Convex recovery of a structured signal from independent random linear measurements

This chapter develops a new theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with recent results for standard Gaussian measurements, but the argument applies to a much wider class of measurement ensembles. To demonstrate the power of this approach, the paper presents a short analysis of phase retrieval by trace-norm minimization. The key technical tool in this work is a method, due to Koltchinskii & Mendelson, for bounding nonnegative empirical processes.