Monotonicity of the jump set for denosining model.

par Riccardo Cristoferi (Radboud University)

mardi 21 oct. 2025, 15:15 → 16:15 Europe/Paris

Fokko (ICJ)

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).