In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution. While this line of works has predominantly been driven by practical algorithms and experiments, it has also given rise to a variety of intriguing theoretical problems. In this paper, we survey some of the prominent theoretical developments in this line of works, focusing in particular on generative priors, untrained neural network priors, and unfolding algorithms. In addition to summarizing existing results in these topics, we highlight several ongoing challenges and open problems.

翻译：近年来，深度学习在逆问题中的应用取得了显著进展，涵盖去噪、压缩感知、图像修复和超分辨率等任务。尽管这一研究方向主要由实际算法和实验驱动，但也催生了一系列引人入胜的理论问题。本文综述了该方向中若干重要的理论发展，重点关注生成先验、未训练神经网络先验及展开算法。除总结这些主题的现有成果外，我们还强调了若干持续存在的挑战与开放性问题。