Sohail Bahmani and Justin Romberg received a Best Paper Award at the Artificial Intelligence and Statistics Conference, held April 20-22 in Fort Lauderdale, Florida. Romberg is the associate chair for research and holds the Schlumberger Professorship in the Georgia Tech School of Electrical and Computer Engineering (ECE), and Bohmani is a postdoctoral fellow in Romberg’s research group.
Their paper is entitled "Phase Retrieval Meets Statistical Learning Theory: A Flexible Convex Relaxation,” and it presents a new methodology for solving a classic signal processing problem: reconstructing a signal from observations of the magnitude of a series of linear measurements.
The paper introduces a very tractable procedure for solving this problem based on linear programming, and the analysis of its effectiveness makes new connections between the theory of generalization (i.e., VC bounds) and convex programming. Phase retrieval arises in many scientific imaging applications, including astronomical imaging, x-ray crystallography, and certain kinds of microscopy such as Fourier ptychography.