Deep Learning Methods for Solving Linear Inverse Problems: Research Directions and Paradigms

TL;DR

This survey reviews recent deep learning approaches for linear inverse problems, highlighting architectures that incorporate traditional knowledge, and discusses open challenges and future research directions.

Contribution

It provides a comprehensive overview of deep learning methods for linear inverse problems, emphasizing structured neural networks and future research opportunities.

Findings

Deep learning achieves state-of-the-art performance in linear inverse problems.

Structured neural networks effectively incorporate traditional knowledge.

Open challenges include model interpretability and generalization.

Abstract

The linear inverse problem is fundamental to the development of various scientific areas. Innumerable attempts have been carried out to solve different variants of the linear inverse problem in different applications. Nowadays, the rapid development of deep learning provides a fresh perspective for solving the linear inverse problem, which has various well-designed network architectures results in state-of-the-art performance in many applications. In this paper, we present a comprehensive survey of the recent progress in the development of deep learning for solving various linear inverse problems. We review how deep learning methods are used in solving different linear inverse problems, and explore the structured neural network architectures that incorporate knowledge used in traditional methods. Furthermore, we identify open challenges and potential future directions along this research line.