Regularity for solutions of the total variation denoising problem

Abstract

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.