Image denoising using common vector approach

Common vector approach (CVA) is an increasingly popular classification method in recognition problems where probability of having the dimensionality of the problem higher than the number of data items is not zero. In CVA, common component of the members of classes is separated from the discriminating difference parts and used to determine whether a given vector (a block of data) belongs to the class in question, or to find out the class it belongs to. In this study, overlapping image blocks near the current pixel to be denoised are used as input data and a class is constructed per pixel position. Denoised image block is then constructed with the sum of common vector of the class and difference vector of the centre block denoised by linear minimum mean square error estimation technique. Since the classes are formed using similar blocks, the edges are preserved while denoising the image.

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

[2]  Olga Veksler,et al.  Fast Approximate Energy Minimization via Graph Cuts , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Marshall F. Tappen,et al.  Learning non-local range Markov Random field for image restoration , 2011, CVPR 2011.

[4]  M. Bilginer Gülmezoglu,et al.  A novel approach to isolated word recognition , 1999, IEEE Trans. Speech Audio Process..

[5]  D. Donoho,et al.  Translation-Invariant De-Noising , 1995 .

[6]  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).

[7]  Pangan Ting,et al.  A Shrinkage Linear Minimum Mean Square Error Estimator , 2013, IEEE Signal Processing Letters.

[8]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[9]  Thomas W. Parks,et al.  Adaptive principal components and image denoising , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[10]  M. Bilginer Gülmezoglu,et al.  The common vector approach and its relation to principal component analysis , 2001, IEEE Trans. Speech Audio Process..

[11]  Kannan Ramchandran,et al.  Low-complexity image denoising based on statistical modeling of wavelet coefficients , 1999, IEEE Signal Processing Letters.

[12]  Bryan C. Russell,et al.  Exploiting the sparse derivative prior for super-resolution , 2003 .

[13]  Mislav Grgic,et al.  Independent comparative study of PCA, ICA, and LDA on the FERET data set , 2005, Int. J. Imaging Syst. Technol..

[14]  M. Bilginer Gülmezoglu,et al.  The common vector approach and its comparison with other subspace methods in case of sufficient data , 2007, Comput. Speech Lang..

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

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

[17]  D. L. Donoho,et al.  Ideal spacial adaptation via wavelet shrinkage , 1994 .

[18]  Hakan Cevikalp,et al.  Discriminative common vectors for face recognition , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

[20]  Qi Gao,et al.  A generative perspective on MRFs in low-level vision , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

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

[22]  Michael J. Black,et al.  Fields of Experts , 2009, International Journal of Computer Vision.

[23]  Adrian Barbu,et al.  Training an Active Random Field for Real-Time Image Denoising , 2009, IEEE Transactions on Image Processing.

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

[25]  Martin Vetterli,et al.  Spatially adaptive wavelet thresholding with context modeling for image denoising , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[26]  Balázs Kégl,et al.  Image denoising with complex ridgelets , 2007, Pattern Recognit..

[27]  Geoffrey E. Hinton Products of experts , 1999 .

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

[29]  Aleksandra Pizurica,et al.  A joint inter- and intrascale statistical model for Bayesian wavelet based image denoising , 2002, IEEE Trans. Image Process..

[30]  Arnak S. Dalalyan,et al.  Image denoising with patch based PCA: local versus global , 2011, BMVC.

[31]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .