E. Candes, X. Li, Y. Ma, J. Wright, “Robust Principal Component Analysis”, ACM, Volume 58, No. 3, May 2011.
Conventional Algorithms for Solving PCP (117 papers)
1. Basic Solvers (39 papers)
J. Cai, E. Candès, Z. Shen, “A Singular Value Thresholding Algorithm for Matrix Completion”, 2008.
J. Wright, Y. Peng, Y. Ma, A. Ganesh, S. Rao, “Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices by Convex Optimization”, Neural Information Processing Systems, NIPS 2009, December 2009.
Z. Lin, M. Chen, L. Wu, Y. Ma, “The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices”, UIUC Technical Report, November 2009.
Z. Lin, A. Ganesh, J. Wright, L. Wu, M. Chen, Y. Ma, “Fast Convex Optimization Algorithms for Exact Recovery of a Corrupted Low-Rank Matrix”, UIUC Technical Report, August 2009.
X. Yuan, J. Yang, “Sparse and Low-Rank Matrix Decomposition via Alternating Direction Methods”, Optimization Online, November 2009.
S. Ma, “Algorithms for Sparse and Low-Rank Optimization: Convergence, Complexity and Applications”, Thesis, Columbia University, 2011.
R. Chartrand, “Non convex splitting for regularized low-rank and sparse decomposition”, IEEE Transactions on Signal Processing, 2012.
S. Gandy, I. Yamada, "Convex optimization techniques for the efficient recovery of a sparsely corrupted low-rank matrix", Journal of Math-for-Industry, Volume 2, pages 147-156, 2010.
H. Zhang, L. Liu,"Recovering low-rank and sparse components of matrices for object detection", Electronics Letter,Volume 49, No. 2, January 2013.
W. Zhu, S. Shu, L. Cheng, "Proximity point algorithm for low-rank matrix recovery from sparse noise corrupted data", Applied Mathematics and Mechanics, Volume 35, No. 2, pages 259-268, February 2014.
J. Wang, M. Wan, X. Hu, S. Yan, "Image Denoising with a Unified Schattern-p Norm and lq Norm Regularization",Journal of Optimization Theory, April 2014.
E. Kim, M. Lee, C. Choi, N. Kwak, S. Oh, "Efficient l1-Norm-Based Low-Rank Matrix Approximations for Large-Scale Problems Using Alternating Rectified Gradient Method", International Conference on Multimedia and Expo, ICME 2014, 2014.
H. Wang, A. Banerjee, Z. Luo, "Parallel Direction Method of Multipliers", Preprint, June 2014.
R. He, T. Tan, L. Wang, "Recovery of Corrupted Low-rank Matrix by Implicit Regularizers", IEEE Transaction on Pattern Analysis and Machine Intelligence, PAMI 2013, September 2013.
Y. Chai, S. Xu,H. Yin, "An Improved ADM algorithm for RPCA optimization problem", Chinese Control Conference, CCC 2013, pages 4769-4880, July 2013.
R. Fan, H. Wang, H. Zhang, "A New Analysis of the Iterative Threshold Algorithm for RPCA by Primal-Dual Method", Advanced Materials Research, pages 989-994, July 2014.
B. Moore, R. Nadakuditi, J. Fessler, "Improved Robust PCA using low-rank denoising with optimal singular value shrinkage",IEEE Workshop on Statistical Signal Processing, SSP 2014, pages 13-16, June 2014.
Q. Gu, Z. Wang, H. Liu, “Low-Rank and Sparse Structure Pursuit via Alternating Minimization”, International Conference on Artificial Intelligence and Statistics, AISTATS 2016, May 2016.
D. Park, A. Kyrillidis, C. Caramanis, S. Sanghavi, "Finding low-rank solutions to matrix problems, efficiently and provably", Preprint, June 2016.
H. Li, Z. Miao, Y. Li, Y. Xu, Y. Zhang, "Moving object detection via box constrained RPCA", Journal of PLA University of Science and Technology, Volume 17, No. 5, pages 403-407, October 2016.
U. Niranjan, A. Rajkumar, T. Tulabandhula, "Provable Inductive Robust PCA via Iterative Hard Thresholding", Preprint, April 2017.
Z. Xu, M. Figueiredo, X. Yuan, C. Studer, T. Goldstein, "Adaptive Relaxed ADMM: Convergence Theory and Practical Implementation", Preprint, April 2017.
S. Ma, “Algorithms for Sparse and Low-Rank Optimization: Convergence, Complexity and Applications”, Thesis, Columbia University, 2011.
R. Chartrand, “Non convex splitting for regularized low-rank and sparse decomposition”, IEEE Transactions on Signal Processing, 2012.
S. Gandy, I. Yamada, "Convex optimization techniques for the efficient recovery of a sparsely corrupted low-rank matrix", Journal of Math-for-Industry, Volume 2, pages 147-156, 2010.
H. Zhang, L. Liu,"Recovering low-rank and sparse components of matrices for object detection", Electronics Letter,Volume 49, No. 2, January 2013.
W. Zhu, S. Shu, L. Cheng, "Proximity point algorithm for low-rank matrix recovery from sparse noise corrupted data", Applied Mathematics and Mechanics, Volume 35, No. 2, pages 259-268, February 2014.
J. Wang, M. Wan, X. Hu, S. Yan, "Image Denoising with a Unified Schattern-p Norm and lq Norm Regularization",Journal of Optimization Theory, April 2014.
E. Kim, M. Lee, C. Choi, N. Kwak, S. Oh, "Efficient l1-Norm-Based Low-Rank Matrix Approximations for Large-Scale Problems Using Alternating Rectified Gradient Method", International Conference on Multimedia and Expo, ICME 2014, 2014.
H. Wang, A. Banerjee, Z. Luo, "Parallel Direction Method of Multipliers", Preprint, June 2014.
R. He, T. Tan, L. Wang, "Recovery of Corrupted Low-rank Matrix by Implicit Regularizers", IEEE Transaction on Pattern Analysis and Machine Intelligence, PAMI 2013, September 2013.
Y. Chai, S. Xu,H. Yin, "An Improved ADM algorithm for RPCA optimization problem", Chinese Control Conference, CCC 2013, pages 4769-4880, July 2013.
R. Fan, H. Wang, H. Zhang, "A New Analysis of the Iterative Threshold Algorithm for RPCA by Primal-Dual Method", Advanced Materials Research, pages 989-994, July 2014.
B. Moore, R. Nadakuditi, J. Fessler, "Improved Robust PCA using low-rank denoising with optimal singular value shrinkage",IEEE Workshop on Statistical Signal Processing, SSP 2014, pages 13-16, June 2014.
Q. Gu, Z. Wang, H. Liu, “Low-Rank and Sparse Structure Pursuit via Alternating Minimization”, International Conference on Artificial Intelligence and Statistics, AISTATS 2016, May 2016.
D. Park, A. Kyrillidis, C. Caramanis, S. Sanghavi, "Finding low-rank solutions to matrix problems, efficiently and provably", Preprint, June 2016.
H. Li, Z. Miao, Y. Li, Y. Xu, Y. Zhang, "Moving object detection via box constrained RPCA", Journal of PLA University of Science and Technology, Volume 17, No. 5, pages 403-407, October 2016.
U. Niranjan, A. Rajkumar, T. Tulabandhula, "Provable Inductive Robust PCA via Iterative Hard Thresholding", Preprint, April 2017.
Z. Xu, M. Figueiredo, X. Yuan, C. Studer, T. Goldstein, "Adaptive Relaxed ADMM: Convergence Theory and Practical Implementation", Preprint, April 2017.
A. Dutta, B. Gong, X. Li, M. Shah, “Weighted Singular Value Thresholding and its Application to Background Estimation”, Journal of Machine Learning Research, Volume 17, pages 1-22, 2017.
C. Wang, C. Li, J. Wang, "Two modified augmented Lagrange multiplier algorithms for Toeplitz matrix compressive recovery", Computers and Mathematics with Applications, 2017.
N. Zarmehi, F. Marvasti, “Sparse and low-rank recovery using adaptive thresholding”, Digital Signal Processing, Volume 73, pages 145-152, 2018.
J. Bai, "Hybrid Middle Proximal ADMM for Linearly Constrained Convex Optimization", Preprint, 2018.
P. Giampouras, A. Rontogiannis, K. Koutroumbas, “Robust PCA via Alternating Iteratively Reweighted Low-Rank Matrix Factorization”, IEEE International Conference on Image Processing, ICIP 2018, pages 3383-3387, Athens, Greece, 2018.
J. Zhao, Q. Feng, L. Zhao, “Alternating direction and Taylor expansion minimization algorithms for unconstrained nuclear norm optimization”, Numerical Algorithms, 2018.
S. Shah, T. Goldstein, C. Studer, “Estimating Sparse Signals with Smooth Support via Convex Programming and Block Sparsity”, IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016, 2016.
D. Garber, “Linear Convergence of Frank-Wolfe for Rank-One Matrix Recovery Without Strong Convexity”, Preprint, December 2019.
J. Liu ,Y. Duan, T. Wang , “A Parallel Splitting Augmented Lagrangian Method for Two-Block Separable Convex Programming with Application in Image Processing”, Mathematical Problems in Engineering, 2020.
C. Chen, R. Chan, S. Ma, J. Yang, "Inertial proximal ADMM for linearly constrained separable convex optimization", SIAM Journal on Imaging Sciences, pages 2239-2267, 2015.
Y. Yang, Y. Tang, “An inertial alternating direction method of multipliers for solving a two-block separable convex minimization problem”, Preprint, 2020.
D. Bertsimas, R. Wright, N. Johnson, “Sparse Plus Low Rank Matrix Decomposition: A Discrete Optimization Approach”, Preprint, September 2021.
Z. Zhu, Y. Liu, J. Huang, Y. Ding, "Efficient Image and Video Processing via Symmetric Inertial Proximal ADMM with RPCA Model", Neurocomputing, March 2025.
L. Wang, J. Jiang, Z. Deng, Y. Feng, C. Hou, “Inertial Proximal Strictly Contractive PRSM for Solving Multi-Block Separable Convex Optimization”, Pure Mathematics, Volume 15, No. 3, pages 203-218, March 2025.
N. Vaswani, “AltGDmin: Alternating GD and Minimization for Partly-Decoupled (Federated) Optimization” Preprint, April 2025.
T. Huang, X. Liu, S. Huang, “A Modified Peaceman-Rachford Splitting Method with Correction Steps for Three-Block Convex Problem”, Optimization, June 2025.
2. Linearized Solvers (7 papers)
J. Yang, X. Yuan, “Linearized Augmented Lagrangian and Alternating Direction Methods for Nuclear Norm Minimization”, 2011.
Z. Lin, R. Liu Z. Su, “Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation”, NIPS 2011, 2011.
Y. Shen, Z. Wen, Y. Zhang, “Augmented Lagrangian Alternating Direction method for Matrix Separation based on Low-rank Factorization”, January 2011.
G. Gu, B. He, J. Yang, "Inexact Alternating Direction Based Contraction Methods for Separable Linearly Constrained Convex Programming", Journal of Optimization Theory and Applications, December 2013.
H. Xu, W. Zhou, Y. Wang, W. Wang, Y. Mo, "Matrix separation Based on LMaFit-Seed", Computer Journal, pages 1-10, 2017.
S. Ma, “Algorithms for Sparse and Low-Rank Optimization: Convergence, Complexity and Applications”, Thesis, Columbia University, 2011.
