Phase retrieval using a conjugate symmetric reference

Kejun Huang, Yonina C. Eldar

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

2 Scopus citations

Abstract

It was recently shown that finding a compactly supported vector that solves the 1D Fourier phase retrieval problem in the least-squares sense can be computed in polynomial-time, although the solution is not unique. To resolve identifiability, we previously proposed adding a Kronecker delta reference with sufficiently large intensity to the signal before measuring its Fourier magnitude. In practice, however, it is difficult to add a reference that is both strong enough to meet the intensity requirement, and narrow enough to be considered a Kronecker delta after sampling. In this paper we propose a physically more accessible approach to correctly recover a signal from Fourier magnitude measurements, assuming we can 1) generate a reference that is conjugate symmetric (no specific requirement on the power), and 2) measure the Fourier intensity of both the desired signal alone and the signal plus the reference. Numerical simulations showcase the effectiveness of the proposed method in exact signal recovery, as well as noise robustness for certain choices of the references, which cannot be achieved by other methods under the same measuring settings.

Original languageEnglish (US)
Title of host publication2017 12th International Conference on Sampling Theory and Applications, SampTA 2017
EditorsGholamreza Anbarjafari, Andi Kivinukk, Gert Tamberg
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages331-335
Number of pages5
ISBN (Electronic)9781538615652
DOIs
StatePublished - Sep 1 2017
Event12th International Conference on Sampling Theory and Applications, SampTA 2017 - Tallinn, Estonia
Duration: Jul 3 2017Jul 7 2017

Publication series

Name2017 12th International Conference on Sampling Theory and Applications, SampTA 2017

Other

Other12th International Conference on Sampling Theory and Applications, SampTA 2017
CountryEstonia
CityTallinn
Period7/3/177/7/17

Fingerprint Dive into the research topics of 'Phase retrieval using a conjugate symmetric reference'. Together they form a unique fingerprint.

Cite this