Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact Publication 19-CNA-001 Adaptive Image Processing: First Order PDE Constraint Regularizers And A Bilevel Training Scheme Elisa DavoliDepartment of Mathematics University of Vienna Oskar-Morgenstern-Platz 1 1090 Vienna, Austriaelisa.davoli@univie.ac.at Irene FonsecaDepartment of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213fonseca@andrew.cmu.edu Pan LiuCentre of Mathematical Imaging and Healthcare Department of Pure Mathematics and Mathematical Statistics University of Cambridge, UKpanliu.0923@maths.cam.ac.ukAbstract: 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 $\Gamma$-convergence. Explicit examples and numerical results are given.Get the paper in its entirety as  19-CNA-001.pdf