| [1] BERCHTOLD S, BHM C, KRIEGAL H P. The Pyramid-Technique: Towards Breaking the Curse of Dimensionality // Proc of the ACM SIGMOD International Conference on Management of Data. New York, USA: ACM, 1998: 142-153.
[2] HIGGINS J R. Sampling Theory in Fourier and Signal Analysis: Foundations. Oxford, UK: Oxford University Press, 1996.
[3] SALOMON D. Data Compression: the Complete Reference. 4th Edition. Northridge, USA: Springer Science & Business Media, 2007.
[4] OLSHAUSEN B A, FIELD D J. Sparse Coding with an Overcomplete Basis Set: A Strategy Employed by V1? Vision Research, 1997, 37(23): 3311-3325.
[5] ADLER A, ELAD M, HEL R Y. Probabilistic Subspace Clustering via Sparse Representations. IEEE Signal Processing Letters, 2012, 20(1): 63-66.
[6] WRIGHT J, YANG A Y, GANESH A, et al. Robust Face Recognition via Sparse Representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31(2): 210-227.
[7] DONOHO D L. Compressed Sensing. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.
[8] ELDAR Y C, KUTYNIOK G. Compressed Sensing: Theory and Applications. Cambridge, UK: Cambridge University Press, 2012.
[9] BARANIUK R G. Compressive Sensing. IEEE Signal Processing Magazine, 2007, 24(4): 118-121.
[10] BOYD S, VANDENBERGHE L. Convex Optimization. Cambridge, UK: Cambridge University Press, 2004.
[11] MALLAT S G, ZHANG Z F. Matching Pursuits with Time-Frequency Dictionaries. IEEE Transactions on Signal Processing, 1993, 41(12): 3397-3415.
[12] TROPP J A, GILBERT A C. Signal Recovery from Random Mea-surements via Orthogonal Matching Pursuit. IEEE Transactions on Information Theory, 2007, 53(12): 4655-4666.
[13] DONOHO D L, TSAIG Y, DRORI I, et al. Sparse Solution of Underdetermined Systems of Linear Equations by Stage-Wise Orthogonal Matching Pursuit. IEEE Transactions on Information Theory, 2012, 58(2): 1094-1121.
[14] NEEDELL D, VERSHYNIN R. Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit. Foundations of Computational Mathematics, 2009, 9(3): 317-334.
[15] DO T T, GAN L, NGUYEN N, et al. Sparsity Adaptive Matching Pursuit Algorithm for Practical Compressed Sensing // Proc of the 42nd Asilomar Conference on Signals, Systems and Computers. Washington, USA: IEEE, 2009: 581-587.
[16] EDMONDS J. Matroids and the Greedy Algorithm. Mathematical Programming, 1971, 1(1): 127-136.
[17] DONOHO D L, ELAD M, TEMLYAKOV V. Stable Recovery of Sparse Overcomplete Representations in the Presence of Noise. IEEE Transactions on Information Theory, 2006, 52: 6-18.
[18] CHEN S S, DONOHO D L, SAUNDERS M A. Atomic Decomposition by Basis Pursuit. SIAM Review, 2001, 43(1): 129-159.
[19] CANDS E J, ROMBERG J. Sparsity and Incoherence in Compressive Sampling. Inverse Problems, 2007, 23(3): 969-985.
[20] KOH K, KIM S J, BOYD S. An Interior-Point Method for Large-Scale l1-Regularized Logistic Regression. Journal of Machine Learning Research, 2007, 8: 1519-1555.
[21] DONOHO D L, TSAIG Y. Fast Solution of l1-Norm Minimization Problems When the Solution May Be Sparse. IEEE Transactions on Information Theory, 2008, 54(11): 4789-4812.
[22] FIGUEIREDO M A T, NOWAK R D, WRIGHT S J. Gradient Projection for Sparse Reconstruction: Application to Compressed Sen-sing and Other Inverse Problems. IEEE Journal of Selected Topics in Signal Processing, 2007, 1(4): 586-597.
[23] YIN W T, OSHER S, GOLDFARB D, et al. Bregman Iterative Algorithms for l1-Minimization with Applications to Compressed Sen-sing. SIAM Journal on Imaging Sciences, 2008, 1(1): 143-168.
