Random matrix route to image denoising

TL;DR

This paper introduces a novel image denoising method leveraging random matrix theory to identify noise thresholds by analyzing eigenvalues of correlation matrices, effectively separating noise from image features.

Contribution

It presents a new denoising approach based on random matrix theory, providing an analytical noise threshold for Gaussian noise using eigenvalue distributions.

Findings

Effective noise separation using eigenvalue thresholds

Applicable to images with correlated noise

Improved denoising performance demonstrated

Abstract

We make use of recent results from random matrix theory to identify a derived threshold, for isolating noise from image features. The procedure assumes the existence of a set of noisy images, where denoising can be carried out on individual rows or columns independently. The fact that these are guaranteed to be correlated makes the correlation matrix an ideal tool for isolating noise. The random matrix result provides lowest and highest eigenvalues for the Gaussian random noise for which case, the eigenvalue distribution function is analytically known. This provides an ideal threshold for removing Gaussian random noise and thereby separating the universal noisy features from the non-universal components belonging to the specific image under consideration.