CANCELLED: Numerica Corp Technical Seminar: Detecting Weak Distributed Patterns in Sensor Networks
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Compressed Sensing allows for perfect recovery of a sparse signal from very few measurements. The key idea is that finding the L1-minimizing solution also recovers the sparsest solution. This L1-minimizing approach has been extended to the problem of matrix completion which allows for perfect recovery of a low rank matrix from only a few observations of its entries (motivated by the Netflix Prize, for example). More recently, Candes et. al. have used L1 methods to perform robust principal component analysis where a low-rank matrix is recovered from partial observations that include sparse corruptions of arbitrarily large size. We present an algorithm for performing robust principal component analysis in the presence of large sparse errors and dense noise. Motivating applications of the algorithm include detection of anomalous behavior on sensor networks (the Internet, for example), increasing the resolution of low-resolution cameras, face recognition, analysis of surveillance video, cyber security, and compression of high-resolution geographic data.
Philip du Toit, Ph.D., is a research scientist at Numerica Corporation in Loveland, Colorado working on the design of fuel-efficient trajectories for space vehicles, detection of patterns and anomalies on sensor networks, L1 methods for producing high-resolution images from low-resolution cameras, and various tracking and nonlinear filtering problems. In 2009, Philip received his Ph.D. in Control and Dynamical Systems from the California Institute of Technology as a student of Dr. Jerry Marsden. In his thesis research, he studied coherent structures in aperiodic flows with specific application to oceanic and atmospheric flows. During his doctoral research, he also studied optimal design of search strategies for under-actuated vehicles, optimal design of particle interactions for the purpose of self-assembly, and particle methods for computing solutions to geometry-preserving PDEs. Philip also received his M.S. Degree in Applied Math from the University of Michigan through the Applied and Inter-disciplinary Math Program.
Ph.D. – Control and Dynamical Systems, California Institute of Technology
M.S. – Applied Mathematics, University of Michigan, Ann Arbor
B.S. – Physics with University Honors, Brigham Young University