EECS Special Seminar: Carlos Fernandez-Granda (Stanford
University) - "A Convex-Programming Framework for Super-
Resolution"   Event Speaker:   Carlos Fernandez-Granda  Event
Location:   Grier A, 34-401A  Event Date/Time:   Thursday, March
6, 2014 - 3:00pm  We propose a general framework to perform
statistical estimation from low-resolution data, a crucial
challenge in applications ranging from microscopy, astronomy and
medical imaging to geophysics, signal processing and
spectroscopy. First, we show that solving a simple convex
program allows to super-resolve a superposition of point sources
from bandlimited measurements with infinite precision. This
holds as long as the sources are separated by a distance related
to the cut-off frequency of the data. The result extends to
higher dimensions and to the super-resolution of piecewise-
smooth functions. Then, we provide theoretical guarantees that
establish the robustness of our methods to noise in a non-
asymptotic regime. Finally, we illustrate the flexibility of