# Optimization Methods for Inverse Problems

arXiv: https://arxiv.org/abs/1712.00154 · HTML: https://mlsanity.com/paper/1712.00154/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2017.

## Built on by (most cited first, 6 of 6)

- [Regularization-Agnostic Compressed Sensing MRI Reconstruction with Hypernetworks](https://mlsanity.com/paper/2101.02194/) (2021)
- [Computing Multiple Image Reconstructions with a Single Hypernetwork](https://mlsanity.com/paper/2202.11009/) (2022)
- [Scale-invariant Learning by Physics Inversion](https://mlsanity.com/paper/2109.15048/) (2021)
- [Half-Inverse Gradients for Physical Deep Learning](https://mlsanity.com/paper/2203.10131/) (2022)
- [Solving Inverse Problems in Stochastic Self-Organizing Systems through Invariant Representations](https://mlsanity.com/paper/2506.11796/) (2025)
- [Accelerating SAV-based optimization via randomized low-rank Hessian approximation](https://mlsanity.com/paper/2606.10562/) (2026)

## Abstract (arXiv)

Optimization plays an important role in solving many inverse problems. Indeed, the task of inversion often either involves or is fully cast as a solution of an optimization problem. In this light, the mere non-linear, non-convex, and large-scale nature of many of these inversions gives rise to some very challenging optimization problems. The inverse problem community has long been developing various techniques for solving such optimization tasks. However, other, seemingly disjoint communities, such as that of machine learning, have developed, almost in parallel, interesting alternative methods which might have stayed under the radar of the inverse problem community. In this survey, we aim to change that. In doing so, we first discuss current state-of-the-art optimization methods widely used in inverse problems. We then survey recent related advances in addressing similar challenges in problems faced by the machine learning community, and discuss their potential advantages for solving inverse problems. By highlighting the similarities among the optimization challenges faced by the inverse problem and the machine learning communities, we hope that this survey can serve as a bridge in bringing together these two communities and encourage cross fertilization of ideas.