Interdisciplinary Distinguished Lecturer: Dr. Galen Reeves

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Robust compressed sensing: How undersampling introduces noise and what we can do about it

Dr. Galen Reeves, Assistant Professor, Department of Electrical & Computer Engineering and the Department of Statistical Science
Duke University

Dr. Galen Reeves spoke on Friday, October 18th, 2013 at 1:00PM in Engineering Building II, Room 1230

Successful high-resolution signal reconstruction -- in problems ranging from astronomy to biology to medical imaging -- depends crucially upon our ability to make the most out of indirect, incomplete, and inaccurate data. A large and active area of research, known as compressed sensing, has drawn researchers from applied mathematics, information theory, mathematical statistics, and optimization theory to focus on the design and analysis of computational reconstruction methods. These methods take advantage of low dimensional structure inherent in the data (e.g. sparsity, low rank) to overcome that fact that the number of unknowns may far exceed the number of knowns.

In this talk, I will explain a key theoretical insight about signal recovery from undersampled data: In many cases, the effect on the end user is the same as if each component of the unknown signal had been observed directly after being corrupted by independent random noise. Using this insight as a guiding principle, I will then show how we can give precise answers to a variety of key engineering questions concerning the relaxation of model assumptions, the minimax sensitivity to noise, and the design of near-optimal adaptive strategies which learn the statistics of the underlying data.