研究U-Net在高分辨率逆成像问题中的表现,发现其对分辨率变化比预期更鲁棒。
A neural operator view on U-Nets for inverse imaging problems

- 将U-Net视为神经算子,分析其在高分辨率逆问题中的行为
- 实验表明经典U-Net在不同分辨率间泛化能力优于预期
- 适用于医学成像中分辨率变化较大的逆问题场景
深度神经网络在解决各类成像逆问题中表现出色,但很少有研究关注当离散化分辨率不断提高、问题趋于真正病态时的表现。本文回顾了类似U-Net结构的神经算子学习方法,分析其优劣,并通过一个1D简化模型提升可解释性。在有限角度CT重建任务上进行了大量数值实验,探究不同类型的神经算子U-Net如何改进初始重建结果。重点考察了在特定分辨率下训练的网络在其他分辨率上的泛化能力。结果表明,尽管U型神经算子架构设计为分辨率不变,但经典U-Net在面对分辨率变化时表现出比预期更强的鲁棒性。
原文摘要 · Abstract (English)
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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