Z. Zhou, X. Li, J. Wright, E. Candes, Y. Ma, “Stable Principal Component Pursuit”, IEEE ISIT, pages 1518-1522, June 2010.
Algorithms for solving SPCP (23 papers)
M. Tao, X. Yuan “Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations”, SIAM Journal on Optimization Volume 21,Issue 1, pages 57-81, 2011.
N. Aybat, D. Goldfarb, G. Iyengar, “Fast First-Order Methods for Stable Principal Component Pursuit”, Preprint 2011.
N. Aybat, D. Goldfarb, G. Iyengar, “Efficient Algorithms for Robust and Stable Principal Component Pursuit”, Preprint 2012.
N. Aybat, G. Iyengar, "A Unified Approach for Minimizing Composite Norms", Preprint, August 2012
N. Aybat, G. Iyenga, "An Alternating Direction Method with Increasing Penalty for Stable Principal Component Pursuit", Computational Optimization and Applications, 2014.
T. Zhou, D. Tao, "Greedy Bilateral Sketch, Completion and Smoothing for large-scale matrix completion, robust PCA and low-rank approximation", International Conference on Artificial Intelligence and Statistics, AISTATS 2013, 2013
J. Parker, P. Schniter, “Bilinear Generalized Approximate Message Passing (BiG-AMP) for Matrix Completion”, Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, November 2012.
J. Parker, P. Schniter, V. Cevher, “Bilinear Generalized Approximate Message Passing”, Preprint, October 2013
J. Parker, P. Schniter, V. Cevher, “Bilinear Generalized Approximate Message Passing-Part I: Derivation”, IEEE Transactions on Signal Processing, Volume 62, No. 22, pages 5839-5853, November 2014.
J. Parker, P. Schniter, V. Cevher, “Bilinear Generalized Approximate Message Passing-Part II: Applications”, IEEE Transactions on Signal Processing, Volume 62, No. 22, pages 5854-5867, November 2014.
J. Parker, “Approximate Message Passing Algorithms for Generalized Bilinear Inference”, Thesis, Ohio State University, 2014.
M. Hintermüller, T. Wu, “Robust Principal Component Pursuit via Inexact Alternating Minimization on Matrix Manifolds”, Journal of Mathematics and Imaging Vision, 2014.
K. Huai, M. Ni, F. Ma, Z. Yu, "A customized proximal point algorithm for stable principal component pursuit with nonnegative constraint", Journal of Inequalities and Applications, pages 148, 2015.
F. Wang, W. Cao, Z. Xu, “Convergence of multi-block Bregman ADMM for nonconvex composite problems”, Preprint, May 2015.
L. Hou, H. He, J. Yang, “A partially parallel splitting method for multiple-block separable convex programming with applications to robust PCA”, Computational Optimization and Applications, June 2015.
D. Cheng, J. Yang, J. Wang, D. Shi, X. Liu, “Double-noise-dual-problem approach to the augmented Lagrange multiplier method for robust principal component analysis”, Soft Computing, December 2015.
J. Mao, Z. Zhang, “A local convex method for rank-sparsity factorization”, Pattern Recognition Letters, pages 31-37, Volume 71, February 2016.
H. He, D. Han, “A distributed Douglas-Rachford splitting method for multi-block convex minimization problems”, Advances in Computational Mathematics, Volume 42, pages 27–53, 2016.
J. Wang, W. Song, "An algorithm twisted from generalized ADMM for multi-block separable convex minimization models", Journal of Computational and Applied Mathematics, 2016.
A. Aravkin and S. Becker, "Dual Smoothing and Level Set Techniques for Variational Matrix Decomposition", Preprint, 2016.
K. Huai, M. Ni, Z. Yu, X. Zheng, F. Ma, "A generalized inexact Uzawa method for stable principal component pursuit problem with nonnegative constraints", Numerical Algorithms, pages 1-22, 2017.
M. Sun and H. Sun and Y. Wang, "Two proximal splitting methods for multi-block separable programming with applications to stable principal component pursuit", Journal of Applied Mathematics and Computing, pages 1-28, 2017.
Y. Chen, J. Fan, C. Ma, Y. Ya, “Bridging Convex and Nonconvex Optimization in Robust PCA: Noise, Outliers, and Missing Data”, 2020.
Incremental SPCP (2 papers)
P. Sprechmann, A. Bronstein, G. Sapiro, “Learning Robust Low-Rank Representations”, Optimization and Control, 2012.
H. Yang , S. Qu, "Real-time vehicle detection and counting in complex traffic scenes using background subtraction model with low-rank decomposition”, IET Intelligent Transport Systems, Volume 12, No. 1, pages 75-85, 2018.
Spatio-temporal SPCP (1 paper)
H. Yang , S. Qu, "Real-time vehicle detection and counting in complex traffic scenes using background subtraction model with low-rank decomposition”, IET Intelligent Transport Systems, Volume 12, No. 1, pages 75-85, 2018.
Real time implementation of SPCP (2 papers)
L. Mackey, A. Talwalkar, M. Jordan, “Divide-and-Conquer Matrix Factorization”, Neural Information Processing Systems, Neural Information Processing Systems, NIPS 2011, Granada, Spain, December 2011.
S. Kumar, M. Mohri, A. Talwalkar, "Ensemble Nyström method", Annual Conference on Neural Information Processing Systems, NIPS 2009, 2009.
Compressive Sensing (3 papers)
C. Mu, Y. Zhang, J. Wright, D. Goldfarb, "Scalable Robust Matrix Recovery: Frank-Wolfe Meets Proximal Methods", Preprint, 2014.
X. Li, J. Haupt, “Robust Low-Complexity Methods for Matrix Column Outlier Identification”, Preprint, 2017.
X. Li, J. Haupt, “Robust Low-Complexity Randomized Methods for Locating Outliers in Large Matrices”, Preprint, 2017.
Modified SPCP (9 papers)
T. Zhou, D. Tao, "Greedy Bilateral Sketch, Completion and Smoothing for large-scale matrix completion, robust PCA and low-rank approximation", AISTATS 2013, 2013.
X. Yuan, “Nuclear-norm-free Variational Models for Background Extraction from Surveillance Video”, Cross-straits Optimization Workshop, COW 2013, Taipei, Taiwan, March 2013.
P. Sprechmann, A. Bronstein, G. Sapiro, “Learning Robust Low-Rank Representations”, Optimization and Control, 2012.
A. Aravkin, S. Becker, V. Cevher, P. Olsen, "A variational approach to stable principal component pursuit", Preprint, June 2014.
O. Oreifej, X. Li, M. Shah, "Simultaneous Video Stabilization and Moving Object Detection in Turbulence", IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012.
F. Zhang, M. Jin, Y. Chen, “Tri-decomposition model for image recovery”, Electronics Letters, Volume 54, No. 23, September 2018.
L. Yin, A. Parekh, I. Selesnick, "Stable Principal Component Pursuit via Convex Analysis”, IEEE Transactions on Signal Processing, 2019.
J. Zhang, J. Yan, J. Wright, “Square Root Principal Component Pursuit: Tuning-Free Noisy Robust Matrix Recovery”, Conference on Neural Information Processing Systems, NeurIPS 2021, 2021.
J. Peng, H. Wang, X. Cao, X. Jia, H. Zhang, D. Meng, "Stable Local-Smooth Principal Component Pursuit", SIAM Journal on Imaging Sciences, Volume 17, No. 2, pages 1182-1205, June 2024.