Convergence Theorems for the Non-Local Means Filter

TL;DR

This paper proves convergence theorems for the Non-Local Means Filter in Gaussian noise removal, providing practical parameter choices that enhance image restoration quality.

Contribution

It introduces convergence theorems for the filter and proposes improved parameter selection methods based on Oracle estimation techniques.

Findings

Convergence theorems established for the Non-Local Means Filter.

Practical parameter choices improve image restoration quality.

Enhanced understanding of parameter selection impacts on filter performance.

Abstract

In this paper, we establish convergence theorems for the Non-Local Means Filter in removing the additive Gaussian noise. We employ the techniques of "Oracle" estimation to determine the order of the widths of the similarity patches and search windows in the aforementioned filter. We propose a practical choice of these parameters which improve the restoration quality of the filter compared with the usual choice of parameters.