Compressive phase retrieval via generalized approximate message passing

Philip Schniter, Sundeep Rangan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we propose a novel approach to compressive phase retrieval based on loopy belief propagation and, in particular, on the generalized approximate message passing (GAMP) algorithm. Numerical results show that the proposed PR-GAMP algorithm has excellent phase-transition behavior, noise robustness, and runtime. In particular, for successful recovery of synthetic Bernoulli-circular-Gaussian signals, PR-GAMP requires ≈4 times the number of measurements as a phase-oracle version of GAMP and, at moderate to large SNR, the NMSE of PR-GAMP is only ≈3 dB worse than that of phase-oracle GAMP. A comparison to the recently proposed convex-relation approach known as 'CPRL' reveals PR-GAMP's superior phase transition and orders-of-magnitude faster runtimes, especially as the problem dimensions increase. When applied to the recovery of a 65k-pixel grayscale image from 32k randomly masked magnitude measurements, numerical results show a median PR-GAMP runtime of only 13.4 seconds.

Original languageEnglish (US)
Title of host publication2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
Pages815-822
Number of pages8
DOIs
StatePublished - 2012
Event2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012 - Monticello, IL, United States
Duration: Oct 1 2012Oct 5 2012

Publication series

Name2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012

Other

Other2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012
CountryUnited States
CityMonticello, IL
Period10/1/1210/5/12

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Science Applications

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