T. Pham, M. Dao, A. Eberhard, “Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions”, Preprint, 2024.
3. Fast Solvers (29 papers)
Y. Mu, J. Dong, X. Yuan, S. Yan, “Accelerated Low-Rank Visual Recovery by Random Projection”, International Conference on Computer Vision, CVPR 2011, 2011.
R. Liu, Z. Lin, S. Wei, Z. Su, “Solving Principal Component Pursuit in Linear Time via l1 Filtering”, International Journal on Computer Vision, IJCV 2011, 2011.
A. Abdel-Hakim, M. El-Saban, “FRPCA: Fast Robust Principal Component Analysis”, International Conference on Pattern Recognition, ICPR 2012, Tsukuba, Japan, November 2012
Y. Liu, L. Jiao, F. Shang, “An efficient matrix factorization based low-rank representation for subspace clustering”, Pattern Recognition, PR 2013, Volume 46, pages 284–292, January 2013.
Y. Liu, L. Jiao, F. Shang, “A fast tri-factorization method for low-rank matrix recovery and completion”, Pattern Recognition, PR 2013, Volume 46, pages 163-173, January 2013.
F. Orabona, A. Argyriou, N. Srebro, “PRISMA: PRoximal Iterative Smoothing Algorithm”, Optimization and Control, 2012.
P. Rodríguez, B. Wohlberg, "Fast Principal Component Pursuit Via Alternating Minimization", IEEE International Conference on Image Processing, ICIP 2013, Melbourne, Autralia, September, 2013.
M. Yang, Y. Wang, "Fast alternating direction method of multipliers for robust PCA", Journal of Nanjing University, Volume 34, Issue 2, pages 83-88, April 2014.
M. Yang,"Smoothing technique and fast alternating direction method for robust PCA", Chinese Control Conference, CCC 2014, pages 4782-4785, July 2014.
T. Oh, Y. Matsushita, Y. Tai, I. Kweon, "Fast Randomized Singular Value Thresholding for Nuclear Norm Minimization", IEEE International Conference on Computer Vision and Pattern Recognition, CVPR 2015, June 2015.
M. Rahmani, G. Atia, "Coherence Pursuit: Fast, Simple, and Robust Principal Component Analysis", Preprint, 2016.
M. Rahmani, P. Li, "Fast and Provable Robust PCA via Normalized Coherence Pursuit", IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2021, pages 5305-5309, 2021.
N. Zarmehi, F. Marvasti, "Recovery of Sparse and Low Rank Components of Matrices using Iterative Method with Adaptive Thresholding", Preprint, 2017.
Y. Li, W. Yu, "A Fast Implementation of Singular Value Thresholding Algorithm using Recycling Rank Revealing Randomized Singular Value Decomposition", Preprint, April 2017.
Q. Li, Z. Wang, "Riemannian Submanifold Tracking on Low-Rank Algebraic Variety", AAAI Conference on Artificial Intelligence, AAAI 2017, 2017.
H. Cai, J. Cai, K. Wei, “Accelerated Alternating Projections for Robust Principal Component Analysis”, Preprint, 2017.
P. Zheng, A. Aravkin, “Fast methods for nonsmooth nonconvex minimization”, Preprint, 2018.
S. Liu, C. Zhang, “Randomized Method for Robust Principal Component Analysis”, CSAE 2018, 2018.
H. Fu, Z. Gao, H. Liu, "Fast Robust PCA on Background Modeling", Chinese Intelligent Systems Conference, CISC 2017, pages 399-411, 2017.
H. Fu , B. Wang, H. Liu, "Fast background estimation on long video sequence", IET Electronics Letters, 2019.
H. Zhang, J. Qian, J. Gao, J. Yang, C. Xu, "Scalable Proximal Jacobian Iteration Method With Global Convergence Analysis for Nonconvex Unconstrained Composite Optimizations", IEEE Transactions on Neural Networks and Learning, 2019.
J. Liu ,Y. Duan, T. Wang , “A Parallel Splitting Augmented Lagrangian Method for Two-Block Separable Convex Programming with Application in Image Processing”, Mathematical Problems in Engineering, 2020.
H. Wang, A. Jiang, P. Li, “Newton-soft threshold iteration algorithm for robust principal component analysis”, Journal of Computer Applications, 2020.
N. Sha, L. Shi, M. Yan, “Fast algorithms for robust principal component analysis with an upper bound on the rank”, Preprint, 2020.
K. Axiotis, M. Sviridenko, “Local Search Algorithms for Rank-Constrained Convex Optimization”, Preprint, January 2021.
T. Tong, C. Ma, Y. Chi, "Accelerating Ill-Conditioned Low-Rank Matrix Estimation via Scaled Gradient Descent", Preprint, September 2020.
W. Qu, X. Xiu, H. Zhang, J. Fan, “An efficient semi-proximal ADMM algorithm for low-rank and sparse regularized matrix minimization problems with real-world applications“, Journal of Computational and Applied Mathematics, December 2022.
R. Wen, W. Li, “An accelerated alternating directional method with non-monotone technique for matrix recovery”, AIMS Mathematics, pages 14047-14063, 2023.
M. Raus, Y. Elshiaty, S. Petra, “Accelerated Bregmann divergence optimization with SMART: an information geometry point of view”, Preprint, February 2024.
4. Online Solvers (1 paper)
H. Wang, A. Banerjee, "Online Alternating Direction Method", Preprint, 2013.
5. Non convex Solvers (34 papers)
Q. Sun, S. Xiang, J. Ye, “Robust principal component analysis via capped norms”, International Conference on Knowledge Discovery and Data Mining, KDD 2013, pages 311-319, 2013.
P. Netrapalli, U. Niranjan, S. Sanghavi, A. Anandkumar, P. Jain, "Non-convex Robust PCA", Preprint, October 2014.
L. Yang, T. Pong, X. Chen, “Alternating Direction Method of Multipliers for Nonconvex Background/Foreground Extraction”, Preprint, June 2015.
X. Zhong, L. Xu, Y. Li, Z. Liu, E. Chen", "A Nonconvex Relaxation Approach for Rank Minimization Problems", National Conference on Artificial Intelligence, AAAI 2015, January 2015.
Q. Tran-Dinh, Z. Zhang, "Extended Gauss-Newton and Gauss-Newton-ADMM Algorithms for Low-Rank Matrix Optimization, Preprint, June 2016.
Q. Yao, J. Kwok, W. Zhong, "Fast Low-Rank Matrix Learning with Nonconvex Regularization", Preprint, 2015.
X. Yi, D. Park, Y. Chen, C. Caramanis, "Fast Algorithms for Robust PCA via Gradient Descent", Preprint, 2016.
C. Peng, Z Kang, Q. Cheng, "A Fast Factorization-based Approach to Robust PCA", IEEE International Conference on Data Mining, ICDM 2016, December 2016
X. Zhang, L. Wang, Q. Gu, "Nonconvex Free Lunch for Low-Rank plus Sparse Matrix Recovery", Preprint, 2017.
Y. Chen, Y. Wang, M. Li, G. He, "Augmented Lagrangian alternating direction method for low-rank minimization via non-convex approximation", Signal, Image and Video Processing, SIViP 2017, 2017.
F. Shang, J. Cheng, Y. Liu, Z. Q. Luo and Z. Lin, "Bilinear Factor Matrix Norm Minimization for Robust PCA: Algorithms and Applications”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017.
A. Dutta, F. Hanzely, P. Richtarik, “A Nonconvex Projection Method for Robust PCA”, Preprint, May 2018.
Z. Yang, Z. Yang, D. Han, “Alternating Direction Method of Multipliers for Sparse and Low-Rank Decomposition Based on Non-convex Non-smooth Weighted Nuclear Norm”, Access 2018, October 2018.
A. Dutta, F. Hanzely, J. Liang, P. Richtarik, "Best Pair Formulation and Accelerated Scheme for Non-convex Principal Component Pursuit", Preprint, May 2019.
M. Balcan, Y. Liang, Z. Song, D. Woodruff, H. Zhang, “Non-Convex Matrix Completion and Related Problems via Strong Duality”, Journal of Machine Learning Research, Volume 20, pages 1-56, 2019.
Z. Yang, L. Fan, Y. Yang, Z. Yang, G. Gui, “Generalized Singular Value Thresholding Operator based Nonconvex Low-Rank and Sparse Decomposition for Moving Object Detection”, Journal of the Franklin Institute, 2019.
F. Wen, R. Ying, P. Liu, T. Truong, “Nonconvex Regularized Robust PCA using the Proximal Block Coordinate Descent Algorithm”, IEEE Transactions on Signal Processing, 2019.
Y. Wang, W. Yin, J. Zeng, “Global convergence of ADMM in nonconvex nonsmooth optimization”, Journal of Scientific Computing, Volume 78, No. 1, pages 29-63, 2019.
H. Cai, K. Hamm, L. Huang, J. Li, T. Wang, “Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation”, Preprint, October 2020.
Z. Wang, Y. Liu, X. Luo, J. Wang, C. Gao, D. Peng, W. Chen, "Large-Scale Affine Matrix Rank Minimization With a Novel Nonconvex Regularizer", IEEE Transactions on Neural Networks and Learning Systems, March 2021.
Q. Yao, J. Kwok, T. Wang, T. Liu, "Large-scale low-rank matrix learning with nonconvex regularizers", IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 41, No. 11, pages 2628–2643, November 2019.
L. Yang, T. Pong , X. Chen, "Alternating direction method of multipliers for a class of nonconvex and nonsmooth problems with applications to background/foreground extraction", SIAM Journal on Imaging Sciences, Volume 10, pages 74-110, 2017.
P. Wang, C. Lin, X. Yang, S. Xiong, “Low-rank and sparse matrix recovery from noisy observations via 3-block ADMM algorithm”, Journal of Applied Analysis and Computation, Volume 10, Issue 3, Pages 1024-1037, 2020.
C. Zhang, Y. Yang, Z. Wang, Y. Chen, “A Linearized Alternating Direction Method of Multipliers for a Special Three-Block Nonconvex Optimization Problem of Background/Foreground Extraction”, IEEE Access, 2020.
C. Zhang, Y. Song, X. Cai, D. Han, “An extended proximal ADMM algorithm for three-block nonconvex optimization problems”, Journal of Computational and Applied Mathematics, 2021.
Z. Wang, X. Li, H. So, Z. Liu, “Robust PCA via Non-convex Half-quadratic Regularization”, Signal Processing, 2022.
Y. Li, L. Balzano, D. Needell, H. Lyu, “Convergence and complexity of block majorization-minimization for constrained block-Riemannian optimization”, Preprint, December 2023.
Z. Lin, “An Extended ADMM for Three-block Nonconvex Nonseparable Problem with Applications”, Preprint, February 2024.
L. Li, Z. Wang, Q. Hu, Y. Dong, "Adaptive Nonconvex Sparsity based Background Subtraction for Intelligent Video Surveillance”, IEEE Transactions on Industrial Informatics, Volume 17, No. 6, pages.4168-4178, June 2021.
Q. Wang, Z. Liu, C. Cui, D. Han, “A Bregman Proximal Stochastic Gradient Method with Extrapolation for Nonconvex Nonsmooth Problems”, Conference on Artificial Intelligence AAAI 2024, Vancouver, Canada, February 2024.
J. Yin, C. Tang, J. Jian, Q. Huang, “A partial Bregman ADMM with a general relaxation factor for structured non-convex and non-smooth optimization”, Journal of Global Optimization, March 2024.
