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arXiv · 2608.05839

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

Alexander Auras·Martin Burger·Samira Kabri·Michael Moeller·Michael Schopf-Kuester
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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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Alexander Auras, Martin Burger, Samira Kabri, Michael Moeller, Michael Schopf-Kuester. 2026-08-06. A neural operator view on U-Nets for inverse imaging problems. https://arxiv.org/abs/2608.05839

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