Learning Regularization Functionals for Inverse Problems: A Comparative Study
Machine Learning
2026-01-16 v2 Numerical Analysis
Numerical Analysis
Optimization and Control
Abstract
In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural design and training strategies, making direct comparison challenging due to non-modular implementations. We address this gap by collecting and unifying the available code into a common framework. This unified view allows us to systematically compare the approaches and highlight their strengths and limitations, providing valuable insights into their future potential. We also provide concise descriptions of each method, complemented by practical guidelines.
Cite
@article{arxiv.2510.01755,
title = {Learning Regularization Functionals for Inverse Problems: A Comparative Study},
author = {Johannes Hertrich and Hok Shing Wong and Alexander Denker and Stanislas Ducotterd and Zhenghan Fang and Markus Haltmeier and Željko Kereta and Erich Kobler and Oscar Leong and Mohammad Sadegh Salehi and Carola-Bibiane Schönlieb and Johannes Schwab and Zakhar Shumaylov and Jeremias Sulam and German Shâma Wache and Martin Zach and Yasi Zhang and Matthias J. Ehrhardt and Sebastian Neumayer},
journal= {arXiv preprint arXiv:2510.01755},
year = {2026}
}