# An Unsupervised Approach to Solving Inverse Problems using Generative Adversarial Networks

arXiv: https://arxiv.org/abs/1805.07281 · HTML: https://mlsanity.com/paper/1805.07281/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2018.

## Built on by (most cited first, 7 of 7)

- [GibbsDDRM: A Partially Collapsed Gibbs Sampler for Solving Blind Inverse Problems with Denoising Diffusion Restoration](https://mlsanity.com/paper/2301.12686/) (2023)
- [Regularising Inverse Problems with Generative Machine Learning Models](https://mlsanity.com/paper/2107.11191/) (2021)
- [PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization](https://mlsanity.com/paper/2205.12021/) (2022)
- [Survey of Deep Learning Methods for Inverse Problems](https://mlsanity.com/paper/2111.04731/) (2021)
- [Learning to sample in Cartesian MRI](https://mlsanity.com/paper/2312.04327/) (2023)
- [Deep Invertible Approximation of Topologically Rich Maps between Manifolds](https://mlsanity.com/paper/2210.00577/) (2022)
- [Optimization Landscapes Learned: Proxy Networks Boost Convergence in Physics-based Inverse Problems](https://mlsanity.com/paper/2501.16573/) (2025)

## Abstract (arXiv)

Solving inverse problems continues to be a challenge in a wide array of applications ranging from deblurring, image inpainting, source separation etc. Most existing techniques solve such inverse problems by either explicitly or implicitly finding the inverse of the model. The former class of techniques require explicit knowledge of the measurement process which can be unrealistic, and rely on strong analytical regularizers to constrain the solution space, which often do not generalize well. The latter approaches have had remarkable success in part due to deep learning, but require a large collection of source-observation pairs, which can be prohibitively expensive. In this paper, we propose an unsupervised technique to solve inverse problems with generative adversarial networks (GANs). Using a pre-trained GAN in the space of source signals, we show that one can reliably recover solutions to under determined problems in a `blind' fashion, i.e., without knowledge of the measurement process. We solve this by making successive estimates on the model and the solution in an iterative fashion. We show promising results in three challenging applications -- blind source separation, image deblurring, and recovering an image from its edge map, and perform better than several baselines.