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This paper deals with the so-called staircasing phenomenon, which frequently arises in total variation-based denoising models in image analysis. We prove in particular that staircasing always occurs at global extrema of the datum and at all extrema of the minimizer. It is also shown that, for radial images, the staircasing always appears at the extrema and(More)
We review some results obtained in collaboration with Vicent Caselles (formerly with DTIC, U. Pompeu Fabra, Barcelona) and Matteo Novaga (U. Pisa) and recent extensions obtained by the first author on the properties of the jump sets of solutions of total variation minimizing problems, including some results on explicit solutions in the 1D and radial cases.(More)
Dans cet article, nous introduisons une nouvelle variante de la variation totale (T V) dont l'objectif est de simpli-fier la restauration d'images à base de T V lorsque celles-ci sont dégradées par un noyau qui se calcule facilement du côté Fourier (flou, transformée de Radon,...). L'idée est de remplacer simplement le terme T V par la norme L 1 d'un(More)
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