# Bayesian Image Super-Resolution with Deep Modeling of Image Statistics

arXiv: https://arxiv.org/abs/2204.00623 · HTML: https://mlsanity.com/paper/2204.00623/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 80 references that are in the map.
- First posted on arXiv 31 Mar 2022.

## Builds on (most cited first, 30 of 37)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Enhanced Deep Residual Networks for Single Image Super-Resolution](https://mlsanity.com/paper/1707.02921/) (2017)
- [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)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Accurate Image Super-Resolution Using Very Deep Convolutional Networks](https://mlsanity.com/paper/1511.04587/) (2015)
- [Pre-Trained Image Processing Transformer](https://mlsanity.com/paper/2012.00364/) (2020)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [Deep Multi-scale Convolutional Neural Network for Dynamic Scene Deblurring](https://mlsanity.com/paper/1612.02177/) (2016)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Deep Laplacian Pyramid Networks for Fast and Accurate Super-Resolution](https://mlsanity.com/paper/1704.03915/) (2017)
- [Noise2Void - Learning Denoising from Single Noisy Images](https://mlsanity.com/paper/1811.10980/) (2018)
- [Deeply-Recursive Convolutional Network for Image Super-Resolution](https://mlsanity.com/paper/1511.04491/) (2015)
- ["Zero-Shot" Super-Resolution using Deep Internal Learning](https://mlsanity.com/paper/1712.06087/) (2017)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [SRFlow: Learning the Super-Resolution Space with Normalizing Flow](https://mlsanity.com/paper/2006.14200/) (2020)
- [EnhanceNet: Single Image Super-Resolution Through Automated Texture Synthesis](https://mlsanity.com/paper/1612.07919/) (2016)
- [Blind Super-Resolution Kernel Estimation using an Internal-GAN](https://mlsanity.com/paper/1909.06581/) (2019)
- [High-Quality Self-Supervised Deep Image Denoising](https://mlsanity.com/paper/1901.10277/) (2019)
- [Variational Denoising Network: Toward Blind Noise Modeling and Removal](https://mlsanity.com/paper/1908.11314/) (2019)
- [Meta-Transfer Learning for Zero-Shot Super-Resolution](https://mlsanity.com/paper/2002.12213/) (2020)
- [To learn image super-resolution, use a GAN to learn how to do image degradation first](https://mlsanity.com/paper/1807.11458/) (2018)
- [Denoising Prior Driven Deep Neural Network for Image Restoration](https://mlsanity.com/paper/1801.06756/) (2018)

## Built on by (most cited first, 11 of 11)

- [BayeSeg: Bayesian Modeling for Medical Image Segmentation with Interpretable Generalizability](https://mlsanity.com/paper/2303.01710/) (2023)
- [Image Super-resolution with An Enhanced Group Convolutional Neural Network](https://mlsanity.com/paper/2205.14548/) (2022)
- [A Generalized Tensor Formulation for Hyperspectral Image Super-Resolution Under General Spatial Blurring](https://mlsanity.com/paper/2409.18731/) (2024)
- [Variational Bayes image restoration with compressive autoencoders](https://mlsanity.com/paper/2311.17744/) (2023)
- [Deep priors for satellite image restoration with accurate uncertainties](https://mlsanity.com/paper/2412.04130/) (2024)
- [BUFF: Bayesian Uncertainty Guided Diffusion Probabilistic Model for Single Image Super-Resolution](https://mlsanity.com/paper/2504.03490/) (2025)
- [Combination of Single and Multi-frame Image Super-resolution: An Analytical Perspective](https://mlsanity.com/paper/2303.03212/) (2023)
- [A Single-Frame and Multi-Frame Cascaded Image Super-Resolution Method](https://mlsanity.com/paper/2412.09846/) (2024)
- [MambaX: Image Super-Resolution with State Predictive Control](https://mlsanity.com/paper/2511.18028/) (2025)
- [Probabilistic Modeling of Multi-rater Medical Image Segmentation for Diversity and Personalization](https://mlsanity.com/paper/2512.00748/) (2025)
- [Multi-Level Contextual Token Relation Modeling for Machine-Generated Text Detection](https://mlsanity.com/paper/2605.16107/) (2026)

## Abstract (arXiv)

Modeling statistics of image priors is useful for image super-resolution, but little attention has been paid from the massive works of deep learning-based methods. In this work, we propose a Bayesian image restoration framework, where natural image statistics are modeled with the combination of smoothness and sparsity priors. Concretely, firstly we consider an ideal image as the sum of a smoothness component and a sparsity residual, and model real image degradation including blurring, downscaling, and noise corruption. Then, we develop a variational Bayesian approach to infer their posteriors. Finally, we implement the variational approach for single image super-resolution (SISR) using deep neural networks, and propose an unsupervised training strategy. The experiments on three image restoration tasks, textiti.e., ideal SISR, realistic SISR, and real-world SISR, demonstrate that our method has superior model generalizability against varying noise levels and degradation kernels and is effective in unsupervised SISR. The code and resulting models are released via urlhttps://zmiclab.github.io/projects.html.