EE Systems Seminar

Friday February 6, 2015 3:00 PM

Online Robust PCA or Online Sparse + Low-Rank Matrix Recovery

Speaker: Namrata Vaswani, ECE, Iowa State University
Location: Moore 239

This work studies the problem of sequentially recovering a sparse vector x_t and a vector from a low-dimensional subspace l_t from knowledge of their sum m_t:=x_t+l_t. If the primary goal is to recover the low-dimensional subspace in which the l_t's lie, then the problem is one of online or recursive robust principal components analysis (PCA). An example of where such a problem might arise is in separating a sparse foreground and a slowly changing dense background in a surveillance video. We develop a novel algorithm called ReProCS to solve this problem and demonstrate its significant advantage over other robust PCA based methods for this video layering problem.

We prove that  if a good estimate of the initial subspace is available (easy to obtain using a short sequence of background-only frames in video surveillance); the l_t's obey certain denseness and slow subspace change assumptions; and the support of x_t changes by at least a certain amount at least every so often, then with high probability, the support of x_t will be recovered exactly. Also, the error made in estimating x_t and l_t will be small and the subspace recovery error will decay to a small value within a short delay of a subspace change time. To the best of our knowledge, this is the first complete correctness result for online robust PCA or equivalently for online sparse plus low-rank recovery.  (based on joint work with Cheniu Qiu and Brian Lois)

Namrata Vaswani received a B.Tech. from Indian Institute of Technology (IIT), Delhi, in 1999 and a Ph.D. from University of Maryland, College Park, in 2004, both in Electrical Engineering. During 2004-05, she was a research scientist at Georgia Tech. Since Fall 2005, she has been with the Iowa State University where she is currently an Associate Professor of Electrical and Computer Engineering. She has held the Harpole-Pentair Assistant Professorship at Iowa State during 2008-09. During 2009 to 2013, she served as an Associate Editor for IEEE Transactions on Signal Processing. She is the recipient of the 2014 Iowa State Early Career Engineering Faculty Research Award and the 2014 IEEE Signal Processing Society Best Paper Award for her Modified-CS paper (jointly with her former graduate student Wei Lu).

Vaswani's research interests lie at the intersection of signal and information processing and machine learning for high dimensional problems. She also works on applications in video and big-data analytics and in bio-imaging. In the last several years her work has focused on developing provably accurate online algorithms for various high-dimensional structured data recovery problems such as online sparse matrix recovery (recursive recovery of sparse vector sequences) or dynamic compressed sensing, online robust principal components' analysis (PCA) and online matrix completion; and on demonstrating their usefulness in dynamic magnetic resonance imaging (MRI) and video analytics.

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