Matrix Recovery from Measurements with Structured Randomness

ECE Seminar: Matrix Recovery from Measurements with Structured Randomness


Starts at: March 21, 2013 4:30 PM

Ends at: 5:30 PM

Location: Scaife Hall Auditorium Room 125 at 4:30 p.m. Refreshments at 4:00 p.m.

Speaker: Justin Romberg

Affiliation: Associate Professor, School of Electrical & Computer Engineering, Georgia Institute of Technology

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Abstract
The past decade has seen tremendous progress in our understanding of recovering structured signals (e.g. sparse vectors or low rank matrices) from underdetermined measurements. In this talk, we will show how two problems can be recast as low-rank matrix recovery problems and then solved using convex programming. The corresponding systems of equations in each case have random aspects to them, but exhibit structure imposed by the way the problem is recast. The first problem we will look at is blind deconvolution: we observe the convolution of two vectors, and want to untangle them. We show that if the length L vectors are known to live in known subspaces of N and K, then under some assumptions on these subspaces we can deconvolve them when L ~ N + K to within a logarithmic factor. The second topic we will discuss is compressive sampling of ensembles of signals which have latent correlation structure. We will show that even if this structure is unknown, the signals can be dramatically undersampled if they randomly ``pre-coded'' using simple analog computations.

Bio
Dr. Justin Romberg is an Associate Professor in the School of Electrical and Computer Engineering at the Georgia Institute of Technology. Dr. Romberg received the B.S.E.E. (1997), M.S. (1999) and Ph.D. (2004) degrees from Rice University in Houston, Texas. From Fall 2003 until Fall 2006, he was a Postdoctoral Scholar in Applied and Computational Mathematics at the California Institute of Technology. He spent the summer of 2000 as a researcher at Xerox PARC, the fall of 2003 as a visitor at the Laboratoire Jacques-Louis Lions in Paris, and the fall of 2004 as a Fellow at UCLA's Institute for Pure and Applied Mathematics. In the fall of 2006, he joined the ECE faculty as a member of the Center for Signal and Image Processing. In 2008 he received an ONR Young Investigator Award, in 2009 he received a PECASE award and a Packard Fellowship, and in 2010 he was named a Rice University Outstanding Young Engineering Alumnus. In 2006-2007 he was a consultant for the TV show "Numb3rs" and from 2008-2011, he was an Associate Editor for the IEEE Transactions on Information Theory.