SURE-Based Non-Local Means

Non-local means (NLM) provides a powerful framework for denoising. However, there are a few parameters of the algorithm-most notably, the width of the smoothing kernel-that are data-dependent and difficult to tune. Here, we propose to use Stein's unbiased risk estimate (SURE) to monitor the mean square error (MSE) of the NLM algorithm for restoration of an image corrupted by additive white Gaussian noise. The SURE principle allows to assess the MSE without knowledge of the noise-free signal. We derive an explicit analytical expression for SURE in the setting of NLM that can be incorporated in the implementation at low computational cost. Finally, we present experimental results that confirm the optimality of the proposed parameter selection.

[1]  Thierry Blu,et al.  Monte-Carlo Sure: A Black-Box Optimization of Regularization Parameters for General Denoising Algorithms , 2008, IEEE Transactions on Image Processing.

[2]  Aleksandra Pizurica,et al.  An improved non-local denoising algorithm , 2008 .

[3]  Charles Kervrann,et al.  Optimal Spatial Adaptation for Patch-Based Image Denoising , 2006, IEEE Transactions on Image Processing.

[4]  Daniel Cremers,et al.  Efficient Nonlocal Means for Denoising of Textural Patterns , 2008, IEEE Transactions on Image Processing.

[5]  Wilfried Philips,et al.  A fast non-local image denoising algorithm , 2008, Electronic Imaging.

[6]  G. Peyré.  Image Processing with Non-local Spectral Bases , 2008 .

[7]  Nikos Paragios,et al.  Image Denoising Based on Adapted Dictionary Computation , 2007, 2007 IEEE International Conference on Image Processing.

[8]  Amel Benazza-Benyahia,et al.  Building robust wavelet estimators for multicomponent images using Stein's principle , 2005, IEEE Transactions on Image Processing.

[9]  J. Weickert,et al.  A ROTATIONALLY INVARIANT BLOCK MATCHING STRATEGY IMPROVING IMAGE DENOISING WITH NON-LOCAL MEANS , 2008 .

[10]  Pierrick Coupé,et al.  An Optimized Blockwise Nonlocal Means Denoising Filter for 3-D Magnetic Resonance Images , 2008, IEEE Transactions on Medical Imaging.

[11]  Mithun Uliyar,et al.  Fast Non-Local algorithm for image denoising , 2009, 2009 16th IEEE International Conference on Image Processing (ICIP).

[12]  Thierry Blu,et al.  A New SURE Approach to Image Denoising: Interscale Orthonormal Wavelet Thresholding , 2007, IEEE Transactions on Image Processing.

[13]  Yonina C. Eldar.  Generalized SURE for Exponential Families: Applications to Regularization , 2008, IEEE Transactions on Signal Processing.

[14]  C. Stein.  Estimation of the Mean of a Multivariate Normal Distribution , 1981 .

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

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

[17]  Gabriel Peyré,et al.  Image Processing with Nonlocal Spectral Bases , 2008, Multiscale Model. Simul..

[18]  Peyman Milanfar,et al.  A generalization of non-local means via kernel regression , 2008, Electronic Imaging.

[19]  Mehran Ebrahimi,et al.  Efficient nonlocal-means denoising using the SVD , 2008, 2008 15th IEEE International Conference on Image Processing.

[20]  Guillermo Sapiro,et al.  Fast image and video denoising via nonlocal means of similar neighborhoods , 2005, IEEE Signal Processing Letters.