Theoretical Perspectives on Deep Learning Methods in Inverse Problems
It provides a theoretical overview for researchers in machine learning and inverse problems, but is incremental as it is a survey paper.
This paper surveys theoretical developments in deep learning methods for inverse problems like denoising and compressive sensing, summarizing existing results and highlighting ongoing challenges without presenting new experimental outcomes.
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.