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

Mon., April 7, 2014

3:00 - 4:00 PM

521 Cory Hall (Hogan Room)

3:00 - 4:00 PM

521 Cory Hall (Hogan Room)

Abstract:

Successful high-resolution signal reconstruction -- in problems ranging from astronomy to biology to medical imaging -- depends crucially 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.

Biography: Galen Reeves joined the faculty at Duke University in Fall 2013, and is currently an Assistant Professor with a joint appointment in the Department of Electrical \& Computer Engineering and the Department of Statistical Science. He completed his PhD in Electrical Engineering and Computer Sciences at the University of California, Berkeley in 2011. From 2011 to 2013 he was a postdoctoral associate in the Departments of Statistics at Stanford University, where he was supported by an NSF VIGRE fellowship. In the summer of 2011, he was a postdoctoral researcher in the School of Computer and Communication Sciences at EPFL, Switzerland; in the spring of 2009, he was a visiting scholar at the Technical University of Delft, The Netherlands; and in the summer of 2008, he was a research intern in the Networked Embedded Computing Group at Microsoft Research, Redmond. He received his MS in Electrical Engineering from UC Berkeley in 2007, and BS in Electrical and Computer Engineering from Cornell University in 2005.

Successful high-resolution signal reconstruction -- in problems ranging from astronomy to biology to medical imaging -- depends crucially 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.

Biography: Galen Reeves joined the faculty at Duke University in Fall 2013, and is currently an Assistant Professor with a joint appointment in the Department of Electrical \& Computer Engineering and the Department of Statistical Science. He completed his PhD in Electrical Engineering and Computer Sciences at the University of California, Berkeley in 2011. From 2011 to 2013 he was a postdoctoral associate in the Departments of Statistics at Stanford University, where he was supported by an NSF VIGRE fellowship. In the summer of 2011, he was a postdoctoral researcher in the School of Computer and Communication Sciences at EPFL, Switzerland; in the spring of 2009, he was a visiting scholar at the Technical University of Delft, The Netherlands; and in the summer of 2008, he was a research intern in the Networked Embedded Computing Group at Microsoft Research, Redmond. He received his MS in Electrical Engineering from UC Berkeley in 2007, and BS in Electrical and Computer Engineering from Cornell University in 2005.