A Convex-Programming Framework for Super-Resolution
Mon., Feb 10, 2014
2:00 - 3:00 PM
521 Cory Hall (Hogan Room)
Title: A Convex-Programming Framework for Super-Resolution

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.
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Varun Jog and Ka Kit Lam Last Modification Date: Sunday, January 26, 2014