# Adaptive image processing: a bilevel structure learning approach for mixed-order total variation regularizers

## TL;DR

This paper introduces a bilevel learning approach for mixed-order PDE-based regularizers in image processing, optimizing both parameters and regularizers simultaneously, with a finite approximation method for solving the global optimization problem.

## Contribution

It proposes a novel bilevel training scheme for mixed-order PDE regularizers and analyzes a finite approximation method for global optimization in this context.

## Key findings

- Effective optimization of regularizer parameters and structure.
- The finite approximation method converges to global solutions.
- Enhanced image processing performance with the new regularizers.

## Abstract

A class of mixed-order \emph{PDE}-constraint regularizer for image processing problem is proposed, generalizing the standard first order total variation $(TV)$. A semi-supervised (bilevel) training scheme, which provides a simultaneous optimization with respect to parameters and the new class of regularizers, is studied. Also, A finite approximation method, which used to solve the global optimization solutions of such training scheme, is introduced and analyzed.