September 5, 2013
Hosted by: Prof. John Wright
Speaker: Dr. Michael McCoy , Postdoctoral Scholar, Applied and Computational Mathematics, CalTech
Demixing is the problem of disentangling multiple informative signals from a single observation. These problems appear frequently in image processing, wireless communications, machine learning, statistics, and other data-intensive fields. Convex optimization provides a framework for creating tractable demixing procedures that work right out of the box.
In this talk, we describe a geometric theory that characterizes the performance of convex demixing methods under a generic model. This theory precisely identifies when demixing can succeed, and when it cannot, and further indicates that a sharp phase transition between success and failure is a ubiquitous feature of these programs. Our results admit an elegant interpretation: Each signal has an intrinsic dimensionality, and demixing can succeed if (and only if) the number of measurements exceeds the total dimensionality in the signal.
Joint work with J.A. Tropp, with contributions from D. Amelunxen and M. Lotz.