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

2026-08-06

AI Summary

This study addresses the challenge that increasing resolution in imaging inverse problems often degrades the generalization performance of deep networks. The authors systematically investigate the generalization behavior of U-Net and its neural operator variants across varying discretization resolutions. Through interpretable one-dimensional models and two-dimensional limited-angle computed tomography reconstruction experiments, they find that although neural operator-based U-Nets are theoretically resolution-invariant, conventional U-Nets exhibit superior robustness and practical generalization. This work highlights a notable gap between theoretical resolution invariance and empirical performance, offering new insights for architecture selection in high-resolution inverse problem solving.

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.

Problem

• inverse imaging problems
• ill-posed problems
• resolution invariance
• U-Net
• neural operators

Innovation

• neural operator
• U-Net
• inverse imaging problems
• resolution invariance
• limited-angle CT