K. Zhang, H. Shao, T. Wu, X. Wang, “A class of accelerated GADMM-based method for multi-block nonconvex optimization problems”, Numerical Algorithms, April 2024.
Y. Zhou, X. Shi, L. Guo, J. Cao, M. Aty, “Perturbed Proximal Gradient ADMM for,Nonconvex Composite Optimization”, Preprint, April 2025.
6. 2D solvers (1 paper)
Y. Sun, X. Tao, Y. Li, J. Lu, "Robust two-dimensional principal component analysis via alternating optimization", International Conference on Image Processing, ICIP 2013, September 2013.
7. Free solvers (6 papers)
7.1 Free SVD solvers (5 papers)
S. Erfanian Ebadi, E. Izquierdo, "Efficient Background Subtraction with Low-rank and Sparse Matrix Decomposition", IEEE International Conference on Image Processing, ICIP 2015, September 2015.
S. Erfanian Ebadi, V. Guerra One, E. Izquierdo, "Efficient Background Subtraction with Low-rank and Sparse Matrix Decomposition", Workshop on Signal Processing with Adaptive Sparse Structured Representations, SPARS 2015, July 2015.
M. Onuki, S. Ono, K. Shirai, Y. Tanaka, "Fast Singular Value Shrinkage with Chebyshev Polynomial Approximation Based on Signal Sparsity", Preprint, 2017.
A. Dutta, J. Liang, X. Li, "A Fast and Adaptive SVD-free Algorithm for General Weighted Low-rank Recovery", Preprint, January 2021.
Q. Wang, D. Han, W. Zhang, "A Customized Inertial Proximal Alternating Minimization for SVD-free Robust Principal Component Analysis", Journal of Optimization, Taylor and Francis, 2023.
7.2 Parameter free solvers (1 paper)
V. Menon, S. Kalyani, “Structured and Unstructured Outlier Identification for Robust PCA: A Non iterative, Parameter free Algorithm”, Preprint, September 2018.
Unrolled RPCA (6 papers)
S. Markowitz, C. Snyder, Y. Eldar, M. Do, "Multimodal Unrolled Robust PCA for Background Foreground Separation", Preprint, August 2021.
H. Luong, B. Joukovsky, Y. Eldar, N. Deligiannis, "A Deep-Unfolded Reference-Based RPCA Network For Video Foreground-Background Separation", Preprint, January 2021.
H. Cai, J. Liu, W. Yin, "Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection", Conference on Neural Information Processing Systems, NeurIPS 2021, 2021.
V. Monga, Y. Li, Y. Eldar, “Algorithm unrolling: Interpretable, efficient deep learning for signal and image processing,” IEEE Signal Processing Magazine, Volume 38, No. 2, pages 18-44, 2021.
B. Joukovsky, N. Deligiannis, Y. Eldar, “Interpretable Neural Networks for Video Separation: Deep Unfolding RPCA with Foreground Masking”, TechRxiv, 2022.
S. Imran, M. Tahir, Z. Khalid, M. Uppal, "A Deep-Unfolded Spatiotemporal RPCA Network for L+S Decomposition", Preprint, 2023.
Incremental PCP (49 papers)
C. Qiu, N. Vaswani, “Real-time Robust Principal Components Pursuit”, International Conference on Communication Control and Computing, 2010.
C. Qiu, N. Vaswani, “Support Predicted Modified-CS for Recursive Robust Principal Components' Pursuit”, IEEE International Symposium on Information Theory, ISIT 2011, 2011.
C. Qiu, N. Vaswani, “Automated Recursive Projected CS (ReProCS) for Real-time Video Layering", IEEE International Conference on Computer Vision and Pattern Recognition, CVPR 2012, June 2012.
C. Qiu, N. Vaswani, “ReProCS: A Missing Link between Recursive Robust PCA and Recursive Sparse Recovery in Large but Correlated Noise”, Preprint, 2011.
C. Qiu N. Vaswani, "Recursive Sparse Recovery in Large but Structured Noise - Part 1", Preprint, November 2012.
C. Qiu N. Vaswani, "Recursive Sparse Recovery in Large but Structured Noise - Part 2", Preprint, November 2012.
C. Qiu, N. Vaswani, L. Hogben, “Recursive Robust PCA or Recursive Sparse Recovery in Large but Structured Noise”, Preprint, November 2012.
C. Qiu, N. Vaswani, B. Lois, L. Hogben, "Recursive Robust PCA or Recursive Sparse Recovery in Large but Structured Noise", IEEE Transactions on Information Theory, 2014.
C. Qiu, N. Vaswani, B. Lois, L. Hogben, "Recursive Robust PCA or Recursive Sparse Recovery in Large but Structured Noise", IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2013, 2013.
H. Guo, C. Qiu, N. Vaswani, "Practical ReProCS for Separating Sparse and Low-dimensional Signal Sequences from their Sum", Preprint, October 2013.
H. Guo, C. Qiu, N. Vaswani, "Practical ReProCS for Separating Sparse and Low-dimensional Signal Sequences from their Sum - Part 1", International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014, May 2014.
H. Guo, C. Qiu, N. Vaswani,"Practical ReProCS for Separating Sparse and Low-dimensional Signal Sequences from their Sum - Part 2", GlobalSIP 2014, 2014.
H. Guo, C. Qiu, N. Vaswani "An Online Algorithm for Separating Sparse and Low-dimensional Signal Sequences from their Sum", IEEE Transactions on Signal Processing, 2014.
H. Guo, “An online algorithm for separating sparse and low-dimensional signal sequences from their sum, and its applications in video processing”, PhD Thesis, Iowa State University, USA, 2019.
J. Zhan, N. Vaswani, C. Qiu, "Performance Guarantees for ReProCS - Correlated Low-Rank Matrix Entries Case", Preprint, 2014.
J. Zhan, “Sparse and low rank signal recovery with partial knowledge”, PhD Thesis, Iowa State University, USA, 2015.
B. Lois, N. Vaswani, C. Qiu, "Performance guarantees for undersampled recursive sparse recovery in large but structured noise", GlobalSIP 2013, pages 1061-1064, December 2013.
B. Lois, N. Vaswani, "A Correctness Result for Online Robust PCA", 2014.
B. Lois, N. Vaswani, "Online Matrix Completion and Online Robust PCA", IEEE International Symposium on Information Theory, ISIT 2015, 2015.
P. Narayanamurthy, N. Vaswani, "New Results for Provable Dynamic Robust PCA", Preprint, May 2017.
P. Narayanamurthy, N. Vaswani, "MEDRoP: Memory-efficient dynamic robust PCA", Preprint, December 2017.
P. Narayanamurthy, N. Vaswani, "A Fast and Memory-efficient Algorithm for Robust PCA (MEROP)", IEEE International Conference on Acoustics, Speech, and Signal, ICASSP 2018, April 2018.
N. Vaswani, P. Narayanamurthy, "Provable Dynamic Robust PCA or Robust Subspace Tracking", ISIT 2018, 2018.
J. Zhan, B. Lois, H. Guo, N. Vaswani, "Online (and Offline) Robust PCA: Novel Algorithms and Performance Guarantees", Journal of Machine Learning Research, 2016.
L. Venugopal, "Real-time detection of foreground in video surveillance cameras using CUDA", Master of Science Thesis, Texas A&M University, USA, May 2018.
C. Wei, Y. Huang, Y. Wang, M. Shih, “Background Recovery in Railroad Crossing Videos via Incremental Low-Rank Matrix Decomposition”, Asian Conference on Pattern Recognition, ACPR 2013, November 2013.
P. Rodríguez, B. Wohlberg, "A Matlab Implementation of a Fast Incremental Principal Component Pursuit Algorithm for Video Background Modeling", IEEE International Conference on Image Processing, ICIP 2014, October 2014.
P. Rodríguez, B. Wohlberg, "Incremental Principal Component Pursuit for Video Background Modeling", Journal of Mathematical Imaging and Vision, 2015.
P. Rodriguez, B. Wohlberg ,"Translational and rotational jitter invariant incremental principalcomponent pursuit for video background modeling", IEEE International Conference on Image Processing, ICIP 2015, 2015.
P. Rodríguez, B. Wohlberg, "An incremental principal component pursuit algorithm via projections onto the l1 ball", IEEE International Conference on Electronics, Electrical Engineering and Computing, INTERCON 2017, Cusco, Peru, pages 1-4, 2017.
X. Xu, "Online Robust Principal Component Analysis for Background Subtraction: A System Evaluation On Toyota Car Data", Master thesis, University of Illinois, Urbana-Champaign, USA, 2014.
W. Song,J. Zhu, Y. Li, C. Chen, "Image Alignment by Online Robust PCA via Stochastic Gradient Descent", IEEE Transactions on Circuits and Systems for Video Technology, July 2015.
H. Lee, J. Lee, "Online update techniques for projection based Robust Principal Component Analysis", ICT Express, 2015.
B. Hong, L. We, Y. Hu, D. Cai, X. He, "Online Robust Principal Component Analysis via Truncated Nuclear Norm Regularization", Neurocomputing, October 2015.
K. Quach , C. Duong, K. Luu, T. Bui, "Non-convex Online Robust PCA Enhance Sparsity via lp-norm Minimization", Computer Vision and Image Understanding, 2017.
J. Feng, H. Xu and S. Mannor, "Outlier Robust Online Learning", Preprint, 2017
J. Yang , J. Yang, X. Yang, H. Yue, "Background recovery from video sequences via online motion-assisted RPCA", Visual Communications and Image Processing, VCIP 2016, pages 1-4, 2016.
R. Dixit, A. Bedi, R. Tripathi, K. Rajawat, “Online Learning with Inexact Proximal Online Gradient Descent Algorithms”, Preprint, June 2018.
H. Li, Z. Miao, Y. Li, J. Wang, Y. Zhang, “Background subtraction via online box constrained RPCA”, International Conference on Mathematics and Artificial, ICMAI 2018, pages 26-29, Chengdu, China, April 2018.
A. Akhriev, J. Marecek, A. Simonetto, “Pursuit of Low-Rank Models of Time-Varying Matrices Robust to Sparse and Measurement Noise”, Preprint, September 2018.
H. Fu, B. Wang, H. Liu, “Online RPCA on Background Modeling”, Chinese Intelligent Systems Conference, pages 415-424, 2018.
X. Jia, X. Feng, W. Wang, H. Huang, C. Xu, “Online Schatten Quasi-Norm Minimization for Robust Principal Component Analysis”, Information Sciences, 2018.
H. Fu, H. Liu, "Online RPCA Background Modeling based on Color and Depth Data", Chinese Intelligent Systems Conference, September 2019.
J. Zhang, X. Jia, J. Hu, J. Chanussot, “Online Structured Sparsity-based Moving Object Detection from Satellite Videos”, Preprint, 2019.
A. Rontogiannis, P. Giampouras, K. Koutroumbas, "Online Reweighted Least Squares Robust PCA", IEEE Signal Processing Letters, Volume 27, pages 1340-1344, 2020.
Y. Sanku, S. Bhattacharjee, S. Bhattacharya, "Multi-object Foreground Extraction in Streaming Video using Low Rank Sparse Decomposition", IEEE India Council International Conference, INDICON 2021, pages 1-6, 2021.
X. Pinzas, “Background Subtraction based on Robust Subspace Tracking”, Master Thesis, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil, 2023.
Q. Zhang, S. Li, J. Duan, J. Qin, Y. Zhou, “Moving Object Detection Method based on the Fusion of Online Moving Window Robust Principal Component Analysis and Frame Difference Method”, Neural Processing Letters, February 2024.
