# Exploring the solution space of linear inverse problems with GAN latent geometry

arXiv: https://arxiv.org/abs/2207.00460 · HTML: https://mlsanity.com/paper/2207.00460/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 16 references that are in the map.
- First posted on arXiv 1 Jul 2022.

## Builds on (most cited first, 11 of 11)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [InterFaceGAN: Interpreting the Disentangled Face Representation Learned by GANs](https://mlsanity.com/paper/2005.09635/) (2020)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [PULSE: Self-Supervised Photo Upsampling via Latent Space Exploration of Generative Models](https://mlsanity.com/paper/2003.03808/) (2020)
- [Exploiting Deep Generative Prior for Versatile Image Restoration and Manipulation](https://mlsanity.com/paper/2003.13659/) (2020)
- [Inverting The Generator Of A Generative Adversarial Network](https://mlsanity.com/paper/1611.05644/) (2016)
- [Image-Adaptive GAN based Reconstruction](https://mlsanity.com/paper/1906.05284/) (2019)

## Built on by (most cited first, 3 of 3)

- [From Posterior Sampling to Meaningful Diversity in Image Restoration](https://mlsanity.com/paper/2310.16047/) (2023)
- [Text-guided Explorable Image Super-resolution](https://mlsanity.com/paper/2403.01124/) (2024)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)

## Abstract (arXiv)

Inverse problems consist in reconstructing signals from incomplete sets of measurements and their performance is highly dependent on the quality of the prior knowledge encoded via regularization. While traditional approaches focus on obtaining a unique solution, an emerging trend considers exploring multiple feasibile solutions. In this paper, we propose a method to generate multiple reconstructions that fit both the measurements and a data-driven prior learned by a generative adversarial network. In particular, we show that, starting from an initial solution, it is possible to find directions in the latent space of the generative model that are null to the forward operator, and thus keep consistency with the measurements, while inducing significant perceptual change. Our exploration approach allows to generate multiple solutions to the inverse problem an order of magnitude faster than existing approaches; we show results on image super-resolution and inpainting problems.