Cauchy noise removal using group-based low-rank prior

Abstract Although the extensive research on Gaussian noise removal, few works consider the Cauchy noise removal problem. In this paper, we propose a novel group-based low-rank method for Cauchy noise removal. By exploiting the nonlocal self-similarity of natural images, we consider a group of similar patches as an approximate low-rank matrix, and formulate the denoising of each group as a low-rank matrix recovery problem. Meanwhile, we develop the alternating direction method of multipliers algorithm to solve the proposed nonconvex model with guaranteed convergence. Experiments illustrate that our method has superior performance over the state-of-the-art methods in terms of both visual and quantitative measures.

[1]  Abderrahim Elmoataz,et al.  Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing , 2008, IEEE Transactions on Image Processing.

[2]  Yong Yu,et al.  Robust Subspace Segmentation by Low-Rank Representation , 2010, ICML.

[3]  Wotao Yin,et al.  Global Convergence of ADMM in Nonconvex Nonsmooth Optimization , 2015, Journal of Scientific Computing.

[4]  Xi-Le Zhao,et al.  Low-Rank Tensor Completion Using Matrix Factorization Based on Tensor Train Rank and Total Variation , 2019, Journal of Scientific Computing.

[5]  Karl Kunisch,et al.  Total Generalized Variation , 2010, SIAM J. Imaging Sci..

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

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

[8]  Ting-Zhu Huang,et al.  Remote sensing images destriping using unidirectional hybrid total variation and nonconvex low-rank regularization , 2020, J. Comput. Appl. Math..

[9]  Zhixun Su,et al.  Fixed-rank representation for unsupervised visual learning , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[10]  Peter J. W. Rayner,et al.  Near optimal detection of signals in impulsive noise modeled with a symmetric /spl alpha/-stable distribution , 1998, IEEE Communications Letters.

[11]  Emmanuel J. Candès,et al.  A Singular Value Thresholding Algorithm for Matrix Completion , 2008, SIAM J. Optim..

[12]  Stanley Osher,et al.  Deblurring and Denoising of Images by Nonlocal Functionals , 2005, Multiscale Model. Simul..

[13]  Michael K. Ng,et al.  A New Convex Optimization Model for Multiplicative Noise and Blur Removal , 2014, SIAM J. Imaging Sci..

[14]  Yiqiu Dong,et al.  Cauchy Noise Removal by Nonconvex ADMM with Convergence Guarantees , 2017, Journal of Scientific Computing.

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

[16]  M. Shinde,et al.  Signal Detection in the Presence of Atmospheric Noise in Tropics , 1974, IEEE Trans. Commun..

[17]  Richard G. Baraniuk,et al.  Fast Alternating Direction Optimization Methods , 2014, SIAM J. Imaging Sci..

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

[19]  Ting-Zhu Huang,et al.  FastDeRain: A Novel Video Rain Streak Removal Method Using Directional Gradient Priors , 2018, IEEE Transactions on Image Processing.

[20]  Mathews Jacob,et al.  Higher Degree Total Variation (HDTV) Regularization for Image Recovery , 2012, IEEE Transactions on Image Processing.

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

[22]  Christine Guillemot,et al.  Image Inpainting : Overview and Recent Advances , 2014, IEEE Signal Processing Magazine.

[23]  Tieyong Zeng,et al.  Variational Approach for Restoring Blurred Images with Cauchy Noise , 2015, SIAM J. Imaging Sci..

[24]  Xi-Le Zhao,et al.  Total Variation Structured Total Least Squares Method for Image Restoration , 2013, SIAM J. Sci. Comput..

[25]  Tieyong Zeng,et al.  A Convex Variational Model for Restoring Blurred Images with Multiplicative Noise , 2013, SIAM J. Imaging Sci..

[26]  Gilles Aubert,et al.  Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing , 2009, SIAM J. Sci. Comput..

[27]  Ting-Zhu Huang,et al.  Group-based image decomposition using 3-D cartoon and texture priors , 2016, Inf. Sci..

[28]  John Wright,et al.  RASL: Robust Alignment by Sparse and Low-Rank Decomposition for Linearly Correlated Images , 2012, IEEE Trans. Pattern Anal. Mach. Intell..

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

[30]  Xue-Cheng Tai,et al.  Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models , 2010, SIAM J. Imaging Sci..

[31]  Raymond H. Chan,et al.  An Efficient Two-Phase ${\rm L}^{1}$-TV Method for Restoring Blurred Images with Impulse Noise , 2010, IEEE Transactions on Image Processing.

[32]  Tieyong Zeng,et al.  A Universal Variational Framework for Sparsity-Based Image Inpainting , 2014, IEEE Transactions on Image Processing.

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

[34]  Ting-Zhu Huang,et al.  Total variation with overlapping group sparsity for deblurring images under Cauchy noise , 2019, Appl. Math. Comput..

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

[36]  Ting-Zhu Huang,et al.  Low-rank tensor completion via combined non-local self-similarity and low-rank regularization , 2019, Neurocomputing.

[37]  Stanley Osher,et al.  Image Recovery via Nonlocal Operators , 2010, J. Sci. Comput..

[38]  Gabriele Steidl,et al.  Nonlocal Myriad Filters for Cauchy Noise Removal , 2017, Journal of Mathematical Imaging and Vision.

[39]  Liangpei Zhang,et al.  Hyperspectral Image Restoration Using Low-Rank Matrix Recovery , 2014, IEEE Transactions on Geoscience and Remote Sensing.

[40]  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).

[41]  Ting-Zhu Huang,et al.  Image deblurring with an inaccurate blur kernel using a group-based low-rank image prior , 2017, Inf. Sci..

[42]  Junfeng Yang,et al.  A New Alternating Minimization Algorithm for Total Variation Image Reconstruction , 2008, SIAM J. Imaging Sci..

[43]  Rob Fergus,et al.  Fast Image Deconvolution using Hyper-Laplacian Priors , 2009, NIPS.

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

[45]  Zuowei Shen,et al.  Robust Video Restoration by Joint Sparse and Low Rank Matrix Approximation , 2011, SIAM J. Imaging Sci..

[46]  Xi-Le Zhao,et al.  Low-rank tensor train for tensor robust principal component analysis , 2020, Appl. Math. Comput..

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

[48]  Xi-Le Zhao,et al.  Mixed Noise Removal in Hyperspectral Image via Low-Fibered-Rank Regularization , 2020, IEEE Transactions on Geoscience and Remote Sensing.

[49]  Tony F. Chan,et al.  Image decomposition combining staircase reduction and texture extraction , 2007, J. Vis. Commun. Image Represent..

[50]  Dong Wang,et al.  Denoising of Hyperspectral Images Using Nonconvex Low Rank Matrix Approximation , 2017, IEEE Transactions on Geoscience and Remote Sensing.

[51]  Monika Agrawal,et al.  Underwater acoustic communication in the presence of heavy-tailed impulsive noise with bi-parameter cauchy-Gaussian mixture model , 2013, 2013 Ocean Electronics (SYMPOL).

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