# Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging

arXiv: https://arxiv.org/abs/2311.08972 · HTML: https://mlsanity.com/paper/2311.08972/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 100 references that are in the map.
- First posted on arXiv 15 Nov 2023.

## Builds on (most cited first, 30 of 54)

- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [GAN Inversion: A Survey](https://mlsanity.com/paper/2101.05278/) (2021)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Image reconstruction by domain transform manifold learning](https://mlsanity.com/paper/1704.08841/) (2017)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [Optimal transport mapping via input convex neural networks](https://mlsanity.com/paper/1908.10962/) (2019)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Neighbor2Neighbor: Self-Supervised Denoising from Single Noisy Images](https://mlsanity.com/paper/2101.02824/) (2021)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Noisier2Noise: Learning to Denoise from Unpaired Noisy Data](https://mlsanity.com/paper/1910.11908/) (2019)
- [Mode Regularized Generative Adversarial Networks](https://mlsanity.com/paper/1612.02136/) (2016)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Adversarial Regularizers in Inverse Problems](https://mlsanity.com/paper/1805.11572/) (2018)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [Invertible generative models for inverse problems: mitigating representation error and dataset bias](https://mlsanity.com/paper/1905.11672/) (2019)

## Built on by (most cited first, 4 of 4)

- [Unsupervised Training of Convex Regularizers using Maximum Likelihood Estimation](https://mlsanity.com/paper/2404.05445/) (2024)
- [An invertible generative model for forward and inverse problems](https://mlsanity.com/paper/2509.03910/) (2025)
- [Equivariant Test-Time Training with Operator Sketching for Imaging Inverse Problems](https://mlsanity.com/paper/2411.05771/) (2024)
- [A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems](https://mlsanity.com/paper/2606.30230/) (2026)

## Abstract (arXiv)

Unsupervised deep learning approaches have recently become one of the crucial research areas in imaging owing to their ability to learn expressive and powerful reconstruction operators even when paired high-quality training data is scarcely available. In this chapter, we review theoretically principled unsupervised learning schemes for solving imaging inverse problems, with a particular focus on methods rooted in optimal transport and convex analysis. We begin by reviewing the optimal transport-based unsupervised approaches such as the cycle-consistency-based models and learned adversarial regularization methods, which have clear probabilistic interpretations. Subsequently, we give an overview of a recent line of works on provably convergent learned optimization algorithms applied to accelerate the solution of imaging inverse problems, alongside their dedicated unsupervised training schemes. We also survey a number of provably convergent plug-and-play algorithms (based on gradient-step deep denoisers), which are among the most important and widely applied unsupervised approaches for imaging problems. At the end of this survey, we provide an overview of a few related unsupervised learning frameworks that complement our focused schemes. Together with a detailed survey, we provide an overview of the key mathematical results that underlie the methods reviewed in the chapter to keep our discussion self-contained.