Fast Convex Optimization Algorithms for Exact Recovery of a Corrupted Low-Rank Matrix

By Zhouchen Lin, Arvind Ganesh, John Wright, Leqin Wu, Minming Chen, Yi Ma. 2009

531 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/a671f862adc5f9d86e8d5f1380b29e38c89865c9

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Citations in the corpus

Sparse Bayesian Methods for Low-Rank Matrix Estimation (2011, methodology): “[35] proposed accelerated proximal gradient (APG) methods which are faster and generally more accurate.”
Weighted Nuclear Norm Minimization and Its Applications to Low Level Vision (2016, methodology): “The recent advancement of NNM in applications such as RPCA andMC (Lin et al. 2009; Ji and Ye 2009; Cai et al. 2010; Lin et al. 2011) has been successfully utilized inmany computer vision tasks (Ji et al.”
Visual Domain Adaptation: A survey of recent advances (2015, methodology): “However, efficient methods do exist for finding low-rank approximation of large matrices [98], [99], [100].”
Recovering Low-Rank and Sparse Components of Matrices from Incomplete and Noisy Observations (2011, methodology): “, the iterative thresholding algorithm [54]; the accelerated proximal gradient algorithm in [40], and the alternating direction method proposed almost simultaneously and independently in [39, 59].”
Fast global convergence rates of gradient methods for high-dimensional statistical recovery (2010, background): “, [3, 7, 6, 5, 12, 18]) focuses on polynomial-time algorithms for solving these types of convex programs.”
Traditional and recent approaches in background modeling for foreground detection: An overview (2014, methodology): “[215] compare RPCA-PCP solved Exact ALM [165], BRPCA [78] and GoDec [326].”
Attention-Guided Pyramid Context Networks for Detecting Infrared Small Target Under Complex Background (2023, background): “…system-based approaches assume that the saliency of a target is only re-lated to the local contrast of its surroundings [9], [10], [11], [12]; 3) optimization-based approaches transform the target detection task into a sparse low-rank tensor decomposition problem [13], [14], [15], [16], [17], [18].”
Online Robust PCA via Stochastic Optimization (2013, methodology): “To solve the problem in (1), iterative optimization methods such as Accelerated Proximal Gradient (APG) [15] or Augmented Lagrangian Multiplier (ALM) [14] methods are often used.”
A unified framework for high-dimensional analysis of $M$-estimators with decomposable regularizers (2009, background): “is a special case of our general estimator (1). From the computational perspective, it is an instance of a semideﬁnite program [79], and there are a number of eﬃcient algorithms for solving it (e.g., [9, 41, 45, 55, 56]). Let us consider some examples to illustrate applications covered by the model ”
Infrared Patch-Image Model for Small Target Detection in a Single Image (2013, methodology): “The solution via APG is described in Algorithm 1 (for details please see [43]), where V t is the transpose of the matrix V and S ε [·] is a soft-thresholding operator [44]: where x ∈ R and ε > 0.”
Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization (2014, methodology): “In fact, two other codes, the dual algorithms in [33] and the exact augmented Lagrangian method in [32], were also tested.”
Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery (2018, methodology): “To speed up computation, Lin et al. proposed the accelerated proximal gradient (APG) [37] and the augmented Lagrangian multiplier (ALM) [36] methods.”
Large Covariance Estimation by Thresholding Principal Orthogonal Complements (2011, unknown): “…methods that address low-rank plus sparse covariance estimation, specifically, LOREC proposed by Luo (2012), the strict factor model (SFM) by Fan, Fan and Lv (2008), the Dual Method (Dual) by Lin et al. (2009), and finally, the singular value thresholding (SVT) by Cai, Candès and Shen (2008).”
Hyperspectral Image Restoration Using Low-Rank Matrix Recovery (2014, unknown): “[31] developed and compared two complementary approaches for solving model (2).”
Stable Principal Component Pursuit (2010, methodology): “Since this convex program can be solved very efficiently [ 6 ], at a cost not so much higher than the classical PCA, our result is expected to have significant impact on many practical problems.”
Decomposition into Low-rank plus Additive Matrices for Background/Foreground Separation: A Review for a Comparative Evaluation with a Large-Scale Dataset (2015, methodology): “The first algorithm is called Exact ALM (EALM) method that has a Q-linear convergence speed, while the APG is in theory only sub-linear.”
Value function approximation via low-rank models (2015, methodology): “The ALM algorithm was implemented by the authors of [22] on a single thread in MATLAB and C, which interacted with MATLAB through a MEX interface [27].”
Fast global convergence of gradient methods for high-dimensional statistical recovery (2011, background): “, [3, 7, 6, 5, 12, 18]) focuses on polynomial-time algorithms for solving these types of convex programs.”