A neural operator view on U-Nets for inverse imaging problems

arXiv:2608.05839 · math.NA, cs.LG · Submitted 2026-08-06 · Read on arXiv

Alexander Auras, Martin Burger, Samira Kabri, Michael Moeller, Michael Schopf-Kuester

math.NA, cs.LG

Submitted: 2026-08-06

Code: https://github.com/AlexanderAuras/neural-operator-view-on-unets

License: http://creativecommons.org/licenses/by/4.0/

The gist: Deep neural networks have shown great empirical success in the solution of a wide variety of ill-posed inverse problems in imaging.

Terminology

Abstract

Deep neural networks have shown great empirical success in the solution of a wide variety of ill-posed inverse problems in imaging. Yet, very few works have studied their behavior in the limit that turns the discretized ill-conditioned problems into truly ill-posed ones, i.e., for an increasing resolution of the discretization. In this work, we review common approaches to neural operator learning in architectures that resemble a U-Net, one of the most common classical architectures for inverse imaging problems. We discuss advantages and drawbacks of the respective approaches, consider a 1D toy example for improved interpretability, and present extensive numerical experiments on how different types of neural operator U-Nets can improve a first (crude) limited angle CT-reconstruction. In particular, we study how well networks trained for a certain resolution of the discretization generalize to other resolutions. Our finding is that while U-shaped neural operator architectures are by design resolution-invariant, the classical U-Net architecture seems to be more robust with respect to resolution changes than expected.

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