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Theoretical Perspectives on Deep Learning Methods in Inverse Problems

Scarlett, Jonathan; Heckel, Reinhard; Rodrigues, Miguel RD; Hand, Paul; Eldar, Yonina C; (2023) Theoretical Perspectives on Deep Learning Methods in Inverse Problems. IEEE Journal on Selected Areas in Information Theory 10.1109/jsait.2023.3241123. Green open access

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Abstract

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.

Type: Article
Title: Theoretical Perspectives on Deep Learning Methods in Inverse Problems
Open access status: An open access version is available from UCL Discovery
DOI: 10.1109/jsait.2023.3241123
Publisher version: https://doi.org/10.1109/JSAIT.2023.3241123
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Inverse problems, generative priors, untrained neural networks, unfolding algorithms, compressive sensing, denoising, theoretical guarantees, information-theoretic limits.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Electronic and Electrical Eng
URI: https://discovery.ucl.ac.uk/id/eprint/10166021
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