Anisotropic Nonlocal Means Denoising

TL;DR

This paper introduces anisotropic nonlocal means algorithms that improve image denoising near edges by adapting to image gradients, achieving near minimax optimality and outperforming traditional NLM methods on real images.

Contribution

The paper develops and analyzes anisotropic NLM algorithms that address the isotropic limitations of standard NLM, demonstrating theoretical optimality and practical superiority.

Findings

ANLM algorithms are near minimax optimal for edge images.

ANLM outperforms NLM on real-world images.

Theoretical analysis confirms the effectiveness of anisotropic neighborhoods.

Abstract

It has recently been proved that the popular nonlocal means (NLM) denoising algorithm does not optimally denoise images with sharp edges. Its weakness lies in the isotropic nature of the neighborhoods it uses to set its smoothing weights. In response, in this paper we introduce several theoretical and practical anisotropic nonlocal means (ANLM) algorithms and prove that they are near minimax optimal for edge-dominated images from the Horizon class. On real-world test images, an ANLM algorithm that adapts to the underlying image gradients outperforms NLM by a significant margin.