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 and some extensions of this result for the total variation minimization flow.
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Vicent Caselles, Antonin Chambolle, Matteo Novaga, Regularity for solutions of the total variation denoising problem. Rev. Mat. Iberoam. 27 (2011), no. 1, pp. 233–252DOI 10.4171/RMI/634