NDLI: Performance guarantees for ReProCS - Correlated low-rank matrix entries case

Content Provider	IEEE Xplore Digital Library
Author	Jinchun Zhan Vaswani, N. Chenlu Qiu
Copyright Year	2014
Description	Author affiliation: Dept. of Electr. & Comput. Eng, Iowa State Univ., Ames, IA, USA (Jinchun Zhan; Vaswani, N.) \|\| Traffic Manage. Res. Inst., Minist. of Public Security, Beijing, China (Chenlu Qiu)
Abstract	Online or recursive robust PCA can be posed as a problem of recovering a sparse vector, $S_{t},$ and a dense vector, $L_{t},$ which lies in a slowly changing low-dimensional subspace, from $M_{t}$ := $S_{t}+L_{t}$ on-the-fly as new data comes in. For initialization, it is assumed that an accurate knowledge of the subspace in which $L_{0}$ lies is available. In recent works, Qiu et al proposed and analyzed a novel solution to this problem called recursive projected compressed sensing or ReProCS. In this work, we relax one limiting assumption of Qiu et al's result. Their work required that the $L_{t}'s$ be mutually independent over time. However this is not a practical assumption, e.g., in the video application, $L_{t}$ is the background image sequence and one would expect it to be correlated over time. In this work we relax this and allow the $L_{t}'s$ to follow an autoregressive model. We are able to show that under mild assumptions and under a denseness assumption on the unestimated part of the changed subspace, with high probability (w.h.p.), ReProCS can exactly recover the support set of $S_{t}$ at all times; the reconstruction errors of both $S_{t}$ and $L_{t}$ are upper bounded by a time invariant and small value; and the subspace recovery error decays to a small value within a finite delay of a subspace change time.
Starting Page	2187
Ending Page	2191
File Size	679894
Page Count	5
File Format	PDF
ISBN	9781479951864
ISSN	21578117
DOI	10.1109/ISIT.2014.6875221
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-06-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Principal component analysis Robustness Integrated circuits Computer vision
Content Type	Text
Resource Type	Article

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