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three_fundamental_measures_of_geometry_and_their_role_in_model_selection_and_sparse_inverse_problems

Three fundamental measures of geometry and their role in model selection and sparse inverse problems

Waheed U. Bajwa, Duke University
Friday Sept 24th. 2010
2:30pm
EEB 248
Note the atypical time and day

Abstract:

In this talk, I discuss three measures of matrix geometry, namely, worst-case coherence, average coherence, and spectral norm, in the context of model selection and sparse inverse problems. These geometric measures are a better alternative to related measures such as the oft-studied restricted isometry property, since they can be explicitly computed in polynomial time. In this talk, I introduce a simple algorithm, termed one-step thresholding (OST) algorithm, and utilize the introduced geometric measures to provide an in-depth analysis of OST for both model selection and recovery of sparse signals. In particular, I show that OST has the ability to perform near-optimally for a number of generic (random or deterministic) matrices. In addition, I also talk about explicitly designing matrices with small average coherence, which is the key to guaranteeing that algorithms such as OST succeed.

Biography:

Waheed U. Bajwa received BE (with Honors) degree in electrical engineering from the National University of Sciences and Technology, Islamabad, Pakistan in 2001, and MS and PhD degrees in electrical engineering from the University of Wisconsin-Madison, Madison, WI in 2005 and 2009, respectively. He was a Postdoctoral Research Associate in the Program in Applied and Computational Mathematics at Princeton University, Princeton, NJ from 2009 to 2010. He is currently a Research Scientist in the Department of Electrical and Computer Engineering at Duke University, Durham, NC. His research interests include high-dimensional inference and inverse problems, statistical signal processing, wireless communications, and applications in biological sciences, networked systems, and radar & image processing.

Dr. Bajwa was affiliated with Communications Enabling Technologies, Islamabad, Pakistan - the research arm of Avaz Networks Inc., Irvine, CA (now Quartics LLC) - from 2000-2003, with the Center for Advanced Research in Engineering, Islamabad, Pakistan during 2003, and with the RF and Photonics Lab of GE Global Research, Niskayuna, NY during the summer of 2006. He received the Best in Academics Gold Medal and President's Gold Medal in Electrical Engineering from the National University of Sciences and Technology (NUST) in 2001, and the Morgridge Distinguished Graduate Fellowship from the University of Wisconsin-Madison in 2003. He was Junior NUST Student of the Year (2000), Wisconsin Union Poker Series Champion (Spring 2008), and President of the University of Wisconsin-Madison chapter of Golden Key International Honor Society (2009). He currently serves as a Guest Associate Editor for Elsevier Physical Communication Journal and is a member of the IEEE, Pakistan Engineering Council, and Golden Key International Honor Society.

Host: Urbashi Mitra, ubli [at] usc.edu

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