Calculus of Variations and Geometric Measure Theory

E. Davoli - I. Fonseca - P. Liu

Adaptive image processing: first order PDE constraint regularizers and a bilevel training scheme

created by davoli on 04 Feb 2019
modified on 16 Feb 2023


Accepted Paper

Inserted: 4 feb 2019
Last Updated: 16 feb 2023

Journal: Journal of Nonlinear Science
Year: 2023


A bilevel training scheme is used to introduce a novel class of regularizers, providing a unified approach to standard regularizers $TGV^2$ and $NsTGV^2$. Optimal parameters and regularizers are identified, and the existence of a solution for any given set of training imaging data is proved by $\Gamma$-convergence under a conditional uniform bound on the trace constant of the operators and a finite-null-space condition. Explicit examples and numerical results are given.