HAL : hal-00264972, version 2

arXiv : 0803.2623

DOI : 10.1109/TIP.2008.2008223

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

IEEE Transactions on Image Processing 18, 2 (2009) 310-321

Versions disponibles :

v1 (18-03-2008)

v2 (27-08-2008)

A proximal iteration for deconvolving Poisson noisy images using sparse representations

François-Xavier Dupé 1, Jalal Fadili 1, Jean Luc Starck 2

(02/02/2009)

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key contributions are: First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a {\it non-linear} degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the minimization of a convex functional with a data-fidelity term reflecting the noise properties, and a non-smooth sparsity-promoting penalties over the image representation coefficients (e.g. $\ell_1$-norm). Third, a fast iterative backward-forward splitting algorithm is proposed to solve the minimization problem. We derive existence and uniqueness conditions of the solution, and establish convergence of the iterative algorithm. Finally, a GCV-based model selection procedure is proposed to objectively select the regularization parameter. Experimental results are carried out to show the striking benefits gained from taking into account the Poisson statistics of the noise. These results also suggest that using sparse-domain regularization may be tractable in many deconvolution applications with Poisson noise such as astronomy and microscopy.

1 :	Groupe de Recherche en Informatique, Image, Automatique et Instrumentation de Caen (GREYC)
	CNRS : UMR6072 – Université de Caen – Ecole Nationale Supérieure d'Ingénieurs de Caen
2 :	Service d'Electronique, des Détecteurs et d'Informatique (SEDI)
	CEA : DSM/IRFU

Équipe de recherche : GREYC UMR 6072 Image

Domaine

:

Informatique/Traitement du signal et de l'image Statistiques/Applications Sciences de l'ingénieur/Traitement du signal et de l'image Mathématiques/Statistiques Statistiques/Théorie Mathématiques/Optimisation et contrôle

Mots Clés : Deconvolution – Poisson noise – Proximal iteration – forward-backward splitting – Iterative thresholding – Sparse representations.

hal-00264972, version 2

http://hal.archives-ouvertes.fr/hal-00264972

oai:hal.archives-ouvertes.fr:hal-00264972

Contributeur : François-Xavier Dupé <>

Soumis le : Mercredi 27 Août 2008, 15:42:07

Dernière modification le : Jeudi 15 Janvier 2009, 13:31:49