Abstract

We consider the minimizer of the ROF functional for denoising, which is the sum of the total variation and the square of the $L^2$ distance from a fixed function $f$. The former term is weighted by a positive parameter alpha. We focus on the one dimensional scalar case. Under mild regularity assumptions on the function $f$, we prove that the jump set of the minimizer is monotone with respect to the parameter alpha. This proves a case of a long-standing conjecture in the field.

This is a joint work in collaboration with Rita Ferreira (KAUST), Irene Fonseca (CMU), and José Iglesias (U. Twente).