Phase retrieval from power spectra of masked signals

Afonso S. Bandeira, Yutong Chen, Dustin G. Mixon

Research output: Contribution to journalArticle

Abstract

In diffraction imaging, one is tasked with reconstructing a signal from its power spectrum. To resolve the ambiguity in this inverse problem, one might invoke prior knowledge about the signal, but phase retrieval algorithms in this vein have found limited success. One alternative is to create redundancy in the measurement process by illuminating the signal multiple times, distorting the signal each time with a different mask. Despite several recent advances in phase retrieval, the community has yet to construct an ensemble of masks which uniquely determines all signals and admits an efficient reconstruction algorithm. In this paper, we leverage the recently proposed polarization method to construct such an ensemble. First, we construct four explicit masks which enable polarization recovery of any signal with non-vanishing Fourier transform, and then we construct Θ(log M) random masks which, with high probability, simultaneously enable polarization recovery of any signal whatsoever. We also present numerical simulations to illustrate the stability of the polarization method in this setting. In comparison to a state-of-the-art phase retrieval algorithm known as PhaseLift, we find that polarization is much faster with comparable stability.

Original languageEnglish (US)
Pages (from-to)83-102
Number of pages20
JournalInformation and Inference
Volume3
Issue number2
DOIs
StatePublished - 2014

Keywords

  • Angular synchronization
  • Diffraction imaging
  • Phase retrieval
  • Polarization

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Analysis
  • Applied Mathematics
  • Statistics and Probability
  • Numerical Analysis

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