Revista Matemática Iberoamericana

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Volume 27, Issue 1, 2011, pp. 233–252
DOI: 10.4171/RMI/634

Published online: 2011-04-30

Regularity for solutions of the total variation denoising problem

Vicent Caselles, Antonin Chambolle[1] and Matteo Novaga[2]

(1) Ecole Polytechnique, Palaiseau, France
(2) Università di Pisa, Italy

The main purpose of this paper is to prove a local Hölder regularity result for the solutions of the total variation based denoising problem assuming that the datum is locally Hölder continuous. We also prove a global estimate on the modulus of continuity of the solution in convex domains of $\mathbb{R}^N$ and some extensions of this result for the total variation minimization flow.

Keywords: Image processing, variational methods, regularity of solutions.

Caselles Vicent, Chambolle Antonin, Novaga Matteo: Regularity for solutions of the total variation denoising problem. Rev. Mat. Iberoamericana 27 (2011), 233-252. doi: 10.4171/RMI/634