# A unified framework of non-local parametric methods for image denoising

arXiv: https://arxiv.org/abs/2402.13816 · HTML: https://mlsanity.com/paper/2402.13816/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 60 references that are in the map.
- First posted on arXiv 21 Feb 2024.

## Builds on (most cited first, 24 of 24)

- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (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)
- [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)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [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)
- [Benchmarking Denoising Algorithms with Real Photographs](https://mlsanity.com/paper/1707.01313/) (2017)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Multi-level Wavelet-CNN for Image Restoration](https://mlsanity.com/paper/1805.07071/) (2018)
- [High-Quality Self-Supervised Deep Image Denoising](https://mlsanity.com/paper/1901.10277/) (2019)
- [Non-Local Recurrent Network for Image Restoration](https://mlsanity.com/paper/1806.02919/) (2018)
- [Noisier2Noise: Learning to Denoise from Unpaired Noisy Data](https://mlsanity.com/paper/1910.11908/) (2019)
- [Neural Nearest Neighbors Networks](https://mlsanity.com/paper/1810.12575/) (2018)
- [Practical Blind Image Denoising via Swin-Conv-UNet and Data Synthesis](https://mlsanity.com/paper/2203.13278/) (2022)
- [Zero-Shot Noise2Noise: Efficient Image Denoising without any Data](https://mlsanity.com/paper/2303.11253/) (2023)
- [A Trilateral Weighted Sparse Coding Scheme for Real-World Image Denoising](https://mlsanity.com/paper/1807.04364/) (2018)
- [Rethinking Deep Image Prior for Denoising](https://mlsanity.com/paper/2108.12841/) (2021)
- [Noise2Fast: Fast Self-Supervised Single Image Blind Denoising](https://mlsanity.com/paper/2108.10209/) (2021)
- [Normalization-Equivariant Neural Networks with Application to Image Denoising](https://mlsanity.com/paper/2306.05037/) (2023)
- [DCT2net: an interpretable shallow CNN for image denoising](https://mlsanity.com/paper/2107.14803/) (2021)
- [Towards a unified view of unsupervised non-local methods for image denoising: the NL-Ridge approach](https://mlsanity.com/paper/2203.00570/) (2022)

## Abstract (arXiv)

We propose a unified view of non-local methods for single-image denoising, for which BM3D is the most popular representative, that operate by gathering noisy patches together according to their similarities in order to process them collaboratively. Our general estimation framework is based on the minimization of the quadratic risk, which is approximated in two steps, and adapts to photon and electronic noises. Relying on unbiased risk estimation (URE) for the first step and on ``internal adaptation'', a concept borrowed from deep learning theory, for the second, we show that our approach enables to reinterpret and reconcile previous state-of-the-art non-local methods. Within this framework, we propose a novel denoiser called NL-Ridge that exploits linear combinations of patches. While conceptually simpler, we show that NL-Ridge can outperform well-established state-of-the-art single-image denoisers.