简介: |
Abstract:
We will start by giving a high-level overview of the fundamental results in the field that has come to be known as compressive sensing. The central theme of this body of work is that underdetermined systems of linear equations can be meaningfully "inverted" if they have structured solutions. Two examples of structure would be if the unknown entity is a vector which is sparse (has only a few "active" entries) or if it is a matrix which is low rank. We discuss some of the applications of this theory in signal processing and statistics.
In the second part of the talk, we will show how some of these structured recovery results give us new insights into solving systems of quadratic and bilinear equations. In particular, we consider the general problem of blind deconvolution: we observe the convolution of two vectors, and show how making some mild structural assumptions about these signals allows us to recover them by solving a convex program.
References:
* A. Ahmed, B. Recht, and J. Romberg, Blind Deconvolution using Convex Programming, arXiv:1211.5608
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. In the Fall of 2006, he joined the Georgia Tech ECE faculty. In 2008 he received an ONR Young Investigator Award, in 2009 he received a PECASE award and a Packard Fellowship, in 2010 he was named a Rice University Outstanding Young Engineering Alumnus, and in 2013 he received an SPIE Pioneer Award. He is currently on the editorial board for the SIAM Journal on Imaging Science. |
