NDLI: Real-time Robust Principal Components' Pursuit

Content Provider	IEEE Xplore Digital Library
Author	Chenlu Qiu Vaswani, N.
Copyright Year	2010
Description	Author affiliation: Dept. of Electrical and Computer Engineering, Iowa State University, Ames, 50010, USA (Chenlu Qiu; Vaswani, N.)
Abstract	In the recent work of Candes et al, the problem of recovering low rank matrix corrupted by i.i.d. sparse outliers is studied and a very elegant solution, principal component pursuit, is proposed. It is motivated as a tool for video surveillance applications with the background image sequence forming the low rank part and the moving objects/persons/abnormalities forming the sparse part. Each image frame is treated as a column vector of the data matrix made up of a low rank matrix and a sparse corruption matrix. Principal component pursuit solves the problem under the assumptions that the singular vectors of the low rank matrix are spread out and the sparsity pattern of the sparse matrix is uniformly random. However, in practice, usually the sparsity pattern and the signal values of the sparse part (moving persons/objects) change in a correlated fashion over time, for e.g., the object moves slowly and/or with roughly constant velocity. This will often result in a low rank sparse matrix. For video surveillance applications, it would be much more useful to have a real-time solution. In this work, we study the online version of the above problem and propose a solution that automatically handles correlated sparse outliers. In fact we also discuss how we can potentially use the correlation to our advantage in future work. The key idea of this work is as follows. Given an initial estimate of the principal directions of the low rank part, we causally keep estimating the sparse part at each time by solving a noisy compressive sensing type problem. The principal directions of the low rank part are updated every-so-often. In between two update times, if new Principal Components' directions appear, the “noise” seen by the Compressive Sensing step may increase. This problem is solved, in part, by utilizing the time correlation model of the low rank part. We call the proposed solution “Real-time Robust Principal Components' Pursuit”. It still requires the singular vectors of the low rank part to be spread out, but it does not require i.i.d.-ness of either the sparse part or the low rank part.
Starting Page	591
Ending Page	598
File Size	598035
Page Count	8
File Format	PDF
ISBN	9781424482153
e-ISBN	9781424482160
DOI	10.1109/ALLERTON.2010.5706961
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-09-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Real time systems Noise Eigenvalues and eigenfunctions Robustness Covariance matrix Sparse matrices Pixel
Content Type	Text
Resource Type	Article

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