[24] GOLDSTEIN T, OSHER S. The Split Bregman Method for l1-Re-gularized Problems. SIAM Journal on Imaging Sciences, 2009, 2(2): 323-343.
[25] WEN Z W, YIN W T, GOLDFARB D, et al. A Fast Algorithm for Sparse Reconstruction Based on Shrinkage, Subspace Optimization, and Continuation. SIAM Journal on Scientific Computing, 2010, 32(4): 1832-1857.
[26] BECK A, TEBOULLE M. A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems. SIAM Journal on Imaging Sciences, 2009, 2(1): 183-202.
[27] BECKER S, BOBIN J, CANDS E J. NESTA: A Fast and Accurate First-Order Method for Sparse Recovery. SIAM Journal on Imaging Sciences, 2011, 4(1): 1-39.
[28] BOYD S, PARIKH N, CHU E, et al. Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. Foundations and Trends in Machine Learning, 2011, 3(1): 1-122.
[29] YANG J F, ZHANG Y. Alternating Direction Algorithms for l1-Problems in Compressive Sensing. SIAM Journal on Scientific Computing, 2011, 33(1): 250-278.
[30] ZHANG H M, YANG J, XIE J C, et al. Weighted Sparse Coding Regularized Nonconvex Matrix Regression for Robust Face Recognition. Information Sciences, 2017, 394/395: 1-17.
[31] NIE F P, WANG H, CAI X, et al. Robust Matrix Completion via Joint Schatten p-norm and lp-Norm Minimization // Proc of the 12th IEEE International Conference on Data Mining. Washington, USA: IEEE, 2012: 566-574.
[32] ZUO W M, MENG D Y, ZHANG L, et al. A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding // Proc of the IEEE International Conference on Computer Vision. Washington, USA: IEEE, 2013: 217-224.
[33] ZHANG C H. Nearly Unbiased Variable Selection under Minimax Concave Penalty. The Annals of Statistics, 2010, 38(2): 894-942.
[34] FAN J Q, LI R Z. Variable Selection via Nonconcave Penalized Likelihood and Its Oracle Properties. Journal of the American Statistical Association, 2001, 96(456): 1348-1360.
[35] JIANG W H, NIE F P, HUANG H. Robust Dictionary Learning with Capped l1-Norm // Proc of the 24th International Joint Conference on Artificial Intelligence. Palo Alto, USA: AAAI Press, 2015: 3590-3596.
[36] GAO C X, WANG N Y, YU Q, et al. A Feasible Nonconvex Relaxation Approach to Feature Selection // Proc of the 25th Confe-rence on Artificial Intelligence. Palo Alto, USA: AAAI Press, 2014: 356-361.
[37] GEMAN D, YANG C. Nonlinear Image Recovery with Half-Quadratic Regularization. IEEE Transactions on Image Processing, 1995, 4(7): 932-946.
[38] TRZASKO J, MANDUCA A. Highly Undersampled Magnetic Re-sonance Image Reconstruction via Homotopic l0-Minimization. IEEE Transactions on Medical imaging, 2009, 28(1): 106-121.
[39] YAO Q M, KWOK J T, ZHONG W L. Fast Low-Rank Matrix Learning with Nonconvex Regularization // Proc of the IEEE International Conference on Data Mining. Washington, USA: IEEE, 2015: 539-548.
[40] LU C Y, TANG J H, YAN S C, et al. Nonconvex Non-smooth Low-Rank Minimization via Iteratively Reweighted Nuclear Norm. IEEE Transactions on Image Processing, 2016, 25(2): 829-839.
[41] BOLTE J, SABACH S, TEBOULLE M. Proximal Alternating Li-nearized Minimization for Nonconvex and Non-smooth Problems. Mathematical Programming, 2014, 146(1/2): 459-494.
[42] ATTOUCH H, BOLTE J, SVAITER B F. Convergence of Descent Methods for Semi-algebraic and Tame Problems: Proximal Algorithms, Forward-Backward Splitting, and Regularized Gauss-Seidel Methods. Mathematical Programming, 2013, 137(1/2): 91-129.
