Non-Local Patch Regression: Robust Image Denoising in Patch Space

TL;DR

This paper explores the use of non-convex l_p regression (0<p<1) in patch space for robust image denoising, building on prior work that improved performance at high noise levels using Euclidean medians.

Contribution

It introduces the idea of applying l_p regression with 0<p<1 in patch space for denoising, extending previous Euclidean median methods to potentially enhance robustness.

Findings

l_p regression can improve denoising performance at high noise levels

Non-convex l_p regression offers robustness against outliers in patch-based denoising

Potential for better edge preservation compared to traditional methods

Abstract

It was recently demonstrated in [Chaudhury et al.,Non-Local Euclidean Medians,2012] that the denoising performance of Non-Local Means (NLM) can be improved at large noise levels by replacing the mean by the robust Euclidean median. Numerical experiments on synthetic and natural images showed that the latter consistently performed better than NLM beyond a certain noise level, and significantly so for images with sharp edges. The Euclidean mean and median can be put into a common regression (on the patch space) framework, in which the l_2 norm of the residuals is considered in the former, while the l_1 norm is considered in the latter. The natural question then is what happens if we consider l_p (0<p<1) regression? We investigate this possibility in this paper.