L. Jayalal, G. Muthukrishnan, S. Kalyani, “Tuning-Free Online Robust Principal Component Analysis through Implicit Regularization”, Preprint, 2024.
Real Time Implementations of PCP (4 papers)
M. Anderson, G. Ballard, J. Demme, K. Keutzer, “Communication-Avoiding QR Decomposition for GPUs”, Technical Report, ECCS, University of Berkeley, USA, 2010.
M. Anderson, G. Ballard, J. Demme, K. Keutzer, “Communication-Avoiding QR Decomposition for GPUs”, IEEE International Parallel and Distributed Processing Symposium, IPDPS 2011, 2011.
G. Pope, M. Baumann, C. Studery, G. Durisi, “Real-Time Principal Component Pursuit”, Asilomar Conference on Signals, Systems, Computation, Pacific Grove, U.S.A., November 2011.
X. Guo, X. Cao, "Speeding Up Low Rank Matrix Recovery for Foreground Separation in Surveillance Videos", International Conference on Multimedia and Expo, ICME 2014, 2014.
Optimal PCP Solutions (3 papers)
I. Ramırez, G. Sapiro, “Low-Rank Data Modeling Via The Minimum Description Length Principle”, ICASSP 2012, May 2012.
I. Ramırez, G. Sapiro, “An MDL framework for sparse coding and dictionary learning”, 2012.
Z. Gao, L. Cheong, M. Shan, "Block-sparse RPCA for consistent foreground detection", European Conference on Computer Vision, ECCV 2012, 2012.
Spatial and temporal (90 papers)
Z. Gao, L. Cheong, M. Shan, "Block-sparse RPCA for consistent foreground detection", European Conference on Computer Vision, ECCV 2012, 2012.
X. Huang, P. Huang, Y. Cao, H. Yan, "A Block-sparse RPCA Algorithm for Moving Object Detection Based on PCP", Journal of East China, Jiaotong University, Volume 5,pages 30-36, October 2013.
X. Guo, X. Wang, L. Yang, X. Cao , Y. Ma, "Robust Foreground Detection using Smoothness and Arbitrariness Constraints", ECCV 2014, September 2014.
X. Cao, L. Yang, X. Guo, "Total Variation Regularized RPCA for Irregularly Moving Object Detection under Dynamic Background", IEEE Transactions on Cybernetics, Volume 46, No. 4, pages 1014-1027, April 2016.
A. Newson, M. Tepper, G. Sapiro, "Low-Rank Spatio-Temporal Video Segmentation", British Machine Vision Conference, BMVC 2015, 2015.
N. Shahid, V. Kalofolias, M. Bronstein, P. Vandergheyns, "Robust Principal Component Analysis on Graphs", International Conference on Computer Vision, ICCV 2015, December 2015.
N. Shahid, N. Perraudin, V. Kalofolias, P. Vandergheynst, "Fast Robust PCA on Graphs", Preprint, 2015.
A. Sobral, T. Bouwmans, E. Zahzah, "Double-constrained RPCA based on Saliency Maps for Foreground Detection in Automated Maritime Surveillance", ISBC 2015 Workshop conjunction with AVSS 2015, 2015.
Y. Pang, L. Ye, X. Li, J. Pan, "Moving Object Detection in Video Using Saliency Map and Subspace Learning", Preprint, 2015.
C. Chen, S. Li, H. Qin, A. Hao, "Robust salient motion detection in non-stationary videos via novel integrated strategies of spatio-temporal coherency clues and low-rank analysis", Pattern Recognition, 2015.
D. Tian, H. Mansour, A. Vetro, "Depth-weighted group-wise principal component analysis for foreground/background separation", IEEE International Conference on Image Processing, ICIP 2015, September 2015.
J. Yao, X. Liu, C. Qi, "Foreground detection using low rank and structured sparsity", IEEE International Conference on Multimedia and Expo, ICME 2014, pages 1-6, 2014.
X. Liu, G. Zhao, J. Yao, C. Qi, "Background Subtraction based on low-rank model and structured sparse decomposition", IEEE Transactions on Image Processing, 2015.
S. Ebadi, V. Guerra One, E. Izquierdo, "Approximated Robust Principal Component Analysis for Improved General Scene Background Subtraction", IEEE Transactions Image Processing, 2015.
S. Ebadi, E. Izquierdo, "Efficient Background Subtraction with Low-rank and Sparse Matrix Decomposition", IEEE International Conference on Image Processing, ICIP 2015, September 2015.
S. Ebadi, V. Guerra One, E. Izquierdo, "Efficient Background Subtraction with Low-rank and Sparse Matrix Decomposition", Workshop on Signal Processing with Adaptive Sparse Structured Representations, SPARS 2015, July 2015.
S. Ebadi, V. Guerra One, E. Izquierdo, "Dynamic Tree Structured Sparse RPCA via Column Subset Selection for Background Modeling and Foreground Detection", IEEE International Conference on Image Processing, ICIP 2016, September 2016.
S. Ebadi, E. Izquierdo, "Foreground Segmentation via Dynamic Tree-Structured Sparse RPCA", European Conference on Computer Vision, ECCV 2016, 2016.
S. Ebadi, E. Izquierdo, "Foreground Detection with Dynamic Tree-Structured Sparse RPCA", IEEE Transactions on Pattern Analysis and Machine Intelligence, 2016.
S. Javed, A. Mahmood, T. Bouwmans, S. Jung, "Motion-Aware Graph Regularized RPCA for Background Modeling of Complex Scenes", Scene Background Modeling Contest, International Conference on Pattern Recognition, ICPR 2016, December 2016.
S. Javed, A. Mahmood, T. Bouwmans, S. Jung, "Spatiotemporal Low-rank Modeling for Complex Scene Background Initialization", IEEE Transactions on Circuits and Systems for Video Technology, December 2016.
S. Javed, S. Oh, A. Sobral, T. Bouwmans, S. Jung, "Background Subtraction via Superpixel-based Online Matrix Decomposition with Structured Foreground Constraints, International Workshop on Robust Subspace Learning and Computer Vision, ICCV 2015 , December 2015.
S. Javed, A. Mahmood, T. Bouwmans, S. Jung,"Background-Foreground Modeling based on Spatiotemporal Sparse Subspace Clustering", IEEE Transactions on Image Processing, September, 2017.
S. Javed, A. Mahmood, T. Bouwmans, S. Jung, "Superpixels based Manifold Structured Sparse RPCA for Moving Object Detection", International Workshop on Activity Monitoring by Multiple Distributed Sensing, BMVC 2017, September 2017.,
S. Javed, A. Mahmood, S. Al-Maadeed, T. Bouwmans, S. Jung, "Moving object detection in complex scene using spatiotemporal structured-sparse RPCA", IEEE Transactions on Image Processing, Volume 28, No. 2, pages 1007-1022, 2019.
S. Javed, T. Bouwmans, M. Sultana, S. Jung, "Moving Object Detection on RGB-D Videos using Graph Regularized Spatiotemporal RPCA", International Workshop on Background learning for detection and tracking from RGBD videos, ICIAP 2017, Catani, Italy, September 2017.
A. Zheng, M. Xu, H. Shi, B. Luo, C. Li, “CLASS: Collaborative Low-rank and Sparse Separation for Moving Object Detection”, Cognitive Computation, pages 1-14, February 2017.
A. ElTantawy, M. Shehata, "Moving object detection from moving platforms using Lagrange multiplier", IEEE International Conference on Image Processing, ICIP 2015, 2015.
A. ElTantawy, M. Shehata, “MARO: matrix rank optimization for the detection of small-size moving objects from aerial camera platforms", Signal, Image and Video Processing, Volume 12, No. 4, pages 641-649, May 2018.
A. ElTantawy, M. Shehata, "A novel method for segmenting moving objects in aerial imagery using matrix recovery and physical spring model", International Conference on Pattern Recognition, ICPR 2016, pages 3898-3903, 2016.
A. ElTantawy, M. Shehata, “UT-MARO: unscented transformation and matrix rank optimization for moving objects detection in aerial imagery”, International Symposium on Visual Computing, ISVC 2015, pages 275–284, 2015.
A. ElTantawy, M. Shehata, "KRMARO: Aerial Detection of Small-Size Ground Moving Objects using Kinematic Regularization and Matrix Rank Optimization", IEEE Transactions on Circuits and Systems for Video Technology, June 2018.
A. ElTantawy, M. Shehata, "Local null space pursuit for real-time moving object detection in aerial surveillance", Signal, Image and Video Processing, July 2019.
A. ElTantawy, M. Shehata, "An Accelerated Sequential PCP-based method for Ground-Moving Objects Detection from Aerial Videos", IEEE Transactions on Image Processing, July 2019.
Y. Li, G. Liu, S. Chen, “Detection of Moving Object in Dynamic Background using Gaussian Max-Pooling and Segmentation Constrained RPCA”, Preprint, September 2017.
M. Xu, C. Li, H. Shi, J. Tang, A. Zheng, "Moving Object Detection via Integrating Spatial Compactness and Appearance Consistency in the Low-Rank Representation", Chinese Conference on Computer Vision, CCCV 2017, pages 50-60, December 2017.
P. Pan, Y. Wang, M. Zhou, Z. Sun, G. He, "Background recovery via motion-based robust principal component analysis with matrix factorization" Journal of Electronic Imaging, March 2018.
M. Ma, R. Hu, S. Chen, J. Xiao, Z. Wang, “Robust Background Subtraction Method via Low-Rank and Structured Sparse Decomposition , Networks and Security, pages 156-167, July 2018.
B. Shijila, T. Anju, G. Sudhish, "Simultaneous Denoising and Moving Object Detection using Low-Rank Approximation", Future Generation Computer Systems, 2018.
B. Shijila, A. Tom, S. George, ”Moving Object Detection by Low Rank Approximation and l1 -TV Regularization on RPCA framework”, Journal of Visual Communication and Image Representation, September 2018.
G. Shi, T. Huang, W. Dong, J. Wu, X. Xie, "Robust Foreground Estimation via Structured Gaussian Scale Mixture Modeling", IEEE Transactions on Image Processing, Volume 27, No. 10, pages 4810-4824, October 2018.
Q. Ning, W. Dong, F. Wu, J. Wu, J. Lin, G. Shi, "Spatial-Temporal Gaussian Scale Mixture Modeling for Foreground Estimation, AAAI Conference on Artificial Intelligence, AAAI 2020, February 2020.
A. Zheng, T. Zou, Y. Zhao, B. Jiang, J. Tang, C. Li, “Background subtraction with multi-scale structured low-rank and sparse factorization”, Neurocomputing, pages 1-9, 2018.
J. Xue, Y. Zhao, W. Liao, J. Cha, “Total Variation and Rank-1 Constraint RPCA for Background Subtraction”, IEEE Access, September 2018.
J. Ju, J. Xing, “Moving object detection based on smoothing three frame difference method fused with RPCA”, Multimedia Tools and Applications, September 2018.
Y. Li, G. Liu, Q. Liu, Y. Sun, S. Chen, “Moving Object Detection via Segmentation and Saliency Constrained RPCA”, Neurocomputing, 2018.
A. Zheng, Y. Zhao, C. Li, J. Tang, B. Luo, “Moving Object Detection via Robust Low-Rank and Sparse Separating with High-Order Structural Constraint”, IEEE International Conference on Multimedia Big Data, BigMM 2018, pages 1-6, Xi'an, China, 2018.
