Mathematics Seminar: "Compressed Sensing: an overview with some details"
4:10pm, Neill 5W
Dr. Kevin R. Vixie
Compressed sensing is an area of applied analysis that came into existence a few years ago because Terry Tao and Emmanuel Candes both had small children in the UCLA day care center. It started with the observation that when Emmanuel reconstructed a particular test image (the Shepp-Logan phantom) from projections by constrained minimization of the L^1 size of the reconstructed gradient, he could reconstruct it perfectly using a ridiculously small number of measurements. That observation prompted the discussion at the day care center that generated the entire, now very hot, research area. In my talk, I will explain how it works under the hood, so to speak. Much of what I say comes from a very nice, short piece by Bryan and Leise in the September 2013 SIAM Review. The rest will be context, history, and good dose of geometry in high dimensions, as well as a few other miscellaneous facts.