The replica-symmetric prediction for compressed sensing with Gaussian matrices is exact

Conference Paper

© 2016 IEEE. This paper considers the fundamental limit of compressed sensing for i.i.d. signal distributions and i.i.d. Gaussian measurement matrices. Its main contribution is a rigorous characterization of the asymptotic mutual information (MI) and minimum mean-square error (MMSE) in this setting. Under mild technical conditions, our results show that the limiting MI and MMSE are equal to the values predicted by the replica method from statistical physics. This resolves a well-known problem that has remained open for over a decade.

Full Text

Duke Authors

Cited Authors

  • Reeves, G; Pfister, HD

Published Date

  • August 10, 2016

Published In

Volume / Issue

  • 2016-August /

Start / End Page

  • 665 - 669

International Standard Serial Number (ISSN)

  • 2157-8095

International Standard Book Number 13 (ISBN-13)

  • 9781509018062

Digital Object Identifier (DOI)

  • 10.1109/ISIT.2016.7541382

Citation Source

  • Scopus