L. Li, Q. Hu, X. Li, “Moving Object Detection in Video via Hierarchical Modeling and Alternating Optimization", IEEE Transactions on Image Processing, 2018.
L. Chen, J. Liu, X. Wang, “Foreground detection with weighted Schatten-p norm and 3D total variation”, Journal of Computer Applications, December 2018.
R. Chen, Y. Tong, J. Yang, M. Wu, “Video Foreground Detection Algorithm Based on Fast Principal Component Pursuit and Motion Saliency”, Hindawi Computational Intelligence and Neuroscience, 2019.
L. Chen, X. Jiang, X. Liu, T. Kirubarajan, Z. Zhou, “Outlier-Robust Moving Object and Background Decomposition via Structured lp-Regularized Low-Rank Representation”, IEEE Transactions on Emerging Topics in Computational Intelligence, 2019.
F. Zhou, Y. Wu, Y. Dai, P. Wang, K. Ni, “Graph-Regularized Laplace Approximation for Detecting Small Infrared Target against Complex Backgrounds”, IEEE Access 2019, 2019.
J. Zhang, X. Jia, J. Hu, “Error Bounded Foreground and Background Modeling for Moving Object Detection in Satellite Videos”, Preprint, 2019.
L. Chen, X. Jiang, X. Liu, T. Kirubarajan, Z. Zhou, "Outlier-Robust Moving Object and Background Decomposition via Structured lp-Regularized Low-Rank Representation”, IEEE Transactions on Emerging Topics in Computational Intelligence, 2019.
A. Zheng, N. Ye, C. Li, X. Wang, J. Tang, “Multi-modal Foreground Detection via Inter- and Intra-Modality-Consistent Low-Rank Separation”, Neurocomputing, 2019.
J. Yang, W. Shi, H. Yue, K. Li, J. Ma, C. Hou, "Spatiotemporally scalable matrix recovery for background modeling and moving object detection", Signal Processing, Volume 168, March 2020.
J. Zhang, X. Jia, “Improved Low Rank plus Structured Sparsity and Unstructured Sparsity Decomposition for Moving Object Detection in Satellite Videos”, IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2019, pages 5421-5424, Yokohama, Japan, 2019.
M. Jin, Y. Chen, “Robust Image Recovery via Mask Matrix”, IScIDE 2019, pages 349-361, 2019.
Z. Hu, Y. Wang, R. Su, X. Bian, H. Wei, G. He, "Moving object detection based on nonconvex RPCA with segmentation constraint", IEEE Access, 2020.
Y. Yang, Z. Yang, J. Li, L. Fan, “Foreground-Background Separation via Generalized Nuclear Norm and Structured Sparse Norm Based Low-Rank and Sparse Decomposition”, IEEE Access, 2020.
G. Yang, D. Yu, J. Wen, J. Lin, L. Liang, "Video denoising and moving object detection by rank-1 and total variation regularization on robust principal component analysis framework", Journal of Electronic Imaging, May 2020.
S. Javed, A. Mahmood, J. Dias, N. Werghi, “CS-RPCA: Clustered Sparse RPCA for Moving Object Detection”, IEEE International Conference on Image Processing, ICIP 2020, Abu Dhabi, UAE, October 2020.
A. Khalilian-Gourtani, S. Minaee, Y. Wang, “Masked-RPCA: Sparse and Low-rank Decomposition Under Overlaying Model and Application to Moving Object Detection”, Preprint, September 2019.
H. Ahn, M. Kang, “Dynamic background subtraction with masked RPCA”, Signal, Image and Video Processing, 2020.
J. Zhang, X. Jia, J. Hu, “Low-Rank Matrix Decomposition with Superpixel-based Structured Sparse Regularization For Moving Object Detection in Satellite Videos”, ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2020.
N. Abdulghafoor, H. Abdullah, "Real-Time Object Detection with Simultaneous Denoising using Low-Rank and Total Variation Models", International Congress on Human-Computer Interaction, Optimization and Robotic Applications, HORA 2020, pages 1-10, Ankara, Turkey, 2020.
Y. Wang, H. Wei, X. Ding, J. Tao, "Video Background/Foreground Separation Model Based on Non-Convex Rank Approximation RPCA and Superpixel Motion Detection”, IEEE Access, pages 157493-157503, 2020.
Y. Wang, H. Wei, X. Ding, J. Tao, "Video Background/Foreground Separation Model Based on Non-Convex Rank Approximation RPCA and Superpixel Motion Detection”, IEEE Access, pages 157493-157503, 2020.
L. Zhu, X. Jiang, J. Li, Y. Hao, Y. Tian, “Motion-Aware Structured Matrix Factorization for Foreground Detection in Complex Scenes”, ACM Transactions on Multimedia Computing, Communications, and Applications, December 2020.
W. Xu, T. Xia, C. Jing, "Background modeling from video sequences via online motion-aware RPCA", Computer Science and Information Systems, 2021.
J. Peng, Y. Wang, H. Zhang, J. Wang, D. Meng, "Exact Decomposition of Joint Low Rankness and Local Smoothness Plus Sparse Matrices", Preprint, January 2022.
Y. Ban, L. Chen, X. Wang, "Background subtraction based on logarithm rank function and structured sparsity", Multimedia Tools and Applications, March 2022.
T. Liu, "Moving Object Detection in Dynamic Environment via Weighted Low-Rank Structured Sparse RPCA and Kalman Filtering", Hindawi Mathematical Problems in Engineering, 2022.
Y. Li, “Moving object detection for unseen videos via truncated weighted robust principal component analysis and salience convolution neural network”, Multimedia Tools and Applications, 2022.
J. Qin, R. Shen, R. Zhu, B. Xie, “Robust Dual-Graph Regularized Moving Object Detection”, Preprint, 2022.
T. Chen, D. Zhao, L. Sun, S. Li, B. Feng, “Moving object detection via RPCA framework using non-convex low-rank approximation and total variational regularization”, Signal, Image and Video Processing, 2022.
H. Gao, "LRSDSFD: low-rank sparse decomposition and symmetrical frame difference method for moving video foreground-background separation", EAI Endorsed Transactions on Scalable Information Systems, 2021.
R. Komatsu, M. Yamagishi, I. Yamada, "A Graph Regularized RPCA by Generalized Moreau Enhanced Model", European Signal Processing Conference, EUSIPCO 2021, pages 2129-2133, 2021.
J. Zhao, Z. Jiang, B. Liu, L. Zhang, "Moving Object Detection based on Weighted Kernel Norm and Saliency Constrained RPCA", Journal of Physics: Conference Series, 2022.
Q. Ning, F. Wu, W. Dong, J. Wu, G. Shi, X. Li, "Robust Dynamic Background Modeling for Foreground Estimation", IEEE International Conference on Visual Communications and Image Processing, VCIP 2022, Suzhou, China, December 2022.
G. Zhang, L. Chen, Z. Zhou, "Background Subtraction Combining l1/2 Norm and Saliency Constraint Background Subtraction Combining l1/2 Norm and Saliency Constraint", Computer Engineering , pages 263-269, 2022.
L. Huang, J. Qin, "Fast Dual-Graph Regularized Background Foreground Separation”, IEEE International Conference on Sampling Theory and Applications, SampTA 2023, pages 1-5, New Haven, USA, 2023.
J. Qin, B. Xie, “Human Motion Detection Based on Dual-Graph and Weighted Nuclear Norm Regularizations”, Preprint, April 2023.
Y. Yang, Z. Yang, J. Le, J. Li, “Nonconvex γ-norm and Laplacian scale mixture with salient map for moving object detection”, Multimedia Tools and Applications, 2023.
Y. Yang, Z. Yang, J. Li, “Video Foreground and Background Separation via Gaussian Scale Mixture and Generalized Nuclear Norm Based Robust Principal Component Analysis”, Digital Signal Processing, 2024.
Q. Yin, W. An, T. Liu, Y. Sun, Z. Lin, Y. Guo, "Satellite Video Object Detection Based on Enhanced 3DTV Regularization and Gaussian Prior", IEEE Transactions on Geoscience and Remote Sensing, Volume 63, pages 1-14, 2025.
H. Zhu, X. Feng, “An Efficient Representative Coefficient Total Variation Method for Moving Object Detection in Noisy Videos”, Signal, Image and Video Processing, May 2025.
Algorithms SVD for PCP (23 papers)
M. Yang, Z. An, "Video background modeling using low-rank matrix recovery, Journal of Nanjing University of Posts and Telecommunications", April 2013.
S. Zhang, J. Tian, "Accelerated algorithms for low-rank matrix recovery", MIPPR 2013: Parallel Processing of Images and Optimization and Medical Imaging Processing, October 2013.
Y. Chai, S. Xu, H. Yin, "An Improved ADM algorithm for RPCA optimization problem", Chinese Control Conference, CCC 2013, pages 4769-4880, July 2013.
X. Liu, Z. Wen, Y. Zhang, "Limited memory block Krylov subspace optimization for computing dominant singular value decomposition", Preprint, 2012.
X. Liu, Z. Wen, Y. Zhang, "An Efficient Gauss-Newton Algorithm for Symmetric Low-Rank Product Matrix Approximations", Technical Report, June 2014.
N. Erichson, S. Voronin, S. Brunton, J. Kutz, "Randomized Matrix Decompositions using R", Preprint, 2016.
M. Brand, "Incremental singular value decomposition of uncertain data with missing values", European Conference on Computer Vision, ECCV 2002, pages 707-720, 2002.
V. Hovhannisyan, Y. Panagakis, P. Parpas, S. Zafeiriou , "Multilevel Approximate Robust Principal Component Analysis", International Workshop on Matrix and Tensor Factorization Methods in Computer Vision in conjunction with ICCV 2017, October 2017.
V. Hovhannisyan, “Multilevel Optimisation for Computer Vision”, PhD Thesis, Imperial College London, UK, 2018.
W. Zhen, Y. Min, "New methods for solving the nuclear norm with random matrix and the application in Robust Principal Component Analysis", Chinese Control and Decision Conference, CCDC 2017, pages 1323-1328, 2017.
B. Erichson, S. Brunton, N. Kutz, “Compressed Singular Value Decomposition for Image and Video Processing”, International Workshop on RSL-CV in conjunction with ICCV 2017, October 2017.
M. Kaloorazi, R. Lamare, “Subspace-Orbit Randomized Decomposition for Low-rank Matrix Approximation”, Preprint, 2018.
M. Kaloorazi, R. Lamare, “Randomized Rank-Revealing UZV Decomposition for Low-Rank Approximation of Matrices”, Preprint, 2018.
M. Kaloorazi, R. Lamare, "Compressed Randomized UTV Decompositions for Low-Rank Matrix Approximations", IEEE Journal of Selected Topics in Signal Processing, December 2018.
M. Kaloorazi, R. Lamare, “Study of compressed randomized UTV decompositions for low-rank matrix approximations in data science”, Preprint, June 2019.
A. Bhaskara, S. Kumar, "Low Rank Approximation in the Presence of Outliers", Approximation, Randomization, and Combinatorial Optimization, 2018.
Y. Lu, F. Ino, Y. Matsushita, “High-Performance Out-of-core Block Randomized Singular Value Decomposition on GPU”, Preprint, 2017.
D. Janekovic, D. Bojanjac, "Randomized Algorithms for Singular Value Decomposition: Implementation and Application Perspective”, IEEE International Symposium ELMAR, pages 165-168, 2021.
