Theoretical Perspectives on Deep Learning Methods in Inverse Problems

Jonathan Scarlett; Reinhard Heckel; Miguel R.D. Rodrigues; Paul Hand; Yonina C. Eldar

doi:https://doi.org/10.1109/JSAIT.2023.3241123

Theoretical Perspectives on Deep Learning Methods in Inverse Problems

Jonathan Scarlett, Reinhard Heckel, Miguel R.D. Rodrigues, Paul Hand, Yonina C. Eldar

Department of Computer Science and Applied Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	433-453
Number of pages	21
Journal	IEEE journal on selected areas in information theory
Volume	3
Issue number	3
DOIs	https://doi.org/10.1109/JSAIT.2023.3241123
State	Published - 1 Sep 2022

Keywords

compressive sensing
denoising
generative priors
information-theoretic limits
inverse problems
theoretical guarantees
unfolding algorithms
untrained neural networks

All Science Journal Classification (ASJC) codes

Computer Networks and Communications
Media Technology
Artificial Intelligence
Applied Mathematics

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https://doi.org/10.1109/JSAIT.2023.3241123

Cite this

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title = "Theoretical Perspectives on Deep Learning Methods in Inverse Problems",

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.",

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KW - information-theoretic limits

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KW - theoretical guarantees

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Theoretical Perspectives on Deep Learning Methods in Inverse Problems

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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