[43] CHEN J H, YANG J, LUO L, et al. Matrix Variate Distribution-induced Sparse Representation for Robust Image Classification. IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(10): 2291-2300.
[44] LUO L, YANG J, QIAN J J, et al. Robust Image Regression Based on the Extended Matrix Variate Power Exponential Distribution of Dependent Noise. IEEE Transactions on Neural Networks and Learning Systems, 2017, 28(9): 2168-2182.
[45] TOIC/ I, FROSSARD P. Dictionary Learning. IEEE Signal Processing Magazine, 2011, 28(2): 27-38.
[46] MAIRAL J, ELAD M, SAPIRO G. Sparse Representation for Color Image Restoration. IEEE Transactions on Image Processing, 2008, 17(1): 53-69.
[47] YANG J C, WRIGHT J, HUANG T S, et al. Image Super-Resolution via Sparse Representation. IEEE Transactions on Image Processing, 2010, 19(11): 2861-2873.
[48] LEE H, EKANADHAM C, NG A Y. Sparse Deep Belief Net Mo-del for Visual Area V2 // Proc of the 21st Annual Conference on Neural Information Processing Systems. Cambridge, USA: The MIT Press, 2008: 873-880.
[49] LI J, ZHANG T, LUO W, et al. Sparseness Analysis in the Pretraining of Deep Neural Networks. IEEE Transactions on Neural Networks and Learning Systems, 2017, 28(6): 1425-1438.
[50] TSO M K S. Reduced-Rank Regression and Canonical Analysis. Journal of the Royal Statistical Society(Methodological), 1981, 43(2): 183-189.
[51] MA Y, SOATTO S, KOSECK J, et al. An Invitation to 3-D Vision: From Images to Geometric Models. New York, USA: Springer-Verlag, 2004.
[52] FAZEL M. Matrix Rank Minimization with Applications. Ph.D. Dissertation. Stanford, USA: Stanford University, 2002.
[53] NIE F P, HUANG H, DING C. Low-Rank Matrix Recovery via Efficient Schatten p-Norm Minimization // Proc of the 26th AAAI Conference on Artificial Intelligence. Palo Alto, USA: AAAI Press, 2012: 655-661.
[54] RECHT B, FAZEL M, PARRILO P A. Guaranteed Minimum-Rank Solutions of Linear Matrix Equations via Nuclear Norm Minimization. SIAM Review, 2010, 52(3): 471-501.
[55] CANDS E J, TAO T. The Power of Convex Relaxation: Near-Optimal Matrix Completion. IEEE Transactions on Information Theory, 2010, 56(5): 2053-2080.
[56] XU Z B, CHANG X Y, XU F M, et al. L1/2 Regularization: A Thresholding Representation Theory and a Fast Solver. IEEE Transactions on Neural Networks and Learning Systems, 2012, 23(7): 1013-1027.
[57] CAO W, SUN J, XU Z B. Fast Image Deconvolution Using Closed-Form Thresholding Formulas of Regularization. Journal of Visual Communication and Image Representation, 2013, 24(1): 31-41.
[58] CAI J F, CANDS E J, SHEN Z W. A Singular Value Thresholding Algorithm for Matrix Completion. SIAM Journal on Optimization, 2010, 20(4): 1956-1982.
[59] LU C Y, LIN Z C, YAN S C. Smoothed Low Rank and Sparse Matrix Recovery by Iteratively Reweighted Least Squares Minimization. IEEE Transactions on Image Processing, 2015, 24(2): 646-654.
[60] GU S H, ZHANG L, ZUO W M, et al. Weighted Nuclear Norm Minimization with Application to Image Denoising // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2014: 2862-2869.
[61] XIE Y, GU S H, LIU Y, et al. Weighted Schatten p-Norm Minimization for Image Denoising and Background Subtraction. IEEE Transactions on Image Processing, 2016, 25(10): 4842-4857.
[62] HU Y, ZHANG D B, YE J P, et al. Fast and Accurate Matrix Completion via Truncated Nuclear Norm Regularization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35(9): 2117-2130.
