Year: 2024
Type: article
Abstract: . We study stability and inclusion of the jump set of minimizers of convex denoising functionals, such as the celebrated “Rudin–Osher–Fatemi” functional, for scalar or vectorial signals. We show that under mild regularity assumptions on the data fidelity term and the regularizer, the jump set of the minimizer is essentially a subset of the original jump set. Moreover, we give an estimate on the magnitude of the jumps in terms of the data. This extends old results, in particular of the first author (with Caselles and Novaga) and of Valkonen, to much more general cases. We also consider the case where the original datum has unbounded variation, and we define a notion of its jump set which, again, must contain the jump set of the solution.
Source: SIAM Journal on Imaging Sciences
DOI: 10.1137/23m1627948
Authors: Antonin Chambolle, Michał Łasica
Institutions: Centre National de la Recherche Scientifique, Institut national de recherche en sciences et technologies du numérique, Centre de Recherche en Mathématiques de la Décision, Université Paris Sciences et Lettres, MOKAPLAN: Avancées en calcul numérique des variations, Université Paris Dauphine-PSL, Institute of Mathematics, Polish Academy of Sciences
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4402319243