S. Roy, A. Basu, A. Ghosh, "A new robust scalable singular value decomposition algorithm for video surveillance background modelling", Preprint, 2021.
W. Chettleburgh, Z. Huang, M. Yan, "Fast Robust Principal Component Analysis using Gauss-Newton Iterations”, IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2023, Rhodes Island, Greece, 2023.
C. Zeng, M. Ng, T. Jiang, “Incremental algorithms for truncated higher-order singular value decompositions”, Numerical Mathematics, Volume 64, No. 4, 2024.
S. Han, K. Kim, S. Jung, “Robust SVD Made Easy: A fast and reliable algorithm for large-scale data analysis”, Preprint, February 2024.
Modified PCP (142 papers)
W. Leow, Y. Cheng, L. Zhang, T. Sim, L. Foo, “Background Recovery by Fixed-rank Robust Principal Component Analysis”, CAIP 2013, 2013
X. Yuan, M. Ng, X. Yuan, “Nuclear-norm-free Variational Models for Background Extraction from Surveillance Video”, Cross-straits Optimization Workshop, IEEE Transactions on Image Processing, 2013
Q. Sun, S. Xiang, J. Ye, “Robust principal component analysis via capped norms”, International Conference on Knowledge Discovery and Data Mining, KDD 2013, pages 311-319, 2013.
B. Bao, G. Liu, C. Xu, S. Yan, “Inductive Robust Principal Component Analysis”, IEEE Transactions on Image Processing, 2012.
J. Zhan, N. Vaswani, "Robust PCA with Partial Subspace Knowledge", Preprint, 2014.
J. Wang, M. Wan, X. Hu, S. Yan, "Image Denoising with a Unified Schattern-p Norm and lq Norm Regularization", Journal of Optimization Theory and Applications", April 2014.
W. Shao, Q. Ge, Z. Gan, H. Deng, H. Li, "A Generalized Robust Minimization Framework for Low-Rank Matrix Recovery", Mathematical Problems in Engineering, 2014.
Y. Sun, X. Tao, Y. Li, J. Lu, "Robust two-dimensional principal component analysis via alternating optimization", International Conference on Image Processing, ICIP 2013, September 2013.
T. Oh, "A Novel Low-Rank Constraint Method with the Sparsity Model for Moving Object Analysis", Master Thesis, KAIST 2012, 2012.
J. Wen, Y. Xu, J. Tang, Y. Zhan, Z. Lai, X. Guo, “Joint video frame set division and low-rank decomposition for background subtraction”, IEEE Transactions on Circuits and Systems For Video Technology, 2014.
S. Wang, X. Feng, “Optimization of the Regularization in Background and Foreground Modeling”, Journal of Applied Mathematics, 2014.
R. He, T. Tan, L. Wang, "Recovery of Corrupted Low-rank Matrix by Implicit Regularizers", IEEE Transaction on Pattern Analysis and Machine Intelligence, PAMI 2013, September 2013.
M. Rahmani, G. Atia, “High Dimensional Low Rank plus Sparse Matrix Decomposition”, Preprint, February 2015.
M. Rahmani, G. Atia, “Randomized subspace learning approach for high dimensional low rank plus sparse matrix decomposition”, Asilomar Conference on Signals, Systems and Computers, Pacific Grove, pages 1796-1800, 2015.
M. Rahmani, G. Atia, “Subspace Learning Approach to High-Dimensional Matrix Decomposition with Efficient Information Sampling”, Preprint, 2016.
X. Yang, X. Gao, D. Tao, X. Li, B. Han, J. Li, "Shape-Constrained Sparse and Low-Rank Decomposition for Auroral Substorm Detection", IEEE Transactions on Neural Networks and Learning Systems, 2015.
B. Xin, Y. Tian, Y. Wang, W. Gao, "Background Subtraction via Generalized Fused Lasso Foreground Modeling", IEEE International Conference on Computer Vision and Pattern Recognition, CVPR 2015, June 2015.
B. Xin, Y. Kawahara, Y. Wang, L. Hu, W. Gao,“Efficient generalized fused Lasso and its applications”, ACM Transactions on Intelligent Systems and Technology, TIST 2016, Volume 7, Issue 4, May 2016.
F. Zhang, J. Yang, Y. Tai, J. Tang, “Double Nuclear Norm-Based Matrix Decomposition for Occluded Image Recovery and Background Modeling”, IEEE Transactions on Image Processing, Volume 24, No. 6, pages 1956-1966, June 2015.
Z. Zhou, Z. Jin ,"Robust Principal Component Analysis for Image Disocclusion and Object Detection", Neurocomputing, 2016.
Q. Zhao, D. Meng, L. Jiang, Q. Xie, Z. Xu, A. Hauptmann, “Self-Paced Learning for Matrix Factorization”, AAAI Conference on Artificial Intelligence, AAAI 2015, January 2015.
M. Karl, C. Osendorfer, "Improving approximate RPCA with a K-sparsity prior", International Conference on Learning Representations, ICLR 2015, 2015.
F. Ong , M. Lustig, "Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition", Preprint, 2015.
Z. Kang, C. Peng, Q. Cheng, “Robust PCA via Nonconvex Rank Approximation”, Preprint, November 2015.
L. Han, Q. Zhang, “Multi-stage convex relaxation method for low-rank and sparse matrix separation problem”, Applied Mathematics and Computation, Volume 284, pages 175-184, July 2016.
C. Li, X. Wang, L. Zhang, J. Tang, H. Wu, L. Lin, "WELD: Weighted Low-rank Decomposition for Robust Grayscale Thermal Foreground Detection", IEEE Transactions on Circuits and Systems for Video Technology, 2016.
S. Yang, B. Luo,C. Li, G. Wang, J. Tang, "Fast Grayscale-Thermal Foreground Detection with Collaborative Low-rank Decomposition", IEEE Transactions on Circuits and Systems for Video Technology, June 2017.
A. Zheng, Y. Zhao, C. Li, J. Tang, B. Luo, "Multispectral Foreground Detection via Robust Cross-Modal Low-Rank Decomposition", PCM 2018, pages 819-829, 2018.
J. Shi, X. Zheng, W. Yang, "Regularized approach for incomplete robust component analysis and its application to background modeling", Journal of Computer Applications, 2016.
K. Chiang, C. Hsieh, I. Dhillon, "Robust Principal Component Analysis with Side Information", International Conference on Machine Learning, ICML 2016, 2016.
J. Lai, W. Leow, T. Sim, V. Sharma, "Think Big, Solve Small: Scaling Up Robust PCA with Coupled Dictionaries", IEEE Winter Conference on Applications of Computer Vision, WACV 2016, 2016.
K. Kiruba, P. Sathiya, P AnandhaKumar, "Modified RPCA with Hessian Matrix for Object Detection in Video Surveillance on Highways", International Conference on Advanced Computing , ICoAC 2014, 2014.
M. Kaloorazi, R. Lamare, "Switched-Randomized Robust PCA for Foreground and Background Separation in Video Surveillance", SAM 2016, 2016.
S. Ebadi, E. Izquierdo, "Approximated RPCA for Fast and Efficient Recovery of Corrupted and Linearly Correlated Images and Video Frames", IEEE International Conference on Systems Signals and Image Processing, IWSSIP 2015, September 2015.
F. Cao, J. Chen, H. Ye, J. Zhao, Z. Zhou, "Recovering low-rank and sparse matrix based on the truncated nuclear norm", Neural Networks,2016.
Y. Zhang, J. Guo , J. Zhao, B. Wang, "Robust principal component analysis via truncated nuclear norm minimization", Journal of Shanghai Jiaotong University, Volume 21, No. 5, pages 576-583, October 2016.
B. Hong, L. We, Y. Hu, D. Cai, X. He,"Online Robust Principal Component Analysis via Truncated Nuclear Norm Regularization", Neurocomputing, October 2015.
T. Chan, Y. Yang, "Polar n-Complex and n-Bicomplex Singular Value Decomposition and Principal Component Pursuit", IEEE Transactions on Signal Processing, 2016.
C. Peng, Z. Kang, M. Yang, Q. Cheng, “RAP: Scalable RPCA for Low-rank Matrix Recovery”, ACM International on Conference on Information and Knowledge Management, CIKM 2016, pages 2113-2118, 2016.
M. Rahmani, G. Atia, "Randomized subspace learning approach for high dimensional low rank plus sparse matrix decomposition", Asilomar Conference on Signals, Systems and Computers, pages1796-1800, 2015.
J. Lee, Y. Choe, "Robust PCA with Incoherence for Low-Rank Matrix Recovery", IEEE Transactions on Image Processing, 2017.
Y. Wang, C. Xu, C. Xu, D. Tao, "Beyond RPCA: Flattening Complex Noise in the Frequency Domain", Advancement of Artificial Intelligence, 2017.
Y. Cherapanamjeri, P. Jain, P. Netrapalli, "Thresholding based Efficient Outlier Robust PCA", Preprint, 2017.
D. Pimentel-Alarcon, R. Nowak, "Random Consensus Robust PCA", AISTATS 2017, 2017.
R. Chalapathy, A. Krishna Menon, S. Chawla, "Robust, Deep and Inductive Anomaly Detection", Preprint, April 2017.
U. Niranjan, A. Rajkumar, T. Tulabandhula, "Provable Inductive Robust PCA via Iterative Hard Thresholding", Preprint, April 2017.
J. Liu, P. Cosman, B. Rao, "Sparsity Regularized Principal Component Pursuit", International Conference on Acoustics, Speech and Signal Processing, ICASSP 2017, 2017.
P. Zheng, A. Aravkin, K. Ramamurthy, "Shape Parameter Estimation", Preprint, 2017.
P. Zheng, A. Aravkin, K. Ramamurthy, J. Thiagarajan, “Learning Robust Representations for Computer Vision”, International Workshop on RSL-CV in conjunction with ICCV 2017, October 2017.
S. Rambhatla, X. Li, J. Haupt, “A Dictionary based Generalization of Robust PCA”, IEEE Global Conference on Signal and Information Processing, GlobalSIP 2016, 2016.
X. Li, J. Ren, Y. Xu, J. Haupt, “An Efficient Dictionary Based Robust PCA via Sketching”, Preprint, 2017.
T. Wu, Y. Lei, J. Shi, M. Gong, “An evolutionary multi-objective method for low-rank and sparse matrix decomposition”, American Institute of Mathematical Sciences, Volume 2, Number 1, pages 23-37, January 2017.
J. Lee, Y. Choe, "Robust PCA Based on Incoherence with Geometrical Interpretation", IEEE Transactions on Image Processing, 2018.
B. Kresnaraman, “Understanding Human Images in Thermal Infrared Spectrum”, PhD Thesis, Nagoya University, Japan, 2018.
X. Jia, X. Feng, W. Wang, C. Xu, L. Zhang, “Bayesian Inference for Adaptive Low Rank and Sparse Matrix Estimation”, Neurocomputing, 2018.
X. Zhang, L Wang, Q. Gu, “A Unified Framework for Low-Rank plus Sparse Matrix Recovery, Preprint, 2018.
J. Fan, T. Chow, “Exactly Robust Kernel Principal Component Analysis”, Preprint, 2018.
S. Wang, Y. Wang, Y. Chen, P. Pan, Z. Sun, G. He, "Robust PCA using Matrix Factorization for Background/Foreground Separation", IEEE Access, 2018.
