从算子视角统一解读学习型迭代网络，揭示其核心机制。
Learned iterative networks: An operator learning perspective
- 将重建过程拆解为‘如何计算’和‘计算什么’两个独立问题
- 统一框架下揭示多种方法的本质关联性
- 适合从事图像重建与逆问题研究的学者参考
学习型图像重建已成为计算成像和逆问题的核心方法。其中最具成效的是学习型迭代网络，它通过展开经典迭代优化算法来求解变分问题。尽管底层算法通常在泛函分析框架中定义，但学习方法常被视为纯离散的。本文提出一种统一的算子视角：将重建过程形式化为一个学习型重建算子，明确‘如何计算’；同时将学习问题单独定义为‘计算什么’。在此框架下，我们综述了常见方法，并展示多种方法在核心上密切相关。我们还在此框架下回顾了线性与非线性逆问题，并进行了简短的数值实验以验证观点。
原文摘要 · Abstract (English)
Learned image reconstruction has become a pillar in computational imaging and inverse problems. Among the most successful approaches are learned iterative networks, which are formulated by unrolling classical iterative optimisation algorithms for solving variational problems. While the underlying algorithm is usually formulated in the functional analytic setting, learned approaches are often viewed as purely discrete. In this survey we present a unified operator view for learned iterative networks. Specifically, we formulate a learned reconstruction operator, defining how to compute, and separately the learning problem, which defines what to compute. In this setting we present common approaches and show that many approaches are closely related in their core. We review linear as well as non-linear inverse problems in this framework and present a short numerical study to conclude.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。