Princeton University

School of Engineering & Applied Science

A Convex-Programming Framework for Super-Resolution

Carlos Fernandez-Granda
E-Quad, B 205
Thursday, February 20, 2014 - 4:30pm

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 the framework by discussing extensions to the demixing of sines and spikes and to super-resolution from multiple measurements.
Carlos Fernandez-Granda is a PhD student in Electrical Engineering at Stanford University. Previously, he received an M.Sc. degree from Ecole Normale Superieure de Cachan and engineering degrees from Universidad Polit├ęcnica de Madrid and Ecole des Mines in Paris. His research interests are at the intersection of optimization, high-dimensional statistics and harmonic analysis, with emphasis on applications to computer vision, medical imaging and big data.