Bilevel Parameter Learning for Nonlocal Image Denoising Models

We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models. The we consider are both fidelity weight and weights within kernel operator. In cases, investigate differentiability solution operator function spaces derive first-order optimality system that characterizes local minima. For numerical problems, use second-order trust-region algorithm combination with finite element discretization models introduce computational strategy resulting dense linear systems. Several experiments illustrate applicability effectiveness our approach.