Efficient algorithms for robust and stable principal component pursuit problems

Necdet Serhat Aybat, Donald Goldfarb, Shiqian Ma

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1-29
Number of pages29
JournalComputational Optimization and Applications
Volume58
Issue number1
DOIs
StatePublished - May 2014

Fingerprint

Pursuit
Principal Components
Efficient Algorithms
Principal component analysis
Low-rank Matrices
Gross
Principal Component Analysis
Convex optimization
Computer vision
Image processing
Video Surveillance
Denoising
Convex Optimization
Computer Vision
Image Processing
Ranking
NP-complete problem
Face
Optimization Problem
Iteration

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Computational Mathematics
  • Applied Mathematics

Cite this

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Efficient algorithms for robust and stable principal component pursuit problems. / Aybat, Necdet Serhat; Goldfarb, Donald; Ma, Shiqian.

In: Computational Optimization and Applications, Vol. 58, No. 1, 05.2014, p. 1-29.

Research output: Contribution to journalArticle

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