# Bilevel parameter learning for nonlocal image denoising models

arXiv: https://arxiv.org/abs/1912.02347 · HTML: https://mlsanity.com/paper/1912.02347/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Dec 2019.

## Built on by (most cited first, 2 of 2)

- [Bilevel Imaging Learning Problems as Mathematical Programs with Complementarity Constraints: Reformulation and Theory](https://mlsanity.com/paper/2110.02273/) (2021)
- [ML-based identification of the interface regions for coupling local and nonlocal models](https://mlsanity.com/paper/2404.15388/) (2024)

## Abstract (arXiv)

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. Several experiments illustrate the applicability and effectiveness of our approach.