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

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.

Numerical Analysis (math.NA); Machine Learning (cs.LG)

arXiv:2608.05839 [math.NA]

(or arXiv:2608.05839v1 [math.NA] for this version)

https://doi.org/10.48550/arXiv.2608.05839 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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