# Michael McCoy : Convex demixing: Sharp bounds for recovering superimposed signals

Real-world data often consists of the superposition of multiple informative signals. Examples include an image of the night sky containing both stars and galaxies; a communications message with impulsive noise; and a low rank matrix obscured by sparse corruptions. Demixing is the problem of determining the constituent signals from the observed superposition. Convex optimization offers a natural framework for solving demixing problems. This talk describes a geometric characterization of success in this framework that, when coupled with a natural incoherence model, leads into the realm of random geometry. A powerful result from spherical integral geometry then provides an exact formula for the probability that the convex demixing approach succeeds. Analysis of this formula reveals sharp phase transitions between success and failure for a large class of demixing methods. We apply our results to demixing the superposition of sparse vectors in random bases, a stylized robust communications protocol, and determining a low rank matrix corrupted by a matrix that is sparse in a random basis. Empirical results closely match our theoretical bounds. Joint work with Joel A. Tropp.

**Category**: Geometry and Topology**Duration**: 01:14:52**Date**: November 12, 2012 at 4:25 PM**Views**: 132-
**Tags:**seminar, Geometry/topology Seminar

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