Journal of Applied Mathematics
Volume 2013 (2013), Article ID 959403, 6 pages
http://dx.doi.org/10.1155/2013/959403
Research Article

Restricted Isometry Property of Principal Component Pursuit with Reduced Linear Measurements

Qingshan You,1,2 Qun Wan,2 and Haiwen Xu1

1School of Computer Science, Civil Aviation Flight University of China, GuangHan, Sichuan 618307, China
2School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China

Received 25 September 2012; Revised 2 April 2013; Accepted 30 April 2013

Academic Editor: Xiaojun Wang

Copyright © 2013 Qingshan You et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The principal component prsuit with reduced linear measurements (PCP_RLM) has gained great attention in applications, such as machine learning, video, and aligning multiple images. The recent research shows that strongly convex optimization for compressive principal component pursuit can guarantee the exact low-rank matrix recovery and sparse matrix recovery as well. In this paper, we prove that the operator of PCP_RLM satisfies restricted isometry property (RIP) with high probability. In addition, we derive the bound of parameters depending only on observed quantities based on RIP property, which will guide us how to choose suitable parameters in strongly convex programming.