# Optimal Transport for Unsupervised Denoising Learning

arXiv: https://arxiv.org/abs/2108.02574 · HTML: https://mlsanity.com/paper/2108.02574/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 69 references that are in the map.
- First posted on arXiv 4 Aug 2021.

## Builds on (most cited first, 30 of 31)

- [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)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [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)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [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)
- [Semantic Scene Completion from a Single Depth Image](https://mlsanity.com/paper/1611.08974/) (2016)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [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)
- [Rethinking Lossy Compression: The Rate-Distortion-Perception Tradeoff](https://mlsanity.com/paper/1901.07821/) (2019)
- [Residual Dense Network for Image Restoration](https://mlsanity.com/paper/1812.10477/) (2018)
- [Neighbor2Neighbor: Self-Supervised Denoising from Single Noisy Images](https://mlsanity.com/paper/2101.02824/) (2021)
- [High-Quality Self-Supervised Deep Image Denoising](https://mlsanity.com/paper/1901.10277/) (2019)
- [The 2018 PIRM Challenge on Perceptual Image Super-resolution](https://mlsanity.com/paper/1809.07517/) (2018)
- [Noisier2Noise: Learning to Denoise from Unpaired Noisy Data](https://mlsanity.com/paper/1910.11908/) (2019)
- [Deep Depth Completion of a Single RGB-D Image](https://mlsanity.com/paper/1803.09326/) (2018)
- [NTIRE 2020 Challenge on Real-World Image Super-Resolution: Methods and Results](https://mlsanity.com/paper/2005.01996/) (2020)
- [Unpaired Learning of Deep Image Denoising](https://mlsanity.com/paper/2008.13711/) (2020)
- [A Poisson-Gaussian Denoising Dataset with Real Fluorescence Microscopy Images](https://mlsanity.com/paper/1812.10366/) (2018)
- [Noise2Same: Optimizing A Self-Supervised Bound for Image Denoising](https://mlsanity.com/paper/2010.11971/) (2020)
- [Probabilistic Noise2Void: Unsupervised Content-Aware Denoising](https://mlsanity.com/paper/1906.00651/) (2019)
- [Training Deep Learning Based Denoisers without Ground Truth Data](https://mlsanity.com/paper/1803.01314/) (2018)
- [Model-blind Video Denoising Via Frame-to-frame Training](https://mlsanity.com/paper/1811.12766/) (2018)
- [On Perceptual Lossy Compression: The Cost of Perceptual Reconstruction and An Optimal Training Framework](https://mlsanity.com/paper/2106.02782/) (2021)
- [Noise Robust Generative Adversarial Networks](https://mlsanity.com/paper/1911.11776/) (2019)

## Built on by (most cited first, 24 of 24)

- [Degradation-Aware Residual-Conditioned Optimal Transport for Unified Image Restoration](https://mlsanity.com/paper/2411.01656/) (2024)
- [OTRE: Where Optimal Transport Guided Unpaired Image-to-Image Translation Meets Regularization by Enhancing](https://mlsanity.com/paper/2302.03003/) (2023)
- [Optimally Controllable Perceptual Lossy Compression](https://mlsanity.com/paper/2206.10082/) (2022)
- [Optimal Transport Guided Unsupervised Learning for Enhancing low-quality Retinal Images](https://mlsanity.com/paper/2302.02991/) (2023)
- [Residual-Conditioned Optimal Transport: Towards Structure-Preserving Unpaired and Paired Image Restoration](https://mlsanity.com/paper/2405.02843/) (2024)
- [CUNSB-RFIE: Context-aware Unpaired Neural Schr"odinger Bridge in Retinal Fundus Image Enhancement](https://mlsanity.com/paper/2409.10966/) (2024)
- [Context-Aware Optimal Transport Learning for Retinal Fundus Image Enhancement](https://mlsanity.com/paper/2409.07862/) (2024)
- [Self-Supervised Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2308.13777/) (2023)
- [Taming Flow Matching with Unbalanced Optimal Transport into Fast Pansharpening](https://mlsanity.com/paper/2503.14975/) (2025)
- [Spatial and Modal Optimal Transport for Fast Cross-Modal MRI Reconstruction](https://mlsanity.com/paper/2305.02774/) (2023)
- [Boosting Visual Recognition in Real-world Degradations via Unsupervised Feature Enhancement Module with Deep Channel Prior](https://mlsanity.com/paper/2404.01703/) (2024)
- [TPOT: Topology Preserving Optimal Transport in Retinal Fundus Image Enhancement](https://mlsanity.com/paper/2411.01403/) (2024)
- [PCE-GAN: A Generative Adversarial Network for Point Cloud Attribute Quality Enhancement based on Optimal Transport](https://mlsanity.com/paper/2503.00047/) (2025)
- [A New Perspective On Denoising Based On Optimal Transport](https://mlsanity.com/paper/2312.08135/) (2023)
- [SP2OT: Semantic-Regularized Progressive Partial Optimal Transport for Imbalanced Clustering](https://mlsanity.com/paper/2404.03446/) (2024)
- [Unsupervised Denoising for Signal-Dependent and Row-Correlated Imaging Noise](https://mlsanity.com/paper/2310.07887/) (2023)
- [Optimal Transport Based Unsupervised Restoration Learning Exploiting Degradation Sparsity](https://mlsanity.com/paper/2305.00273/) (2023)
- [Look-Around Before You Leap: High-Frequency Injected Transformer for Image Restoration](https://mlsanity.com/paper/2404.00279/) (2024)
- [Reconstructing Retinal Visual Images from 3T fMRI Data Enhanced by Unsupervised Learning](https://mlsanity.com/paper/2404.05107/) (2024)
- [VAOT: Vessel-Aware Optimal Transport for Retinal Fundus Enhancement](https://mlsanity.com/paper/2511.18763/) (2025)
- [SGW-GAN: Sliced Gromov-Wasserstein Guided GANs for Retinal Fundus Image Enhancement](https://mlsanity.com/paper/2601.13417/) (2026)
- [Perception-based Image Denoising via Generative Compression](https://mlsanity.com/paper/2602.11553/) (2026)
- [Bridging Restoration and Diagnosis: A Comprehensive Benchmark for Retinal Fundus Enhancement](https://mlsanity.com/paper/2604.03806/) (2026)
- [UOTIP: Unbalanced Optimal Transport Map for Unpaired Inverse Problems](https://mlsanity.com/paper/2605.21094/) (2026)

## Abstract (arXiv)

Recently, much progress has been made in unsupervised denoising learning. However, existing methods more or less rely on some assumptions on the signal and/or degradation model, which limits their practical performance. How to construct an optimal criterion for unsupervised denoising learning without any prior knowledge on the degradation model is still an open question. Toward answering this question, this work proposes a criterion for unsupervised denoising learning based on the optimal transport theory. This criterion has favorable properties, e.g., approximately maximal preservation of the information of the signal, whilst achieving perceptual reconstruction. Furthermore, though a relaxed unconstrained formulation is used in practical implementation, we prove that the relaxed formulation in theory has the same solution as the original constrained formulation. Experiments on synthetic and real-world data, including realistic photographic, microscopy, depth, and raw depth images, demonstrate that the proposed method even compares favorably with supervised methods, e.g., approaching the PSNR of supervised methods while having better perceptual quality. Particularly, for spatially correlated noise and realistic microscopy images, the proposed method not only achieves better perceptual quality but also has higher PSNR than supervised methods. Besides, it shows remarkable superiority in harsh practical conditions with complex noise, e.g., raw depth images. Code is available at https://github.com/wangweiSJTU/OTUR.