Robust image restoration via random projection and partial sorted ℓp norm

Image restoration plays an important role in video technology. In this paper, a robust image and video denoising method, based on random projection and partial sorted p-norm, is proposed. First, the input signal is decomposed into two components: a low rank component and a sparse component. The low rank component is approximated by random projection. Second, the sparse one is recovered by partial sorted p-norm. A generalized iterative thresholding shrinkage solver is developed for the resulting problem. Some theoretical results about sparse random projection are provided. Numerical experiments for mixed Gaussian and random value impulsive noise demonstrated that the proposed method outperforms some state-of-art restoration methods, both quantitatively and visually.

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

[2]  Dimitris Achlioptas,et al.  Database-friendly random projections: Johnson-Lindenstrauss with binary coins , 2003, J. Comput. Syst. Sci..

[3]  Peter Buneman,et al.  Proceedings of the Twentieth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, May 21-23, 2001, Santa Barbara, California, USA , 2001 .

[4]  Jun Yu,et al.  Coupled Deep Autoencoder for Single Image Super-Resolution , 2017, IEEE Transactions on Cybernetics.

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

[6]  Michael Elad,et al.  Image Sequence Denoising via Sparse and Redundant Representations , 2009, IEEE Transactions on Image Processing.

[7]  Glenn R. Easley,et al.  Shearlet-Based Total Variation Diffusion for Denoising , 2009, IEEE Transactions on Image Processing.

[8]  David Zhang,et al.  Fast total-variation based image restoration based on derivative alternated direction optimization methods , 2015, Neurocomputing.

[9]  W. B. Johnson,et al.  Extensions of Lipschitz mappings into Hilbert space , 1984 .

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

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

[12]  Corina Nafornita,et al.  Image Denoising Using a New Implementation of the Hyperanalytic Wavelet Transform , 2009, IEEE Transactions on Instrumentation and Measurement.

[13]  Jieping Ye,et al.  A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems , 2013, ICML.

[14]  David Zhang,et al.  FSIM: A Feature Similarity Index for Image Quality Assessment , 2011, IEEE Transactions on Image Processing.

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

[16]  Sanjoy Dasgupta,et al.  An elementary proof of a theorem of Johnson and Lindenstrauss , 2003, Random Struct. Algorithms.

[17]  Zuowei Shen,et al.  Robust video denoising using low rank matrix completion , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[18]  Xuelong Li,et al.  Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  C. Vogel.  Computational Methods for Inverse Problems , 1987 .

[20]  Zhongliang Jing,et al.  A sparse proximal Newton splitting method for constrained image deblurring , 2013, Neurocomputing.

[21]  Shihwa Lee,et al.  A cross-channel bilateral filter for CFA image denoising , 2013, 2013 IEEE International Conference on Consumer Electronics (ICCE).

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

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

[24]  Joel A. Tropp,et al.  Improved Analysis of the subsampled Randomized Hadamard Transform , 2010, Adv. Data Sci. Adapt. Anal..

[25]  Wei Xie,et al.  Image denoising and enhancement based on adaptive fractional calculus of small probability strategy , 2016, Neurocomputing.

[26]  Jian-Feng Cai,et al.  A framelet-based image inpainting algorithm , 2008 .

[27]  Bahadir K. Gunturk,et al.  Image Restoration , 2012 .

[28]  David Zhang,et al.  A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding , 2013, 2013 IEEE International Conference on Computer Vision.

[29]  H. Wu,et al.  Adaptive impulse detection using center-weighted median filters , 2001, IEEE Signal Processing Letters.

[30]  Patrick Pérez,et al.  Region filling and object removal by exemplar-based image inpainting , 2004, IEEE Transactions on Image Processing.

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

[32]  Gilad Lerman,et al.  Robust Locally Linear Analysis with Applications to Image Denoising and Blind Inpainting , 2013, SIAM J. Imaging Sci..

[33]  Xin Li,et al.  Image Recovery Via Hybrid Sparse Representations: A Deterministic Annealing Approach , 2011, IEEE Journal of Selected Topics in Signal Processing.

[34]  Pinar Çivicioglu,et al.  Removal of random-valued impulsive noise from corrupted images , 2009, IEEE Transactions on Consumer Electronics.

[35]  Peter Frankl,et al.  The Johnson-Lindenstrauss lemma and the sphericity of some graphs , 1987, J. Comb. Theory B.

[36]  Dacheng Tao,et al.  Algorithm-Dependent Generalization Bounds for Multi-Task Learning , 2017, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[37]  Meng Wang,et al.  Image clustering based on sparse patch alignment framework , 2014, Pattern Recognit..

[38]  Michael W. Mahoney.  Randomized Algorithms for Matrices and Data , 2011, Found. Trends Mach. Learn..

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

[40]  Emmanuel J. Candès,et al.  The curvelet transform for image denoising , 2002, IEEE Trans. Image Process..

[41]  Kenneth Ward Church,et al.  Very sparse random projections , 2006, KDD '06.

[42]  Dacheng Tao,et al.  On the Performance of Manhattan Nonnegative Matrix Factorization , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[43]  Dacheng Tao,et al.  Local Rademacher Complexity for Multi-Label Learning , 2014, IEEE Transactions on Image Processing.

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

[45]  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.

[46]  Jian Dong,et al.  Accelerated low-rank visual recovery by random projection , 2011, CVPR 2011.

[47]  Xuelong Li,et al.  Geometric Mean for Subspace Selection , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[48]  Dacheng Tao,et al.  GoDec: Randomized Lowrank & Sparse Matrix Decomposition in Noisy Case , 2011, ICML.

[49]  Onur G. Guleryuz,et al.  Weighted Averaging for Denoising With Overcomplete Dictionaries , 2007, IEEE Transactions on Image Processing.

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

[51]  Henry Leung,et al.  A discrete-time learning algorithm for image restoration using a novel L2-norm noise constrained estimation , 2016, Neurocomputing.

[52]  Dimitris Achlioptas,et al.  Database-friendly random projections , 2001, PODS.

[53]  Dacheng Tao,et al.  Non-Local Auto-Encoder With Collaborative Stabilization for Image Restoration , 2016, IEEE Transactions on Image Processing.