A geometric theory of convex demixing

Start: 10/02/2013 - 1:15pm
End  : 10/02/2013 - 2:15pm

Applied Math Seminar

Mike McCoy (Computing and Mathematical Sciences, 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.

Davidson, CMC