximation gaussienne du bruit de Poisson pour l’estimation du paramètre de régularisation. |
Abstract :
We focus here on the restoration of blurred and Poisson noisy images. Several methods solve this problem by minimizing a convex cost function composed of a data term and a regularizing term chosen from the prior that one have on the image. One of the recurrent problems of this approach is how to choose the regularizing paramater which controls the weight of the regularization term in front of the data term. One method consists in solving the minimization problem for several values of this parameter and by keeping the value which gives an image verifying a quality criterion (either qualitative or quantitative). This technique is obviously time consuming when one deal with high dimensional data such as in 3D microscopy imaging. We propose to formulate the blurred and Poisson noisy images restoration problem as a constrained problem on the antilog of the Poisson likelihood and propose an estimation of the bound from the works of Bertero et al. on the discrepancy principle for the estimation of the regularizing parameter for Poisson noise. We show results on synthetic and real data and we compare these results to the one obtained with the unconstrained formulation using the Gaussian approximation of the Poisson noise for the estimation of the regularizing parameter. |
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3 - Regularizing parameter estimation for Poisson noisy image restoration.
M. Carlavan et L. Blanc-Féraud. Dans International ICST Workshop on New Computational Methods for Inverse Problems, Paris, France, mai 2011.
Mots-clés : Parameter estimation, discrepancy principle, Poisson noise.
@INPROCEEDINGS{NCMIP11,
|
| author |
= |
{Carlavan, M. and Blanc-Féraud, L.}, |
| title |
= |
{Regularizing parameter estimation for Poisson noisy image restoration}, |
| year |
= |
{2011}, |
| month |
= |
{mai}, |
| booktitle |
= |
{International ICST Workshop on New Computational Methods for Inverse Problems}, |
| address |
= |
{Paris, France}, |
| url |
= |
{http://hal.inria.fr/inria-00590906/fr/}, |
| keyword |
= |
{Parameter estimation, discrepancy principle, Poisson noise} |
| } |
Abstract :
Deblurring images corrupted by Poisson noise is a challeng- ing process which has devoted much research in many ap- plications such as astronomical or biological imaging. This problem, among others, is an ill-posed problem which can be regularized by adding knowledge on the solution. Several methods have therefore promoted explicit prior on the im- age, coming along with a regularizing parameter to moder- ate the weight of this prior. Unfortunately, in the domain of Poisson deconvolution, only a few number of methods have been proposed to select this regularizing parameter which is most of the time set manually such that it gives the best visual results. In this paper, we focus on the use of l1 -norm prior and present two methods to select the regularizing pa- rameter. We show some comparisons on synthetic data using classical image fidelity measures. |
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Rapport de recherche et Rapport technique |
1 - Complex wavelet regularization for 3D confocal microscopy deconvolution.
M. Carlavan et L. Blanc-Féraud. Rapport de Recherche 7366, INRIA, août 2010.
Mots-clés : 3D confocal microscopy, Deconvolution, complex wavelet regularization, discrepancy principle, Alternating Direction technique.
@TECHREPORT{RR-7366,
|
| author |
= |
{Carlavan, M. and Blanc-Féraud, L.}, |
| title |
= |
{Complex wavelet regularization for 3D confocal microscopy deconvolution}, |
| year |
= |
{2010}, |
| month |
= |
{août}, |
| institution |
= |
{INRIA}, |
| type |
= |
{Research Report}, |
| number |
= |
{7366}, |
| url |
= |
{http://hal.inria.fr/inria-00509447/fr/}, |
| keyword |
= |
{3D confocal microscopy, Deconvolution, complex wavelet regularization, discrepancy principle, Alternating Direction technique} |
| } |
Abstract :
Confocal microscopy is an increasingly popular technique for 3D
imaging of biological specimens which gives images with a very good resolution
(several tenths of micrometers), even though degraded by both blur and Poisson
noise. Deconvolution methods have been proposed to reduce these degradations,
some of them being regularized on a Total Variation prior, which gives
good results in image restoration but does not allow to retrieve the thin details
(including the textures) of the specimens. We rst propose here to use instead
a wavelet prior based on the Dual-Tree Complex Wavelet transform to retrieve
the thin details of the object. As the regularizing prior e ciency also depends
on the choice of its regularizing parameter, we secondly propose a method to
select the regularizing parameter following a discrepancy principle for Poisson
noise. Finally, in order to implement the proposed deconvolution method, we
introduce an algorithm based on the Alternating Direction technique which allows
to avoid inherent stability problems of the Richardson-Lucy multiplicative
algorithm which is widely used in 3D image restoration. We show some results
on real and synthetic data, and compare these results to the ones obtained with
the Total Variation and the Curvelets priors. We also give preliminary results
on a modi cation of the wavelet transform allowing to deal with the anisotropic
sampling of 3D confocal images. |
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Rapport d'activité 2011
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