S. Ma, F. Wang, L. Wei, H. Wolkowicz, “Robust Principal Component Analysis using Facial Reduction”, Preprint, 2018.
W. Qian, F. Cao, “Adaptive algorithms for low-rank and sparse matrix recovery with truncated nuclear norm”, International Journal of Machine Learning and Cybernetics, April 2018.
V. Menon, S. Kalyani, “Fast, Parameter free Outlier Identification for Robust PCA”, Preprint, 2018.
M. Wu, Y. Sun, R. Hang, Q. Liu, G. Liu, “Multi-Component Group Sparse RPCA Model for Motion Object Detection under Complex Dynamic Background”, Neurocomputing, 2018.
Z. Xue, J. Dong, Y. Zhao, C. Liu, R. Chellali, “Low-rank and sparse matrix decomposition via the truncated nuclear norm and a sparse regularizer”, The Visual Computer, May 2018.
T. Wu, J. Shi, X. Jiang, D. Zhou, M. Gong, “A multi-objective memetic algorithm for low rank and sparse matrix decomposition”, Information Sciences, pages 172–192, 2018.
Y. Chen,Y. Zhou, “Robust Principal Component Analysis with Matrix Factorization”, IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2018, pages 2411-2415, 2018.
M. Sun, Y. Wang, “Modified hybrid decomposition of the augmented Lagrangian method with larger step size for three-block separable convex programming”, Journal of Inequalities and Applications, 2018.
Z. Yang, H. Zhang, D. Xu, F. Zhang, G. Yang, “Double truncated nuclear norm-based matrix decomposition with application to background modeling”, Journal of Ambient Intelligence and Humanized Computing, December 2018.
J. Liu, B. Rao, "Robust PCA via l0-l1 Regularization”, IEEE Transactions on Signal Processing, December 2018.
J. Liu,” Robust PCA and Robust Linear Regression via Sparsity Regularization”, PhD Thesis, University of California, San Diego, USA, 2019.
X. Zhang, Y. Gao, L. Lan, X. Guo, X. Huang, Z. Luo, “Low-Rank Matrix Recovery via Continuation-Based Approximate Low-Rank Minimization”, Pacific Rim International Conference on Artificial Intelligence, PRICAI 2018, pages 559-573, July 2018.
C. Hage, "Robust Structured and Unstructured Low-Rank Approximation on the Grassmannian", PhD Thesis, TUM, Germany, 2016.
S. Shah, T. Goldstein, C. Studer, “Estimating Sparse Signals with Smooth Support via Convex Programming and Block Sparsity”, IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2016, 2016.
X. Wu, X. Lu, “Adaptive pixel-block based background subtraction using low-rank and block-sparse matrix decomposition”, Multimedia Tools and Applications, 2018.
S. Fattahi, S. Sojoudi, “Exact Guarantees on the Absence of Spurious Local Minima for Non-negative Robust Principal Component Analysis”, Preprint, December 2018.
Y. Zhang, B. Lu, W. Zhang, X. Li, “A New Method for Detecting Moving Objects in Video”, Journal of University of Electronic Science and Technology of China, Volume 48, No.1, pages 46-52, January 2019.
J. Bai, J. Feng, “Robust Principal Components Analysis with Non-Sparse Errors”, Preprint, February 2019.
X. Liu, G. Zhao, “Background Subtraction using Multi-Channel Fused Lasso”, International Symposium on Electronic Imaging, 2019.
M. Azghani, A. Esmaeili, K. Behdin, F. Marvasti, “Missing Low-Rank and Sparse Decomposition based on Smoothed Nuclear Norm”, IEEE Transactions on Circuits and Systems for Video Technology, 2019.
M. Farzaneh Kaloorazi, J. Chen, "Randomized Truncated Pivoted QLP Factorization for Low-Rank Matrix Recovery”, IEEE Signal Processing Letters, 2019.
C. Wu, J. Din, “Nonconvex Approach for Sparse and Low-Rank Constrained Models with Dual Momentum”, Preprint, June 2019.
Y. Liu, X. Gao, Q. Gao, L. Shao, J. Han, "Adaptive Robust Principal Component Analysis", Neural Networks, 2019.
N. Zarmehi, A. Amini, F. Marvasti, “Low Rank and Sparse Decomposition for Image and Video Applications”, IEEE Transactions on Circuits and Systems for Video Technology, 2019.
J. Zhao, L. Zhao, “Low-rank and sparse matrices fitting algorithm for low-rank Representation”, Computers and Mathematics with Applications, 2019.
Y. Liu, X. Gao, Q. Gao, L. Shao, J. Han, “Adaptive robust principal component analysis”, Neural Networks, Volume 119, pages 85-92, 2019.
M. Baes, C. Herrera, A. Neufeld, P. Ruyssen, “Low-Rank plus Sparse Decomposition of Covariance Matrices using Neural Network Parametrization”, Preprint, 2019.
J. Lee, N. Bertrand, C. Rozell, “Parallel Unbalanced Optimal Transport Regularization for Large Scale Imaging Problems”, Preprint, 2019.
C. Peng, Y. Chen, Z. Kang, C. Chen, Q. Cheng, “Robust Principal Component Analysis: A Factorization-Based Approach with Linear Complexity”, Information Sciences, October 2019.
Y. Zhan, T. Liu, "Weighted RPCA based Background Subtraction for Automatic Berthing”, Chinese Control Conference, CCC 2019, pages 3519-3524, Guangzhou, China, 2019.
X. Su, Y. Wang, X. Kang, R. Tao, "Nonconvex Truncated Nuclear Norm Minimization Based on Adaptive Bisection Method”, IEEE Transactions on Circuits and Systems for Video Technology, Volume 29, No. 11, pages 3159-3172, November 2019.
X. Xiu, Y. Yang, W. Liu, L. Kong, M. Shang, “An Improved Total Variation Regularized RPCA for Moving Object Detection with Dynamic Background”, AIMS 2019, 2019.
J. Fan, L. Ding, Y. Chen, M. Udell, “Factor Group-Sparse Regularization for Efficient Low-Rank Matrix Recovery”, NeurIPS 2019 , 2019.
L Zhao, X Hou, H Yang, J Li, “GRPCA21 for recovering a corrupted low-rank matrix”, International Journal of Machine Learning and Cybernetics, 2019.
J. Dong, Z. Xue, W. Wang, “Robust PCA using Nonconvex Rank Approximation and Sparse Regularizer”, CSSP 2019, 2019.
Q. Wang, Q. Gao, G. Sun, C. Ding, “Double Robust Principal Component Analysis”, Neurocomputing, 2020.
A. Dutta, F. Hanzely, P. Richtarik,“A Nonconvex Projection Method for Robust PCA”, Preprint, 2020.
D. He, J. Liu, M. Wang, X. Zeng, "Moving Object Detection by Patch Dividing through Low-Rank Framework", Advanced Information Management, Communicates, Electronic and Automation Control Conference, IMCEC 2019, pages 1792-1796, Chongqing, China, 2019.
Z. Yang, L. Fan, Y. Yang, Z. Yang, G. Gui, "Generalized Nuclear Norm and Laplacian Scale Mixture Based Low-Rank and Sparse Decomposition for Video Foreground-Background Separation", Signal Processing, 2020.
Z Shao,Y Pu, J Zhou, B Wen, Y Zhang, "Hyper RPCA: Joint Maximum Correntropy Criterion and Laplacian Scale Mixture Modeling On-the-Fly for Moving Object Detection", Preprint, June 2020.
T. Oh, Y. Tai, J. Bazin, H. Kim, I. Kweon, “Partial Sum Minimization of Singular Values in Robust PCA: Algorithm and Applications", IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 38, No. 4, pages 744–758, 2016.
W. Hou, Q. Li, “Enhanced PSSV for Incomplete Data Analysis”, IEEE Access, September 2020.
A. Qi, L. Xian, Y. Yang, T. Zhang, Y. Tan, "Low-Rank Matrix Recovery from Noisy via an MDL Framework-based Atomic Norm", Preprint, September 2020.
E. Zhu , M. Xu, D. Pi, “A Novel Robust Principal Component Analysis Algorithm of Nonconvex Rank Approximation”, Hindawi Mathematical Problems in Engineering, October 2020.
Z. Xu, Y. Lu, J. Wu, R. He, S. Wu, S. Xie, "Adaptive Weighted Robust Principal Component Analysis”, IEEE Conference on Industrial Electronics and Applications, ICIEA 2020, pages 19-24, Kristiansand, Norway, 2020.
F. Wen, R. Ying, P. Liu, R. C. Qiu, "Robust PCA using Generalized Nonconvex Regularization", IEEE Transactions on Circuits and Systems for Video Technology, Volume30, No. 6, pages 1497-1510, June 2020
P. Pokala, R. Hemadri, C. Seelamantula, “Iteratively reweighted minimax-concave penalty minimization for accurate low-rank plus sparse matrix decomposition”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2021.
Z. Xu, R. He, S. Xie, S. Wu, "Adaptive Rank Estimate in Robust Principal Component Analysis",IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2021, June 2021.
H. Cai, K. Hamm, L. Huang, D. Needell, “Robust CUR Decomposition: Theory And Imaging Applications”, Preprint, January 2021.
H. Cai, K. Hamm, L. Huang, J. Li, T. Wang, "Rapid Robust Principal Component Analysis: CUR Accelerated Inexact Low Rank Estimation", IEEE Signal Processing Letters, 2021.
K. Hamm, M. Meskini, H. Cai, “Riemannian CUR Decompositions for Robust Principal Component Analysis”, Preprint, June 2022.
Z. Wang, Y. Liu, X. Luo, J. Wang, C. Gao, D. Peng, W. Chen, " Affine Matrix Rank Minimization With a Novel Nonconvex Regularizer", IEEE Transactions on Neural Networks and Learning Systems, March 2021.
Q. Yao, J. Kwok, T. Wang, T. Liu, "Large-scale low-rank matrix learning with nonconvex regularizers", IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 41, No. 11, pages 2628–2643, November 2019.
J. Liu, X. Xiu, X. Jiang, W. Liu, X. Zeng, M. Wang, H. Chen, “Manifold constrained joint sparse learning via non-convex regularization”, Neurocomputing, 2021.
S. Maurya, M. Choudhry, "Background Subtraction using A Hybrid Modelling Based Technique', International Conference on Signal Processing and Integrated Networks, SPIN 2021, pages 527-531, 2021.
Q. Tan, J. Pan, Z. Liang, X. Zhang, Y. Jiang, Y. Yang, "TransDRPCA: Joint Label and Image Low-rank Recovery", submitted to Wiley Optimal Control, Applications and Methods, December 2021.
L. Guo, X. Zhang, Q. Wang, X. Xue, Z. Liu, Y. Mu, “Joint enhanced low-rank constraint and kernel rank-order distance metric for low level vision processing”, Expert Systems with Applications, September 2022.
R. Fan, M. Jing, T. Chen, W. Liu, "A Novel Low-rank and Sparse Decomposition Algorithm Based on Laplacian Distribution", International Conference on Intelligent Control, Measurement and Signal Processing, ICMSP 2022, pages 969-972, 2022.
Q. Zheng, P. Xu, A Unified Framework for Nonconvex Nonsmooth Sparse and Low-Rank Decomposition by Majorization-Minimization Algorithm, Journal of the Franklin Institute, 2022.
S. Qin, X. Ke, C. Chen, "Algorithm Exploration and Experimentation of RPCA-Based Matrix Separation", International Conference on Information Technologies and Electrical Engineering, ICITEE 2022, pages 12-18, 2022.
