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

arXiv: https://arxiv.org/abs/2007.13290 · HTML: https://mlsanity.com/paper/2007.13290/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jul 2020.

## Built on by (most cited first, 16 of 16)

- [Gradient-Free Generation for Hard-Constrained Systems](https://mlsanity.com/paper/2412.01786/) (2024)
- [DAN-Net: Dual-Domain Adaptive-Scaling Non-local Network for CT Metal Artifact Reduction](https://mlsanity.com/paper/2102.08003/) (2021)
- [Transformers are Provably Optimal In-context Estimators for Wireless Communications](https://mlsanity.com/paper/2311.00226/) (2023)
- [DRIP: Deep Regularizers for Inverse Problems](https://mlsanity.com/paper/2304.00015/) (2023)
- [Paired Autoencoders for Likelihood-free Estimation in Inverse Problems](https://mlsanity.com/paper/2405.13220/) (2024)
- [Statistical Learning and Inverse Problems: A Stochastic Gradient Approach](https://mlsanity.com/paper/2209.14967/) (2022)
- [Good Things Come in Pairs: Paired Autoencoders for Inverse Problems](https://mlsanity.com/paper/2505.06549/) (2025)
- [Neural Incremental Data Assimilation](https://mlsanity.com/paper/2406.15076/) (2024)
- [Learning Regularization for Graph Inverse Problems](https://mlsanity.com/paper/2408.10436/) (2024)
- [Estimating a potential without the agony of the partition function](https://mlsanity.com/paper/2208.09433/) (2022)
- [Solving inverse problems with deep neural networks driven by sparse signal decomposition in a physics-based dictionary](https://mlsanity.com/paper/2107.10657/) (2021)
- [Generative models and Bayesian inversion using Laplace approximation](https://mlsanity.com/paper/2203.07755/) (2022)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)
- [Near-filed SAR Image Restoration with Deep Learning Inverse Technique: A Preliminary Study](https://mlsanity.com/paper/2211.14990/) (2022)
- [GraIP: A Benchmarking Framework For Neural Graph Inverse Problems](https://mlsanity.com/paper/2601.18917/) (2026)
- [DIPA: Distilled Preconditioned Algorithms for Solving Imaging Inverse Problems](https://mlsanity.com/paper/2605.15456/) (2026)

## Abstract (arXiv)

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.