# Optimal Transport Based Unsupervised Restoration Learning Exploiting Degradation Sparsity

arXiv: https://arxiv.org/abs/2305.00273 · HTML: https://mlsanity.com/paper/2305.00273/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 46 references that are in the map.
- First posted on arXiv 29 Apr 2023.

## Builds on (most cited first, 22 of 22)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks](https://mlsanity.com/paper/1809.00219/) (2018)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Benchmarking Single Image Dehazing and Beyond](https://mlsanity.com/paper/1712.04143/) (2017)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Deep Joint Rain Detection and Removal from a Single Image](https://mlsanity.com/paper/1609.07769/) (2016)
- [FFA-Net: Feature Fusion Attention Network for Single Image Dehazing](https://mlsanity.com/paper/1911.07559/) (2019)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [Residual Non-local Attention Networks for Image Restoration](https://mlsanity.com/paper/1903.10082/) (2019)
- [Recurrent Squeeze-and-Excitation Context Aggregation Net for Single Image Deraining](https://mlsanity.com/paper/1807.05698/) (2018)
- [Image De-raining Using a Conditional Generative Adversarial Network](https://mlsanity.com/paper/1701.05957/) (2017)
- [Spatial Attentive Single-Image Deraining with a High Quality Real Rain Dataset](https://mlsanity.com/paper/1904.01538/) (2019)
- [Residual Dense Network for Image Restoration](https://mlsanity.com/paper/1812.10477/) (2018)
- [The 2018 PIRM Challenge on Perceptual Image Super-resolution](https://mlsanity.com/paper/1809.07517/) (2018)
- [RankSRGAN: Generative Adversarial Networks with Ranker for Image Super-Resolution](https://mlsanity.com/paper/1908.06382/) (2019)
- [Dense Haze: A benchmark for image dehazing with dense-haze and haze-free images](https://mlsanity.com/paper/1904.02904/) (2019)
- [Gated Context Aggregation Network for Image Dehazing and Deraining](https://mlsanity.com/paper/1811.08747/) (2018)
- [Optimal Transport for Unsupervised Denoising Learning](https://mlsanity.com/paper/2108.02574/) (2021)

## Abstract (arXiv)

Optimal transport (OT) has recently been shown as a promising criterion for unsupervised restoration when no explicit prior model is available. Despite its theoretical appeal, OT still significantly falls short of supervised methods on challenging tasks such as super-resolution, deraining, and dehazing. In this paper, we propose a sparsity-aware optimal transport (SOT) framework to bridge this gap by leveraging a key observation: the degradations in these tasks exhibit distinct sparsity in the frequency domain. Incorporating this sparsity prior into OT can significantly reduce the ambiguity of the inverse mapping for restoration and substantially boost performance. We provide analysis to show exploiting degradation sparsity benefits unsupervised restoration learning. Extensive experiments on real-world super-resolution, deraining, and dehazing demonstrate that SOT offers notable performance gains over standard OT, while achieving superior perceptual quality compared to existing supervised and unsupervised methods. In particular, SOT consistently outperforms existing unsupervised methods across all three tasks and narrows the performance gap to supervised counterparts.