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

A bilevel training scheme is used to introduce a novel class of regularizers, providing a unified approach to standard regularizers T G V 2 and N s T G V 2 . Optimal parameters and regularizers are identified, and the existence of a solution for any given set of training imaging data is proved by Γ -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.