Vectorial phase retrieval of 1-d signals

Oren Raz, Nirit Dudovich, Boaz Nadler

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

Reconstruction of signals from measurements of their spectral intensities, also known as the phase retrieval problem, is of fundamental importance in many scientific fields. In this paper we present a novel framework, denoted as vectorial phase retrieval, for reconstruction of pairs of signals from spectral intensity measurements of the two signals and of their interference. We show that this new framework can alleviate some of the theoretical and computational challenges associated with classical phase retrieval from a single signal. First, we prove that for compactly supported signals, in the absence of measurement noise, this new setup admits a unique solution. Next, we present a statistical analysis of vectorial phase retrieval and derive a computationally efficient algorithm to solve it. Finally, we illustrate via simulations, that our algorithm can accurately reconstruct signals even at considerable noise levels.

Original languageEnglish
Article number6410442
Pages (from-to)1632-1643
Number of pages12
JournalIEEE Transactions on Signal Processing
Volume61
Issue number7
DOIs
StatePublished - 19 Mar 2013
Externally publishedYes

Keywords

  • 1-D phase retrieval
  • Convex relaxation
  • signal recovery from modulus Fourier measurements
  • statistical model selection

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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