[63] 张凡龙.基于核范数的低秩理论与方法研究.博士学位论文.南京:南京理工大学, 2015.
(ZHANG F L. Nuclear Norm Based Low Rank: Theory and Algorithms. Ph.D. Dissertation. Nanjing, China: Nanjing University of Science and Technology, 2015.)
[64] CAI T T, ZHOU W X. Matrix Completion via Max-Norm Constrained Optimization. The Computing Research Repository (CoRR), 2013. DOI: 10.1214/16-EJS1147.
[65] SHANG F H, LIU Y Y, TONG H H, et al. Robust Bilinear Factorization with Missing and Grossly Corrupted Observation. Information Sciences, 2015, 307: 53-72.
[66] LIU Y Y, JIAO L C, SHANG F H. An Efficient Matrix Factorization Based Low-Rank Representation for Subspace Clustering. Pa-ttern Recognition, 2013, 46(1): 284-292.
[67] LIU Y Y, JIAO L C, SHANG F H. A Fast Tri-factorization Method for Low-Rank Matrix Recovery and Completion. Pattern Recognition, 2013, 46(1): 163-173.
[68] SREBRO N, RENNIE J D M, JAAKKOLA T S. Maximum-Margin Matrix Factorization // SAUL L K, WEISS Y, BOTTOU L, eds. Advances in Neural Information Processing Systems 17. Cambridge, USA: The MIT Press, 2005: 1329-1336.
[69] SHANG F H, CHENG J, LIU Y Y, et al. Bilinear Factor Matrix Norm Minimization for Robust PCA: Algorithms and Applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017. DOI: 10.1109/TPAMI.2017.2748590.
[70] SHANG F H, LIU Y Y, CHENG J. Tractable and Scalable Scha-tten Quasi-Norm Approximations for Rank Minimization // Proc of the 19th International Conference on Artificial Intelligence and Statistics. New York, USA: ACM, 2016: 620-629.
[71] SHANG F H, LIU Y Y, CHENG J. Unified Scalable Equivalent Formulations for Schatten Quasi-Norms[C/OL]. [2017-10-20]. https://arxiv.org/pdf/1606.00668.pdf.
[72] NESTEROV Y. A Method of Solving a Convex Programming Pro-blem with Convergence Rate O(1/k2 ). Soviet Mathematics Doklady, 1983, 27(2): 372-376.
[73] TOH K C, YUN S. An Accelerated Proximal Gradient Algorithm for Nuclear Norm Regularized Linear Least Squares Problems. Pacific Journal of Optimization, 2010, 6(3): 615-640.
[74] JI S W, YE J P. An Accelerated Gradient Method for Trace Norm Minimization // Proc of the 26th Annual International Conference on Machine Learning. New York, USA: ACM, 2009: 457-464.
[75] LIN Z C, CHEN M M, WU L Q, et al. The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices [C/OL]. [2017-10-20]. http://yima.csl.illinois.edu/psfile/Lin09-MP.pdf.
[76] LIN Z C, LIU R S, SU Z X. Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation // Proc of the 25th Annual Conference on Neural Information Proce-ssing Systems. Cambridge, USA: The MIT Press, 2011: 612-620.
[77] CHEN C H, HE B S, YE Y Y, et al. The Direct Extension of ADMM for Multi-block Convex Minimization Problems Is Not Ne-cessarily Convergent. Mathematical Programming, 2016, 155(1/2): 57-79.
[78] YANG J, LUO L, QIAN J J, et al. Nuclear Norm Based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017, 39(1): 156-171.
[79] HUNTER D R, LI R Z. Variable Selection Using MM Algorithms. Annals of Statistics, 2005, 33(4): 1617-1642.
[80] GONG P H, ZHANG C S, LU Z S, et al. A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems // Proc of the 30th International Conference on Machine Learning. New York, USA: ACM, 2013: 37-45.
[81] GASSO G, RAKOTOMAMONJY A, CANU S. Recovering Sparse Signals with a Certain Family of Nonconvex Penalties and DC Programming. IEEE Transactions on Signal Processing, 2009, 57(12): 4686-4698.
