Image restoration approach using a joint sparse representation in 3D-transform domain

Abstract Image restoration is a crucial problem in image processing and a necessary step before the image segmentation and recognition. A new framework for image restoration in 3D transform domain terms as joint sparse representation (JSR) is proposed in this work. The proposed JSR is able to represent image more sparsely and more precisely in the transform domain by performing 3D transform on each set of similar blocks. In addition to that, in order to overcome the issues of defective block matching and spurious artifact in the 3D sparse representation, JSR introduces a new nonlocal regularization term which characterizes the statistics of the nonlocal image to improve the accuracy of the estimated coefficients. The parameters of regularization terms are calculated based on Bayesian philosophy, and a split Bregman-based technique is developed to obtain the solution in a tractable and robust manner. Extensive experiments on image denoising, image inpainting and image deblurring demonstrate that the proposed JSR algorithm outperforms current state-of-the-art approaches in terms of peak signal-to-noise ratio and visual quality.

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

[2]  Wei Liu,et al.  Dictionary Pair Learning on Grassmann Manifolds for Image Denoising , 2015, IEEE Transactions on Image Processing.

[3]  Fabrizio Argenti,et al.  Speckle removal from SAR images in the undecimated wavelet domain , 2002, IEEE Trans. Geosci. Remote. Sens..

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

[5]  Lei Zhang,et al.  Nonlocally Centralized Sparse Representation for Image Restoration , 2013, IEEE Transactions on Image Processing.

[6]  Luisa Verdoliva,et al.  A Nonlocal SAR Image Denoising Algorithm Based on LLMMSE Wavelet Shrinkage , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[7]  José M. Bioucas-Dias,et al.  Fast Image Recovery Using Variable Splitting and Constrained Optimization , 2009, IEEE Transactions on Image Processing.

[8]  Pheng-Ann Heng,et al.  Adaptive total variation denoising based on difference curvature , 2010, Image Vis. Comput..

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

[10]  Lei Zhang,et al.  Image reconstruction with locally adaptive sparsity and nonlocal robust regularization , 2012, Signal Process. Image Commun..

[11]  Karen O. Egiazarian,et al.  Pointwise Shape-Adaptive DCT for High-Quality Denoising and Deblocking of Grayscale and Color Images , 2007, IEEE Transactions on Image Processing.

[12]  José M. Bioucas-Dias,et al.  Adaptive total variation image deblurring: A majorization-minimization approach , 2009, Signal Process..

[13]  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).

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

[15]  David B. Dunson,et al.  Nonparametric Bayesian Dictionary Learning for Analysis of Noisy and Incomplete Images , 2012, IEEE Transactions on Image Processing.

[16]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[17]  Jian Zhang,et al.  Image Restoration Using Joint Statistical Modeling in a Space-Transform Domain , 2014, IEEE Transactions on Circuits and Systems for Video Technology.

[18]  M. Nikolova.  An Algorithm for Total Variation Minimization and Applications , 2004 .

[19]  Hang Yang,et al.  Low-rank approach for image nonblind deconvolution with variance estimation , 2015, J. Electronic Imaging.

[20]  Wen Gao,et al.  Group-Based Sparse Representation for Image Restoration , 2014, IEEE Transactions on Image Processing.

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

[22]  Guangming Shi,et al.  Image Restoration via Simultaneous Sparse Coding: Where Structured Sparsity Meets Gaussian Scale Mixture , 2015, International Journal of Computer Vision.

[23]  Di Guo,et al.  Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization. , 2013, Magnetic resonance imaging.

[24]  Karen O. Egiazarian,et al.  BM3D Frames and Variational Image Deblurring , 2011, IEEE Transactions on Image Processing.

[25]  Lei Zhang,et al.  Image Deblurring and Super-Resolution by Adaptive Sparse Domain Selection and Adaptive Regularization , 2010, IEEE Transactions on Image Processing.

[26]  Yin Zhang,et al.  An efficient augmented Lagrangian method with applications to total variation minimization , 2013, Computational Optimization and Applications.

[27]  Jean-François Aujol,et al.  Adaptive Regularization of the NL-Means: Application to Image and Video Denoising , 2014, IEEE Transactions on Image Processing.

[28]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[29]  Xavier Bresson,et al.  Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction , 2010, SIAM J. Imaging Sci..

[30]  Stephen P. Boyd,et al.  Enhancing Sparsity by Reweighted ℓ1 Minimization , 2007, 0711.1612.

[31]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[32]  Xue-Cheng Tai,et al.  Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional , 2005, International Journal of Computer Vision.

[33]  Shuaiqi Liu,et al.  Bayesian Shearlet shrinkage for SAR image de-noising via sparse representation , 2014, Multidimens. Syst. Signal Process..

[34]  Karen O. Egiazarian,et al.  Image restoration by sparse 3D transform-domain collaborative filtering , 2008, Electronic Imaging.

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

[36]  Thomas S. Huang,et al.  Image Super-Resolution Via Sparse Representation , 2010, IEEE Transactions on Image Processing.

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

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

[39]  Lei Zhang,et al.  Centralized sparse representation for image restoration , 2011, 2011 International Conference on Computer Vision.

[40]  Lei Zhang,et al.  Weighted Nuclear Norm Minimization with Application to Image Denoising , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[41]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[42]  Michael Elad,et al.  On the Role of Sparse and Redundant Representations in Image Processing , 2010, Proceedings of the IEEE.

[43]  Florence Tupin,et al.  Iterative Weighted Maximum Likelihood Denoising With Probabilistic Patch-Based Weights , 2009, IEEE Transactions on Image Processing.

[44]  Jérôme Darbon,et al.  Enhancement of historical printed document images by combining Total Variation regularization and Non-local Means filtering , 2011, Image Vis. Comput..

[45]  Marc Teboulle,et al.  Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems , 2009, IEEE Transactions on Image Processing.

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