Linear Combinations of Patches are Unreasonably Effective for Single-Image Denoising

TL;DR

This paper demonstrates that simple linear combinations of image patches can achieve state-of-the-art single-image denoising, rivaling complex neural networks while being faster and more interpretable.

Contribution

The authors introduce a novel, fully interpretable linear patch combination method that matches or exceeds current state-of-the-art single-image denoising performance.

Findings

Achieves state-of-the-art results on Gaussian and real-world noisy images.

Outperforms recent neural network-based denoisers in speed and interpretability.

Demonstrates effectiveness of simple linear models for complex denoising tasks.

Abstract

In the past decade, deep neural networks have revolutionized image denoising in achieving significant accuracy improvements by learning on datasets composed of noisy/clean image pairs. However, this strategy is extremely dependent on training data quality, which is a well-established weakness. To alleviate the requirement to learn image priors externally, single-image (a.k.a., self-supervised or zero-shot) methods perform denoising solely based on the analysis of the input noisy image without external dictionary or training dataset. This work investigates the effectiveness of linear combinations of patches for denoising under this constraint. Although conceptually very simple, we show that linear combinations of patches are enough to achieve state-of-the-art performance. The proposed parametric approach relies on quadratic risk approximation via multiple pilot images to guide the estimation of the combination weights. Experiments on images corrupted artificially with Gaussian noise as well as on real-world noisy images demonstrate that our method is on par with the very best single-image denoisers, outperforming the recent neural network based techniques, while being much faster and fully interpretable.