Phase retrieval with polarization

Boris Alexeev, Afonso Bandeira, Matthew Fickus, Dustin G. Mixon

Research output: Contribution to journalArticle

Abstract

In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In this paper, we provide a novel measurement design which is inspired by interferometry and exploits certain properties of expander graphs. We also give an efficient phase retrieval procedure, and use recent results in spectral graph theory to produce a stable performance guarantee which rivals the guarantee for PhaseLift in [Candès, Strohmer, and Voroninski, PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming, preprint, arXiv:1109.4499, 2011]. We use numerical simulations to illustrate the performance of our phase retrieval procedure, and we compare reconstruction error and runtime with a common alternating-projections-type procedure.

Original languageEnglish (US)
Pages (from-to)35-66
Number of pages32
JournalSIAM Journal on Imaging Sciences
Volume7
Issue number1
DOIs
StatePublished - Jan 2 2014

Fingerprint

Phase Retrieval
Polarization
Spectral Graph Theory
Alternating Projections
Expander Graphs
Performance Guarantee
Convex optimization
Graph theory
Convex Programming
Interferometry
Recovery
Imaging
Imaging techniques
Numerical Simulation
Computer simulation

Keywords

  • Angular synchronization
  • Expander graph
  • Phase retrieval
  • Polarization
  • Spectral clustering

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

Cite this

Alexeev, B., Bandeira, A., Fickus, M., & Mixon, D. G. (2014). Phase retrieval with polarization. SIAM Journal on Imaging Sciences, 7(1), 35-66. https://doi.org/10.1137/12089939X

Phase retrieval with polarization. / Alexeev, Boris; Bandeira, Afonso; Fickus, Matthew; Mixon, Dustin G.

In: SIAM Journal on Imaging Sciences, Vol. 7, No. 1, 02.01.2014, p. 35-66.

Research output: Contribution to journalArticle

Alexeev, B, Bandeira, A, Fickus, M & Mixon, DG 2014, 'Phase retrieval with polarization', SIAM Journal on Imaging Sciences, vol. 7, no. 1, pp. 35-66. https://doi.org/10.1137/12089939X
Alexeev B, Bandeira A, Fickus M, Mixon DG. Phase retrieval with polarization. SIAM Journal on Imaging Sciences. 2014 Jan 2;7(1):35-66. https://doi.org/10.1137/12089939X
Alexeev, Boris ; Bandeira, Afonso ; Fickus, Matthew ; Mixon, Dustin G. / Phase retrieval with polarization. In: SIAM Journal on Imaging Sciences. 2014 ; Vol. 7, No. 1. pp. 35-66.
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