On convexity and identifiability in 1-D Fourier phase retrieval

Kejun Huang, Yonina C. Eldar, Nicholas D. Sidiropoulos

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

6 Scopus citations

Abstract

This paper considers phase retrieval from the magnitude of 1-D oversampled Fourier measurements. We first revisit the well-known lack of identifiability in this case, and point out that there always exists a solution that is minimum phase, even though the desired signal is not. Next, we explain how the least-squares formulation of this problem can be optimally solved via PhaseLift followed by spectral factorization, and this solution is always minimum phase. A simple approach is then proposed to circumvent non-identifiability: adding an impulse to an arbitrary complex signal (offset to the Fourier transform) before taking the quadratic measurements, so that a minimum phase signal is constructed and thus can be uniquely estimated. Simulations with synthetic data show the effectiveness of the proposed method.

Original languageEnglish (US)
Title of host publication2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3941-3945
Number of pages5
ISBN (Electronic)9781479999880
DOIs
StatePublished - May 18 2016
Event41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China
Duration: Mar 20 2016Mar 25 2016

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2016-May
ISSN (Print)1520-6149

Other

Other41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
Country/TerritoryChina
CityShanghai
Period3/20/163/25/16

Bibliographical note

Funding Information:
The work of Y. Eldar was funded by the European Unions Horizon 2020 research and innovation programme under grant agreement ERC-BNYQ, by the Israel Science Foundation under Grant no. 335/14, and by ICore: the Israeli Excellence Center Circle of Light

Publisher Copyright:
© 2016 IEEE.

Keywords

  • auto-correlation estimation
  • minimum phase
  • over-sampled Fourier measurements
  • phase retrieval
  • semi-definite programming

Fingerprint

Dive into the research topics of 'On convexity and identifiability in 1-D Fourier phase retrieval'. Together they form a unique fingerprint.

Cite this