  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.