Z. Yuan, Q. Guo, Y. Eldar, Y. Li, “Unitary Approximate Message Passing for Matrix Factorization”, Preprint, July 2022.
Y. Yang, Z. Yang, J. Li, "Novel RPCA with nonconvex logarithm and truncated fraction norms for moving object detection", Digital Signal Processing, Volume 133, March 2023.
R. He, Z. Xu, S. Wu, M. Jia, “Fast Robust Component Analysis with Rank Constraint and Applications”, Acta Electonica Sinica, 2023.
W. Wu, Z. Wu, H. Zhang,"Recovering Clean Data with Low Rank Structure by Leveraging Pre-learned Dictionary for Structured Noise", Neural Processing Letters, 2023.
R. Fan, M. Jing, L. Li, J. Shi, Y. Wei,"Weighted Schatten p-norm and Laplacian scale mixture-based low-rank and sparse decomposition for foreground–background separation", Journal of Electronic Imaging, 2023.
S. Fang, Z. Xu, S. Wu, S. Xie, "Efficient Robust Principal Component Analysis via Block Krylov Iteration and CUR Decomposition", IEEE Computer Vision and Pattern Recognition Conference, CVPR 2023, Vancouver, Canada, June 2023.
R. Gao, X. Liu, J. Yang, H. Yue, "Multi-Channel Fused Lasso for Motion Detection in Dynamic Video Scenarios", IEEE Transactions on Consumer Electronics, 2023.
Y. Dou, X. Liu, M. Zhou, J. Wang, “Robust principal component analysis via weighted nuclear norm with modified second-order total”, The Visual Computer, Volume 39, pages 1-11, 2023.
L. Yang, B. Zhang, Q. Feng, X. Liu, J. Wang, “Schatten Capped p Regularization for Robust Principal Component Analysis”, Computer Graphics International Conference, CGI 2023, December 2023.
R. Keshavarzian, A. Aghagolzadeh,“Low rank and sparse decomposition based on extended llp norm” Multimedia Tools and Applications, 2023.
Y. Huang, Z. Wang, Q. Chen, W. Chen, "Robust Principal Component Analysis via Truncated l1,2 Minimization”, International Joint Conference on Neural Networks, IJCNN 2023, pages 1-19, Gold Coast, Australia, 2023.
D. Zhang, P. Wang, Y. Dong, L. Li, X. Li, “Joint fuzzy background and adaptive foreground model for moving target detection”, Frontiers in Computer Sciences, Volume 18, page 182306, 2024.
R. Xu, S. Feng, Y. Wei, H. Yan, "CUR and Generalized CUR Decompositions of Quaternion Matrices and their Applications", Numerical Functional Analysis and Optimization, February 2024.
J. Wen, D. Hu, T. Jia, Z. Wang, “A new method based on truncated reweighting nuclear norm to robust PCA”, International Journal of Intelligent Systems, 2024.
Z. Qin, L. Zhang, “Reweighted Quasi Norm Regularized Low-Rank Factorization for Matrix Robust PCA”, Preprint, March 2024.
W. Zhai, F. Zhang, “Robust Principal Component Analysis Integrating Sparse and Low-Rank Priors”, Journal of Computer and Communications, April 2024.
X. Liu, Y. Dou, J. Wang, “Modified correlated total variation regularization for low-rank matrix recovery”, Signal, Image and Video Processing, June 2024.
N. Shi, S. Fattahi, R. Kontar, "Triple Component Matrix Factorization: Untangling Global, Local, and Noisy Components” , Preprint, 2024.
K. Li, Y. Wen, X. Xia, M. Zhao, “Robust PCA Based on Adaptive Weighted Least Squares and Low-Rank Matrix Factorization”, Preprint, 2024.
Z. Lin, T. Liu, X. Ying, L. Wang, Y. Guo, "Total Variation Regularized RPCA for Moving Vehicle Detection in Satellite Videos”, Preprint, 2024.
Z. Cheng, J. Liang, M. Zhang, Z. Sun, H. So “Video Background Extraction and Moving Object Detection via Conceptual Beamforming Algorithms”, Digital Signal Processing, 2025.
Y. Mei, X. Feng, W. Wei, “An Efficient Random Low-Rank Sparse Decomposition Method”, SSRN 2025, 2025.
X. Chen, R. Wang, “The Masked Matrix Separation Problem: A First Analysis”, Preprint, April 2025.
L. Chen, L. Ge, X. Jiang, H. Li, "Boosting RPCA by Prior Subspace”, IEEE Transactions on Signal Processing, May 2025.
M. Wang, J. Gao, X. Jiang, C. Hu, Q. Feng, T. Wang, “Rescaled three-mode principal component analysis: An approach to subspace recovery”, Neural Networks, October 2025.
Compressive Sensing (29 papers)
A. Waters, A. Sankaranarayanan, R. Baraniuk, “SpaRCS: Recovering low-rank and sparse matrices from compressive measurements”, Neural Information Processing Systems, NIPS 2011, Granada, Spain, December 2011.
A. Waters, A. Sankaranarayanan, R. Baraniuk, “SpaRCS: Recovering low-rank and sparse matrices from compressive measurements”, Technical Report, 2011.
A. Kyrillidis, V. Cevher, “MATRIX ALPS: Accelerated Low Rank and Sparse Matrix Reconstruction”, 2012.
D. Zoonobi, A. Kassim, "Lowrank and Sparse Matrix Reconstruction with Partial Support Knowledge for Surveillance Video Processing", International Conference on Image Processing, ICIP 2013, Melbourne, Australia, September 2013.
L. Ramesh, P. Shah, “R-SpaRCS: An Algorithm for Foreground-Background Separation of Compressively-Sensed Surveillance Videos”, IEEE International Conference on Advanced Video and Signal based Surveillance, AVSS 2015, Karlsruhe, Germany, 2015.
F. Yang, H. Jiang, Z. Shen, W. Deng, D. Metaxas, “Adaptive low rank and sparse decomposition of video using compressive sensing”, IEEE International Conference on Image Processing, ICIP 2013, pages 1016-1020, September 2013.
H. Jiang, W. Deng, Z. Shen, “Surveillance Video Processing using Compressive Sensing”, Inverse Problems and Imaging, Volume 6, Issue 2, pages 201-214, 2012.
H. Jiang, S. Zhao, Z. Shen, W. Deng, P. Wilford, R. Cohen, “Surveillance Video Analysis Using Compressive Sensing with Low Latency”, 2014.
S. Li, H. Qi, “Recursive Low-rank and Sparse Recovery of Surveillance Video using Compressed Sensing”, International Conference on Distributed Smart Cameras, ICDSC 2014, 2014.
N. Shahid N. Perraudin, G. Puy, P. Vandergheynst, "Compressive PCA on Graphs", Preprint, 2016.
P. Pan, J. Feng, L. Chen, Y. Yang, "Online compressed robust PCA”, International Joint Conference on Neural Networks, IJCNN 2017, pages 1041-1048, Anchorage, AK, USA, 2017.
C. Wang, C. Li, J. Wang, "Two modified augmented Lagrange multiplier algorithms for Toeplitz matrix compressive recovery", Computers and Mathematics with Applications, 2017.
H. Luong, N. Deligiannis, J. Seiler, S. Forchhammer, A. Kaup, "Incorporating prior information in compressive online robust principal component analysis", IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017, November 2017.
S. Prativadibhayankaram, H. Luong, T. Le, A. Kaup, “Compressive Online Robust Principal Component Analysis with Optical Flow for Video Foreground-Background Separation”, Preprint, October 2017.
H. Luong, N. Deligiannis, S. Forchhammer, A. Kaup, “Online Decomposition of Compressive Streaming Data Using n-l1 Cluster-Weighted Minimization”, Data Compression Conference, 2018.
H. Luong, N. Deligiannis, S. Forchhammer, A. Kaup, “Compressive online decomposition of dynamic signals via n-l1Minimization with clustered priors”, IEEE Statistical Signal Processing Workshop, SSP 2018, Freiburg, Germany, June 2018.
S. Prativadibhayankaram, H. Luong, T. Le, A. Kaup, "Compressive Online Video Background–Foreground Separation using Multiple Prior Information and Optical Flow", MDPI Journal of Imaging, June 2018.
J. Wright, A. Ganesh, K. Min, Y. Ma, "Compressive Principal Component Pursuit", IEEE International Symposium on Information Theory, ISIT 2012, Cambridge, USA, pages 1276-1280, 2012.
C. Li, C. Wang, J. Wang, “Convergence analysis of the augmented Lagrange multiplier algorithm for a class of matrix compressive recovery”, Applied Mathematics Letters, 2016.
X. Li, J. Haupt, "Outlier identification via randomized adaptive compressive sampling”, IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2015, 2015.
X. Li, J. Haupt, "Identifying Outliers in Large Matrices via Randomized Adaptive Compressive Sampling”, IEEE Transactions on Signal Processing, Volume 63, no. 7, pages 1792-1807, April 2015.
B. Kang, W. Zhu, J. Yan, "Object detection oriented video reconstruction using compressed sensing", EURASIP Journal on Advances in Signal Processing Sample", February 2015.
B. Kang, W. Zhu, "Robust moving object detection using compressed sensing", IET Image Processing, 2015.
V. Hovhannisyan, Y. Panagakis, P. Parpas, S. Zafeiriou, “Fast Multilevel Algorithms for Compressive Principal Component Pursuit”, Preprint, April 2018.
Z. Xue, X. Yuan, Y. Yang, “Turbo-Type Message Passing Algorithms for Compressed Robust Principal Component Analysis”, IEEE Journal of Selected Topics in Signal Processing, December 2018.
J. Tanner, S. Vary, “Compressed sensing of low-rank plus sparse matrices”, Preprint, July 2020.
Z. Xue, X. Yuan, Y. Yang, "Denoising-based turbo message passing for compressed video background subtraction", IEEE Transactions on Image Processing, 2020.
S. Babu, N. Vaswani, “A Fast Algorithm for Low Rank+ Sparse column-wise Compressive Sensing”, Preprint, 2023.
Z. He, J. Ma, X. Yuan, “Improved Turbo Message Passing for Compressive Robust Principal Component Analysis: Algorithm Design and Asymptotic Analysis”, IEEE Transactions on Information Theory, 2024.
Validation of PCP (5 papers)
RPCA-PCP solved via APG (1 paper)
Y. Wang, Y. Liu, L.Wu, "Study on background modeling method based on Robust Principal Component Analysis", Annual Conference on Electrical and Control Enginneering, ICECE 2011, pages 6787-6790, September 2011.
RPCA solved via IALM (2 papers)
Y. Xue, Y. Gu, X. Cao, "Motion Saliency using Low-rank and Sparse Decomposition", ICASSP 2012, March 2012.
M. Yang, "Background Modeling from Surveillance Video using Rank Minimization", Artificial Intelligence and Computational Intelligence, AICI 2102, pages 769-774, 2012.
RPCA-PCP solved via LADMAP (1 paper)
C. Guyon, T. Bouwmans, E. Zahzah, "Foreground Detection by Robust PCA solved via a Linearized Alternating Direction Method", International Conference on Image Analysis and Recognition, ICIAR 2012, pages 115-122, Aveiro, Portugal, June 2012.
RPCA-PCP solved via LSADM (1 paper)
C. Guyon, T. Bouwmans, E. Zahzah, “Moving Object Detection by Robust PCA solved via a Linearized Symmetric Alternating Direction Method”, International Symposium on Visual Computing, ISVC 2012, pages 427-436, Rethymnon, Crete, Greece, July 2012.