# Deep Variation Prior: Joint Image Denoising and Noise Variance Estimation without Clean Data

arXiv: https://arxiv.org/abs/2209.09214 · HTML: https://mlsanity.com/paper/2209.09214/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 19 Sep 2022.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [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)
- [Noise2Noise: Learning Image Restoration without Clean Data](https://mlsanity.com/paper/1803.04189/) (2018)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [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)
- [Neighbor2Neighbor: Self-Supervised Denoising from Single Noisy Images](https://mlsanity.com/paper/2101.02824/) (2021)
- [Dual Adversarial Network: Toward Real-world Noise Removal and Noise Generation](https://mlsanity.com/paper/2007.05946/) (2020)
- [Practical Blind Image Denoising via Swin-Conv-UNet and Data Synthesis](https://mlsanity.com/paper/2203.13278/) (2022)
- [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)
- [GRDN:Grouped Residual Dense Network for Real Image Denoising and GAN-based Real-world Noise Modeling](https://mlsanity.com/paper/1905.11172/) (2019)
- [FBI-Denoiser: Fast Blind Image Denoiser for Poisson-Gaussian Noise](https://mlsanity.com/paper/2105.10967/) (2021)
- [Real-time Streaming Video Denoising with Bidirectional Buffers](https://mlsanity.com/paper/2207.06937/) (2022)
- [Unsupervised Image Restoration Using Partially Linear Denoisers](https://mlsanity.com/paper/2008.06164/) (2020)
- [Learning-based Noise Component Map Estimation for Image Denoising](https://mlsanity.com/paper/2109.11877/) (2021)
- [Unsupervised Image Noise Modeling with Self-Consistent GAN](https://mlsanity.com/paper/1906.05762/) (2019)

## Built on by (most cited first, 2 of 2)

- [Beyond Image Prior: Embedding Noise Prior into Conditional Denoising Transformer](https://mlsanity.com/paper/2407.09094/) (2024)
- [Learning-based Statistical Refinement for Denoising](https://mlsanity.com/paper/2605.04332/) (2026)

## Abstract (arXiv)

With recent deep learning based approaches showing promising results in removing noise from images, the best denoising performance has been reported in a supervised learning setup that requires a large set of paired noisy images and ground truth for training. The strong data requirement can be mitigated by unsupervised learning techniques, however, accurate modelling of images or noise variance is still crucial for high-quality solutions. The learning problem is ill-posed for unknown noise distributions. This paper investigates the tasks of image denoising and noise variance estimation in a single, joint learning framework. To address the ill-posedness of the problem, we present deep variation prior (DVP), which states that the variation of a properly learnt denoiser with respect to the change of noise satisfies some smoothness properties, as a key criterion for good denoisers. Building upon DVP, an unsupervised deep learning framework, that simultaneously learns a denoiser and estimates noise variances, is developed. Our method does not require any clean training images or an external step of noise estimation, and instead, approximates the minimum mean squared error denoisers using only a set of noisy images. With the two underlying tasks being considered in a single framework, we allow them to be optimised for each other. The experimental results show a denoising quality comparable to that of supervised learning and accurate noise variance estimates.