# Algorithmic Aspects of Inverse Problems Using Generative Models

arXiv: https://arxiv.org/abs/1810.03587 · HTML: https://mlsanity.com/paper/1810.03587/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Oct 2018.

## Built on by (most cited first, 8 of 8)

- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Transformers in Medical Imaging: A Survey](https://mlsanity.com/paper/2201.09873/) (2022)
- [Instance-Optimal Compressed Sensing via Posterior Sampling](https://mlsanity.com/paper/2106.11438/) (2021)
- [Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition](https://mlsanity.com/paper/2106.03668/) (2021)
- [Regularising Inverse Problems with Generative Machine Learning Models](https://mlsanity.com/paper/2107.11191/) (2021)
- [Source Localization of Graph Diffusion via Variational Autoencoders for Graph Inverse Problems](https://mlsanity.com/paper/2206.12327/) (2022)
- [Provably Convergent Algorithms for Solving Inverse Problems Using Generative Models](https://mlsanity.com/paper/2105.06371/) (2021)
- [Imaging Signal Recovery Using Neural Network Priors Under Uncertain Forward Model Parameters](https://mlsanity.com/paper/2405.02944/) (2024)

## Abstract (arXiv)

The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by generative adversarial networks, or GANs). In this work, we study the algorithmic aspects of such a learning-based approach from a theoretical perspective. For certain generative network architectures, we establish a simple non-convex algorithmic approach that (a) theoretically enjoys linear convergence guarantees for certain inverse problems, and (b) empirically improves upon conventional techniques such as back-propagation. We also propose an extension of our approach that can handle model mismatch (i.e., situations where the generative network prior is not exactly applicable.) Together, our contributions serve as building blocks towards a more complete algorithmic understanding of generative models in inverse problems.