Efficient algorithms for robust and stable principal component pursuit problems

The problem of recovering a low-rank matrix from a set of observations corrupted with gross sparse error is known as the robust principal component analysis (RPCA) and has many applications in computer vision, image processing and web data ranking. It has been shown that under certain conditions, th...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 58; no. 1; pp. 1 - 29
Main Authors: Aybat, Necdet Serhat, Goldfarb, Donald, Ma, Shiqian
Format: Journal Article
Language:English
Published: Boston Springer US 01.05.2014
Springer Nature B.V
Subjects:
Algorithms
Analysis
Convex analysis
Convex and Discrete Geometry
Data smoothing
Extraction
Image processing
Industrial engineering
Management Science
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Noise reduction
Operations Research
Operations Research/Decision Theory
Optimization
Principal component analysis
Principal components analysis
Sparsity
Statistics
Studies
Surveillance
Iteration complexity
Convex optimization
Smoothing
Alternating direction augmented Lagrangian method
Alternating linearization method
Accelerated proximal gradient method
Compressed sensing
Principal component analysis
Matrix completion
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary:The problem of recovering a low-rank matrix from a set of observations corrupted with gross sparse error is known as the robust principal component analysis (RPCA) and has many applications in computer vision, image processing and web data ranking. It has been shown that under certain conditions, the solution to the NP-hard RPCA problem can be obtained by solving a convex optimization problem, namely the robust principal component pursuit (RPCP). Moreover, if the observed data matrix has also been corrupted by a dense noise matrix in addition to gross sparse error, then the stable principal component pursuit (SPCP) problem is solved to recover the low-rank matrix. In this paper, we develop efficient algorithms with provable iteration complexity bounds for solving RPCP and SPCP. Numerical results on problems with millions of variables and constraints such as foreground extraction from surveillance video, shadow and specularity removal from face images and video denoising from heavily corrupted data show that our algorithms are competitive to current state-of-the-art solvers for RPCP and SPCP in terms of accuracy and speed.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-013-9613-0