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.