Probabilistic Non-Local Means

In this letter, 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. Our simulation results indicate the PNLM outperforms the classic NLM and many NLM recent variants in terms of the peak signal noise ratio (PSNR) and the structural similarity (SSIM) index. Encouraging improvements are also found when we replace the NLM weights with the PNLM weights in tested NLM variants.

[1]  Alessandro Foi,et al.  Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering , 2007, IEEE Transactions on Image Processing.

[2]  Kunal N. Chaudhury,et al.  On the Convergence of the IRLS Algorithm in Non-Local Patch Regression , 2013, IEEE Signal Processing Letters.

[3]  Jean-Michel Morel,et al.  A Review of Image Denoising Algorithms, with a New One , 2005, Multiscale Model. Simul..

[4]  Joseph Salmon,et al.  On Two Parameters for Denoising With Non-Local Means , 2010, IEEE Signal Processing Letters.

[5]  Neil A. Thacker,et al.  A statistical interpretation of Non-Local Means , 2008 .

[6]  Amit Singer,et al.  Non-Local Euclidean Medians , 2012, IEEE Signal Processing Letters.

[7]  C.-C. Jay Kuo,et al.  Fast Non-Local Means (NLM) Computation With Probabilistic Early Termination , 2010, IEEE Signal Processing Letters.

[8]  Eero P. Simoncelli,et al.  Image quality assessment: from error visibility to structural similarity , 2004, IEEE Transactions on Image Processing.

[9]  Yann Gousseau,et al.  A Bias-Variance Approach for the Nonlocal Means , 2011, SIAM J. Imaging Sci..

[10]  Kunal N. Chaudhury,et al.  Acceleration of the Shiftable $\mbi{O}{(1)}$ Algorithm for Bilateral Filtering and Nonlocal Means , 2012, IEEE Transactions on Image Processing.

[11]  Yue Wu,et al.  James–Stein Type Center Pixel Weights for Non-Local Means Image Denoising , 2012, IEEE Signal Processing Letters.

[12]  Jean-Michel Morel,et al.  A non-local algorithm for image denoising , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[13]  Karen O. Egiazarian,et al.  Image denoising with block-matching and 3D filtering , 2006, Electronic Imaging.

[14]  K. Jayachandra Reddy.  Acceleration of Shiftable O (1) Algorithm for Bilateral Filtering and Non-local means , 2014 .

[15]  Songcan Chen,et al.  Modifying NL-means to a universal filter , 2012 .

[16]  Li-Ling Chuang,et al.  Approximated distributions of the weighted sum of correlated chi-squared random variables , 2012 .

[17]  Dimitri Van De Ville,et al.  SURE-Based Non-Local Means , 2009, IEEE Signal Processing Letters.