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This paper investigates the performance of U-Net-like neural operator architectures in solving ill-posed inverse imaging problems as the discretization resolution increases. By analyzing various neural operator learning approaches and conducting extensive numerical experiments, the authors reveal that while these architectures are designed to be resolution-invariant, the classical U-Net exhibits unexpected robustness to changes in resolution. The key finding highlights that U-Nets can generalize effectively across different discretization resolutions, which is crucial for practical applications in imaging tasks like limited angle CT reconstruction.
U-Nets unexpectedly show greater robustness to resolution changes than anticipated, challenging assumptions about neural operator architectures in inverse imaging.
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.
