# Towards a unified view of unsupervised non-local methods for image denoising: the NL-Ridge approach

arXiv: https://arxiv.org/abs/2203.00570 · HTML: https://mlsanity.com/paper/2203.00570/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 23 references that are in the map.
- First posted on arXiv 1 Mar 2022.

## Builds on (most cited first, 5 of 5)

- [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)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Noise2Self: Blind Denoising by Self-Supervision](https://mlsanity.com/paper/1901.11365/) (2019)
- [A note on patch-based low-rank minimization for fast image denoising](https://mlsanity.com/paper/1506.08353/) (2015)

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

- [Normalization-Equivariant Neural Networks with Application to Image Denoising](https://mlsanity.com/paper/2306.05037/) (2023)
- [Linear Combinations of Patches are Unreasonably Effective for Single-Image Denoising](https://mlsanity.com/paper/2212.00422/) (2022)
- [Self-Calibrated Variance-Stabilizing Transformations for Real-World Image Denoising](https://mlsanity.com/paper/2407.17399/) (2024)
- [On normalization-equivariance properties of supervised and unsupervised denoising methods: a survey](https://mlsanity.com/paper/2402.15352/) (2024)
- [A unified framework of non-local parametric methods for image denoising](https://mlsanity.com/paper/2402.13816/) (2024)

## Abstract (arXiv)

We propose a unified view of unsupervised non-local methods for image denoising that linearily combine noisy image patches. The best methods, established in different modeling and estimation frameworks, are two-step algorithms. Leveraging Stein's unbiased risk estimate (SURE) for the first step and the "internal adaptation", a concept borrowed from deep learning theory, for the second one, we show that our NL-Ridge approach enables to reconcile several patch aggregation methods for image denoising. In the second step, our closed-form aggregation weights are computed through multivariate Ridge regressions. Experiments on artificially noisy images demonstrate that NL-Ridge may outperform well established state-of-the-art unsupervised denoisers such as BM3D and NL-Bayes, as well as recent unsupervised deep learning methods, while being simpler conceptually.