# Wasserstein Patch Prior for Image Superresolution

arXiv: https://arxiv.org/abs/2109.12880 · HTML: https://mlsanity.com/paper/2109.12880/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 67 references that are in the map.
- First posted on arXiv 27 Sep 2021.

## Builds on (most cited first, 23 of 23)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Image Super-Resolution via Iterative Refinement](https://mlsanity.com/paper/2104.07636/) (2021)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- ["Zero-Shot" Super-Resolution using Deep Internal Learning](https://mlsanity.com/paper/1712.06087/) (2017)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Deep Plug-and-Play Super-Resolution for Arbitrary Blur Kernels](https://mlsanity.com/paper/1903.12529/) (2019)
- [Learning Proximal Operators: Using Denoising Networks for Regularizing Inverse Imaging Problems](https://mlsanity.com/paper/1704.03488/) (2017)
- [Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation](https://mlsanity.com/paper/1512.07331/) (2015)
- [CNN-Based Projected Gradient Descent for Consistent Image Reconstruction](https://mlsanity.com/paper/1709.01809/) (2017)
- [Deep Bayesian Inversion](https://mlsanity.com/paper/1811.05910/) (2018)
- [Plug-and-Play Unplugged: Optimization Free Reconstruction using Consensus Equilibrium](https://mlsanity.com/paper/1705.08983/) (2017)
- [Convolutional Proximal Neural Networks and Plug-and-Play Algorithms](https://mlsanity.com/paper/2011.02281/) (2020)
- [Wasserstein GANs Work Because They Fail (to Approximate the Wasserstein Distance)](https://mlsanity.com/paper/2103.01678/) (2021)
- [RAISR: Rapid and Accurate Image Super Resolution](https://mlsanity.com/paper/1606.01299/) (2016)
- [PCA Reduced Gaussian Mixture Models with Applications in Superresolution](https://mlsanity.com/paper/2009.07520/) (2020)
- [3DSNet: Unsupervised Shape-to-Shape 3D Style Transfer](https://mlsanity.com/paper/2011.13388/) (2020)
- [Accelerating GMM-based patch priors for image restoration: Three ingredients for a 100× speed-up](https://mlsanity.com/paper/1710.08124/) (2017)

## Built on by (most cited first, 13 of 13)

- [Generalized Normalizing Flows via Markov Chains](https://mlsanity.com/paper/2111.12506/) (2021)
- [PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization](https://mlsanity.com/paper/2205.12021/) (2022)
- [Manifold Learning by Mixture Models of VAEs for Inverse Problems](https://mlsanity.com/paper/2303.15244/) (2023)
- [WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolution](https://mlsanity.com/paper/2201.08157/) (2022)
- [Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction](https://mlsanity.com/paper/2312.16611/) (2023)
- [T-FAKE: Synthesizing Thermal Images for Facial Landmarking](https://mlsanity.com/paper/2408.15127/) (2024)
- [A User's Guide to Sampling Strategies for Sliced Optimal Transport](https://mlsanity.com/paper/2502.02275/) (2025)
- [Stability of Data-Dependent Ridge-Regularization for Inverse Problems](https://mlsanity.com/paper/2406.12289/) (2024)
- [Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport](https://mlsanity.com/paper/2509.22138/) (2025)
- [Training Adaptive Reconstruction Networks for Blind Inverse Problems](https://mlsanity.com/paper/2202.11342/) (2022)
- [LoFi: Neural Local Fields for Scalable Image Reconstruction](https://mlsanity.com/paper/2411.04995/) (2024)
- [Joint Manifold Learning and Optimal Transport for Dynamic Imaging](https://mlsanity.com/paper/2505.11913/) (2025)
- [Estimating Dataset Dimension via Singular Metrics under the Manifold Hypothesis: Application to Inverse Problems](https://mlsanity.com/paper/2507.07291/) (2025)

## Abstract (arXiv)

In this paper, we introduce a Wasserstein patch prior for superresolution of two- and three-dimensional images. Here, we assume that we have given (additionally to the low resolution observation) a reference image which has a similar patch distribution as the ground truth of the reconstruction. This assumption is e.g. fulfilled when working with texture images or material data. Then, the proposed regularizer penalizes the W2-distance of the patch distribution of the reconstruction to the patch distribution of some reference image at different scales. We demonstrate the performance of the proposed regularizer by two- and three-dimensional numerical examples.