Bilevel parameter learning for nonlocal image denoising models

Understand

We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models.

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