A bilevel training scheme is used to introduce a novel class of regularizers, providing a unified approach to standard regularizers TV, TGV2 and NsTGV2. 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. Explicit examples and numerical results are given.
@article{arxiv.1902.01122,
title = {Adaptive image processing: first order PDE constraint regularizers and a bilevel training scheme},
author = {Elisa Davoli and Irene Fonseca and Pan Liu},
journal= {arXiv preprint arXiv:1902.01122},
year = {2019}
}