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Seminar Abstract
We present a simple technique for estimating parts of the Singular
Value Decomposition (SVD) of a data matrix from a small randomly
compressed "sketch" of that matrix. In sensor network settings--where
each column of the data matrix comes from a separate sensor--the
sketch can be assembled using operations local to each sensor. As an application of this work, we consider the problem of Structural Health Monitoring (SHM). SHM systems are critical for monitoring aging infrastructure (such as buildings or bridges) in a cost-effective manner. Such systems typically involve collections of battery-operated wireless sensors that sample vibration data over time. After the data is transmitted to a central node, modal analysis can be used to detect damage in the structure. We propose and study three frameworks for Compressive Sensing (CS) in SHM systems; these methods are intended to minimize power consumption by allowing the data to be sampled and/or transmitted more efficiently. At the central node, all of these frameworks involve a very simple technique for estimating the structure's mode shapes without requiring a traditional CS reconstruction of the vibration signals; all that is needed is to compute a simple SVD. We support our proposed techniques theoretically and using simulations based on synthetic and real data. This project is joint work with Anna Gilbert and Jae Young Park.
Speaker Bio
Michael B. Wakin received a B.S. in electrical engineering and a B.A.
in mathematics in 2000 (summa cum laude), an M.S. in electrical
engineering in 2002, and a Ph.D. in electrical engineering in 2007,
all from Rice University. He was an NSF Mathematical Sciences
Postdoctoral Research Fellow at Caltech from 2006-2007 and an
Assistant Professor at the University of Michigan from 2007-2008. He
is now an Associate Professor in the Department of Electrical
Engineering and Computer Science at the Colorado School of Mines
(CSM). His research interests include sparse, geometric, and
manifold-based models for signal processing and compressive sensing.
In 2007, Dr. Wakin shared the Hershel M. Rich Invention Award from
Rice University for the design of a single-pixel camera based on
compressive sensing; in 2008, Dr. Wakin received the DARPA Young
Faculty Award for his research in compressive multi-signal processing
for environments such as sensor and camera networks; in 2012, Dr.
Wakin received the NSF CAREER Award for research into dimensionality reduction techniques for structured data sets; and in 2014, Dr. Wakin received the Excellence in Research Award for his research as a junior faculty member at CSM. Dr. Wakin is an Associate Editor for IEEE Signal Processing Letters.
