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Published 2015 | Submitted
Book Section - Chapter Open

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 to 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 chapter 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.

Additional Information

© 2015 Springer International Publishing Switzerland. JAT gratefully acknowledges support from ONR award N00014-11-1002, AFOSR award FA9550-09-1-0643, and a Sloan Research Fellowship. Thanks are also due to the Moore Foundation.

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