Adaptive Image Processing: First Order PDE Constraint Regularizers and a Bilevel Training Scheme

Abstract

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. Some first examples and numerical results are given.