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：近些年来,在利用深层次的学习方法处理诸如脱落、压缩感测、油漆和超分辨率等反面问题方面取得了显著进展。虽然这一行工作主要是由实际算法和实验驱动的,但也引起了各种令人感兴趣的理论问题。在本论文中,我们调查了这一行工作的一些突出的理论发展,特别侧重于基因前科、未经训练的神经网络前科和正在演化的算法。除了概述这些专题的现有结果外,我们还强调了目前存在的一些挑战和公开问题。