Probabilistic Non-Local Means

TL;DR

This paper introduces a probabilistic non-local means (PNLM) method for image denoising that improves upon classic NLM by deriving accurate statistical models and probabilistic weights, leading to better PSNR and SSIM results.

Contribution

The paper identifies flaws in the classic NLM weight function, derives theoretical statistics for Gaussian noise, and formulates a probabilistic weight function that enhances denoising performance.

Findings

PNLM outperforms classic NLM in PSNR and SSIM.

Probabilistic weights improve the performance of NLM variants.

Theoretical basis enables thresholding for faster computation.

Abstract

In this paper, we propose a so-called probabilistic non-local means (PNLM) method for image denoising. Our main contributions are: 1) we point out defects of the weight function used in the classic NLM; 2) we successfully derive all theoretical statistics of patch-wise differences for Gaussian noise; and 3) we employ this prior information and formulate the probabilistic weights truly reflecting the similarity between two noisy patches. The probabilistic nature of the new weight function also provides a theoretical basis to choose thresholds rejecting dissimilar patches for fast computations. Our simulation results indicate the PNLM outperforms the classic NLM and many NLM recent variants in terms of peak signal noise ratio (PSNR) and structural similarity (SSIM) index. Encouraging improvements are also found when we replace the NLM weights with the probabilistic weights in tested NLM variants.