# Unsupervised Image Restoration Using Partially Linear Denoisers

arXiv: https://arxiv.org/abs/2008.06164 · HTML: https://mlsanity.com/paper/2008.06164/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Aug 2020.

## Built on by (most cited first, 5 of 5)

- [Generative Diffusion Prior for Unified Image Restoration and Enhancement](https://mlsanity.com/paper/2304.01247/) (2023)
- [Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging](https://mlsanity.com/paper/2311.08972/) (2023)
- [Deep Variation Prior: Joint Image Denoising and Noise Variance Estimation without Clean Data](https://mlsanity.com/paper/2209.09214/) (2022)
- [Look-Around Before You Leap: High-Frequency Injected Transformer for Image Restoration](https://mlsanity.com/paper/2404.00279/) (2024)
- [Learning-based Statistical Refinement for Denoising](https://mlsanity.com/paper/2605.04332/) (2026)

## Abstract (arXiv)

Deep neural network based methods are the state of the art in various image restoration problems. Standard supervised learning frameworks require a set of noisy measurement and clean image pairs for which a distance between the output of the restoration model and the ground truth, clean images is minimized. The ground truth images, however, are often unavailable or very expensive to acquire in real-world applications. We circumvent this problem by proposing a class of structured denoisers that can be decomposed as the sum of a nonlinear image-dependent mapping, a linear noise-dependent term and a small residual term. We show that these denoisers can be trained with only noisy images under the condition that the noise has zero mean and known variance. The exact distribution of the noise, however, is not assumed to be known. We show the superiority of our approach for image denoising, and demonstrate its extension to solving other restoration problems such as blind deblurring where the ground truth is not available. Our method outperforms some recent unsupervised and self-supervised deep denoising models that do not require clean images for their training. For blind deblurring problems, the method, using only one noisy and blurry observation per image, reaches a quality not far away from its fully supervised counterparts on a benchmark dataset.