Convex Recovery of a Structured Signal from Independent Random Linear Measurements

  • Joel A. Tropp
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


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.



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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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Joel A. Tropp
    • 1
  1. 1.Department of Computing and Mathematical SciencesCalifornia Institute of TechnologyPasadenaUSA

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