# Learning-based Statistical Refinement for Denoising

arXiv: https://arxiv.org/abs/2605.04332 · HTML: https://mlsanity.com/paper/2605.04332/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 53 references that are in the map.
- First posted on arXiv 5 May 2026.

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

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [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)
- [Deblurring via Stochastic Refinement](https://mlsanity.com/paper/2112.02475/) (2021)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Residual Dense Network for Image Restoration](https://mlsanity.com/paper/1812.10477/) (2018)
- [Optimal whitening and decorrelation](https://mlsanity.com/paper/1512.00809/) (2015)
- [Practical Blind Image Denoising via Swin-Conv-UNet and Data Synthesis](https://mlsanity.com/paper/2203.13278/) (2022)
- [Unsupervised Learning with Stein's Unbiased Risk Estimator](https://mlsanity.com/paper/1805.10531/) (2018)
- [Denoising Criterion for Variational Auto-Encoding Framework](https://mlsanity.com/paper/1511.06406/) (2015)
- [Training Deep Learning Based Denoisers without Ground Truth Data](https://mlsanity.com/paper/1803.01314/) (2018)
- [Image Restoration by Denoising Diffusion Models with Iteratively Preconditioned Guidance](https://mlsanity.com/paper/2312.16519/) (2023)
- [Noise2Fast: Fast Self-Supervised Single Image Blind Denoising](https://mlsanity.com/paper/2108.10209/) (2021)
- [Fast Samplers for Inverse Problems in Iterative Refinement Models](https://mlsanity.com/paper/2405.17673/) (2024)
- [Noise Learning Based Denoising Autoencoder](https://mlsanity.com/paper/2101.07937/) (2021)
- [Unsupervised Image Restoration Using Partially Linear Denoisers](https://mlsanity.com/paper/2008.06164/) (2020)
- [Probabilistic Non-Local Means](https://mlsanity.com/paper/1302.5762/) (2013)
- [Deep Variation Prior: Joint Image Denoising and Noise Variance Estimation without Clean Data](https://mlsanity.com/paper/2209.09214/) (2022)

## Abstract (arXiv)

This work proposes a learning-based statistical refinement method for improving the denoising results of a given denoiser without knowing the precise noise distribution or accessing clean images or calibration data. While there are many existing successful denoising approaches for handling different kinds of noise, they typically require accurate modelling of the images and the noise (implicitly or explicitly), and hence the denoising results can be suboptimal due to different practical factors such as imperfect models, unreliable noise assumptions, or low quality data. In particular, when clean image samples are not available and there is a lack of knowledge of the underlying noise distribution, which is the case in various practical situations, the results may not well align with the noise statistics. The unawareness of the useful statistical information leads to suboptimal results. This work aims to make the best use of the statistical information to improve the consistency between the given denoising results and the noise statistics, under the assumption that the noise is conditionally pixel-wise independent given the clean signal. A method, based on a Bayesian formulation of an auxiliary signal in the noisy data, is proposed for evaluating the consistency of the denoising results, without precise information on noise distribution. By leveraging the statistical information from noisy data, the method enhances the statistical noise consistency and improves denoising quality.