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An introduction to Total Variation for Image Analysis

Antonin Chambolle 1, Vicent Caselles 2, Matteo Novaga 3, Daniel Cremers 4, Thomas Pock 5

(30/11/2009)

These are the lecture notes of a course taught in Linz in Sept., 2009, at the school "summer school on sparsity", organized by Massimo Fornasier and Ronny Romlau. They address various theoretical and practical topics related to Total Variation-based image reconstruction. They focu first on some theoretical results on functions which minimize the total variation, and in a second part, describe a few standard and less standard algorithms to minimize the total variation in a finite-differences setting, with a series of applications from simple denoising to stereo, or deconvolution issues, and even more exotic uses like the minimization of minimal partition problems.

1 :	Centre de Mathématiques Appliquées (CMAP)
	CNRS : UMR7641 – Université de Versailles Saint-Quentin-en-Yvelines – Polytechnique - X
2 :	Departament de Tecnologies de la Informació i les Comunicacions
	Universitat Pompeu-Fabra
3 :	Dipartimento di Matematica Pura ed Applicata
	Università degli studi di Padova
4 :	Department of Computer Science
	Bonn Universität - University of Bonn
5 :	Institute for Computer Graphics and Vision [Graz] (ICG)
	Graz University of Technology

Domaine

:

Mathématiques/Analyse numérique

Mots Clés : Total Variation. Variational Image Reconstruction. Functions with Bounded Variation. Level sets. Convex Optimization. Splitting algorithms. Denoising. Deconvolution. Stereo reconstruction.

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Contributeur : Antonin Chambolle <>

Soumis le : Lundi 30 Novembre 2009, 23:38:32

Dernière modification le : Mercredi 2 Décembre 2009, 16:12:25