[82] SUN T, JIANG H, CHENG L Z. Convergence of Proximal Iteratively Reweighted Nuclear Norm Algorithm for Image Processing. IEEE Transactions on Image Processing, 2017, 26(12): 5632-5644.
[83] LI H, LIN Z. Accelerated Proximal Gradient Methods for Nonconvex Programming // Proc of the Annual Conference on Neural Information Processing Systems. Cambridge, USA: The MIT Press, 2015: 379-387.
[84] LI Q W, ZHOU Y, LIANG Y B, et al. Convergence Analysis of Proximal Gradient with Momentum for Nonconvex Optimization // Proc of the 34th International Conference on Machine Learning. New York, USA: ACM, 2017: 2111-2119.
[85] HONG M, LUO Z Q, RAZAVIYAYN M. Convergence Analysis of Alternating Direction Method of Multipliers for a Family of Noncon-vex Problems. SIAM Journal on Optimization, 2016, 26(1): 337-364.
[86] OH T H, MATSUSHITA Y, TAI Y W, et al. Fast Randomized Singular Value Thresholding for Nuclear Norm Minimization // Proc of the IEEE Conference on Computer Vision and Pattern Re-cognition. Washington, USA: IEEE, 2015: 4484-4493.
[87] YAO Q M, KWOK J T, GAO F, et al. Efficient Inexact Proximal Gradient Algorithm for Nonconvex Problems // Proc of the 26th International Joint Conference on Artificial Intelligence. San Francisco, USA: Morgan Kaufmann, 2017: 3308-3314.
[88] GHADIMI S, LAN G H. Accelerated Gradient Methods for Nonconvex Nonlinear and Stochastic Programming. Mathematical Programming, 2016, 156(1/2): 59-99.
[89] XIAO L. Dual Averaging Methods for Regularized Stochastic Lear-ning and Online Optimization. Journal of Machine Learning Research, 2010, 11: 2543-2596.
[90] CANDS E J, LI X D, MA Y, et al. Robust Principal Component Analysis. Journal of the ACM(JACM), 2011, 58(3). DOI:10.1145/1970392.1970395.
[91] LIU G C, LIN Z C, YAN S C, et al. Robust Recovery of Subspace Structures by Low-Rank Representation. IEEE Transactions on Pa-ttern Analysis and Machine Intelligence, 2013, 35(1): 171-184.
[92] CHEN J H, YANG J. Robust Subspace Segmentation via Low-Rank Representation. IEEE Transactions on Cybernetics, 2014, 44(8): 1432-1445.
[93] ZHANG H M, YANG J, SHANG F H, et al. LRR for Subspace Segmentation via Tractable Schatten-p Norm Minimization and Factorization[EB/OL] .[2018-01-23]. http://blog.sciencenet.cn/home.php?mod=space&uid=910693&do=blog&quickfor ward=1&id=1096324.
[94] LU C Y, FENG J S, CHEN Y D, et al. Tensor Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Tensors via Convex Optimization // Proc of the IEEE Conference on Computer Vision and Pattern Recognition. Washington, USA: IEEE, 2016: 5249-5257.
[95] BOUWMANS T, SOBRAL A, JAVED S, et al. Decomposition into Low-Rank Plus Additive Matrices for Background/Foreground Se-paration: A Review for a Comparative Evaluation with a Large-Scale Dataset. Computer Science Review, 2017, 23: 1-71.
[96] 彭义刚,索津莉,戴琼海,等.从压缩传感到低秩矩阵恢复:理论与应用.自动化学报, 2013, 39(7): 981-994.
(PENG Y G, SUO J L, DAI Q H, et al. From Compressed Sen-sing to Low-Rank Matrix Recovery: Theory and Applications. Acta Automatica Sinica, 2013, 39(7): 981-994.)
[97] 马坚伟,徐 杰,鲍跃全,等.压缩感知及其应用:从稀疏约束到低秩约束优化.信号处理, 2012, 28(5): 609-623.
(MA J W, XU J, BAO Y Q, et al. Compressive Sensing and Its Application: From Sparse to Low-Rank Regularized Optimization.
Signal Processing, 2012, 28(5): 609-623.) |
2018, Vol. 31 
