Adaptive image processing: first order PDE constraint regularizers and a bilevel training scheme

TL;DR

This paper introduces a bilevel training scheme for adaptive image processing that unifies various regularizers like TV, TGV^2, and NsTGV^2, with proven existence of solutions and demonstrated numerical effectiveness.

Contribution

It presents a novel bilevel training framework that identifies optimal regularizers and parameters, unifying multiple regularization methods in image processing.

Findings

Unified approach to TV, TGV^2, NsTGV^2 regularizers

Existence of solutions proved via Γ-convergence

Numerical results validate the method

Abstract

A bilevel training scheme is used to introduce a novel class of regularizers, providing a unified approach to standard regularizers $TV$, $TGV^2$ and $NsTGV^2$. 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.