Convex recovery of a structured signal from independent random linear measurements
Abstract
This chapter develops a 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 is a framework, due to Mendelson and coauthors, for bounding a nonnegative empirical process.
Keywords
Cite
@article{arxiv.1405.1102,
title = {Convex recovery of a structured signal from independent random linear measurements},
author = {Joel A. Tropp},
journal= {arXiv preprint arXiv:1405.1102},
year = {2014}
}
Comments
18 pages, 1 figure. To appear in "Sampling Theory, a Renaissance." v2: minor corrections. v3: updated citations and increased emphasis on Mendelson's contributions