Nonlocal image denoising via collaborative spatial-domain LMMSE estimation

In recent years, the performance of image denoising has been boosted drastically by nonlocal algorithms and sparse coding techniques. In this paper, we also take a nonlocal approach to image denoising and formulate the problem as one of collaborative LMMSE estimation from grouped image patches. We show that our optimal LMMSE solution amounts to shrinking the singular values of the matrix representation of the grouped image patches. This interpretation of our solution allows us to relate our estimation-theoretic approach to other nonlocal algorithms and sparse coding techniques in the literature. In addition, we develop an iterative algorithm to find the best LMMSE estimate. Experimental results show that our proposed denoising algorithm achieves better PSNR and subjective performance than the state of the art.

[1]  Jaakko Astola,et al.  From Local Kernel to Nonlocal Multiple-Model Image Denoising , 2009, International Journal of Computer Vision.

[2]  Guangming Shi,et al.  Nonlocal Image Restoration With Bilateral Variance Estimation: A Low-Rank Approach , 2013, IEEE Transactions on Image Processing.

[3]  David Zhang,et al.  Two-stage image denoising by principal component analysis with local pixel grouping , 2010, Pattern Recognit..

[4]  Martin Vetterli,et al.  Adaptive wavelet thresholding for image denoising and compression , 2000, IEEE Trans. Image Process..

[5]  Anand Rangarajan,et al.  Image Denoising Using the Higher Order Singular Value Decomposition , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Minh N. Do,et al.  The Nonsubsampled Contourlet Transform: Theory, Design, and Applications , 2006, IEEE Transactions on Image Processing.

[7]  Karen O. Egiazarian,et al.  Video denoising by sparse 3D transform-domain collaborative filtering , 2007, 2007 15th European Signal Processing Conference.

[8]  Martin J. Wainwright,et al.  Image denoising using scale mixtures of Gaussians in the wavelet domain , 2003, IEEE Trans. Image Process..

[9]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[10]  Hayder Radha,et al.  Translation-Invariant Contourlet Transform and Its Application to Image Denoising , 2006, IEEE Transactions on Image Processing.

[11]  Lei Zhang,et al.  Sparsity-based image denoising via dictionary learning and structural clustering , 2011, CVPR 2011.

[12]  Michael Elad,et al.  Sparse Representation for Color Image Restoration , 2008, IEEE Transactions on Image Processing.

[13]  Guy Gilboa,et al.  Nonlocal Operators with Applications to Image Processing , 2008, Multiscale Model. Simul..

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

[15]  Peyman Milanfar,et al.  Clustering-Based Denoising With Locally Learned Dictionaries , 2009, IEEE Transactions on Image Processing.

[16]  Guillermo Sapiro,et al.  Non-local sparse models for image restoration , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[17]  E. Candès,et al.  Recovering edges in ill-posed inverse problems: optimality of curvelet frames , 2002 .

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

[19]  Michael Elad,et al.  Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries , 2006, IEEE Transactions on Image Processing.

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

[21]  Charles Kervrann,et al.  Unsupervised Patch-Based Image Regularization and Representation , 2006, ECCV.

[22]  A. Bruckstein,et al.  K-SVD : An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation , 2005 .

[23]  Michael Elad,et al.  Multi-Scale Dictionary Learning Using Wavelets , 2011, IEEE Journal of Selected Topics in Signal Processing.

[24]  Emmanuel J. Candès,et al.  The curvelet transform for image denoising , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).