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

Other

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

Fingerprint

Message passing
Phase transitions
Recovery
Pixels

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computer Science Applications

Cite this

Schniter, P., & Rangan, S. (2012). Compressive phase retrieval via generalized approximate message passing. In 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012 (pp. 815-822). [6483302] https://doi.org/10.1109/Allerton.2012.6483302

Compressive phase retrieval via generalized approximate message passing. / Schniter, Philip; Rangan, Sundeep.

2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012. 2012. p. 815-822 6483302.

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

Schniter, P & Rangan, S 2012, Compressive phase retrieval via generalized approximate message passing. in 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012., 6483302, pp. 815-822, 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012, Monticello, IL, United States, 10/1/12. https://doi.org/10.1109/Allerton.2012.6483302
Schniter P, Rangan S. Compressive phase retrieval via generalized approximate message passing. In 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012. 2012. p. 815-822. 6483302 https://doi.org/10.1109/Allerton.2012.6483302
Schniter, Philip ; Rangan, Sundeep. / Compressive phase retrieval via generalized approximate message passing. 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012. 2012. pp. 815-822
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