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ICIP'09, Cairo : Egypt (2009)

Total Variation Projection with First Order Schemes

Jalal Fadili 1, Gabriel Peyré 2

(07/11/2009)

This paper proposes a new class of algorithms to compute the projection onto the set of images with a total variation bounded by a constant. The projection is computed on a dual formulation of the problem that is minimized using either a one-step gradient descent method or a multi-step Nesterov scheme. This yields iterative algorithms that compute soft thresholding of the dual vector fields. We show the convergence of the method with a convergence rate of O(1/k) for the one step method and O(1/k^2) for the multi-step one, where k is the iteration number. The projection algorithm can be used as a building block in several applications, and we illusrtate it by solving linear inverse problems under total variation constraint. Numerical results show that our algorithm competes favorably with state-of-the-art TV projection methods to solve denoising, inpainting and deblurring problems.

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 :	CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
	CNRS : UMR7534 – Université Paris IX - Paris Dauphine

Domaine

:

Informatique/Traitement du signal et de l'image Sciences de l'ingénieur/Traitement du signal et de l'image

Mots Clés : Total variation – projection – duality – forward-backward splitting – Nesterov – inverse problems

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Contributeur : Gabriel Peyré <>

Soumis le : Jeudi 2 Juillet 2009, 17:03:08

Dernière modification le : Dimanche 2 Janvier 2011, 16:05:21