Sparse phase retrieval of structured signals by Prony's method

Sparse phase retrieval of structured signals by Prony's method The phase retrieval problem consists in the recovery of a complex‐valued signal from the magnitudes of its Fourier transform. Restricting ourselves to the case of sparse structured signals f, which can be represented as a linear combination of N arbitrary translations of a given generator function, we show that almost all f can be recovered from 𝒪 (N2) intensity measurements |ℱ[f](ω)| up to trivial ambiguities. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Proceedings in Applied Mathematics & Mechanics Wiley

Sparse phase retrieval of structured signals by Prony's method

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Publisher
Wiley
Copyright
Copyright © 2017 Wiley Subscription Services
ISSN
1617-7061
eISSN
1617-7061
D.O.I.
10.1002/pamm.201710382
Publisher site
See Article on Publisher Site

Abstract

The phase retrieval problem consists in the recovery of a complex‐valued signal from the magnitudes of its Fourier transform. Restricting ourselves to the case of sparse structured signals f, which can be represented as a linear combination of N arbitrary translations of a given generator function, we show that almost all f can be recovered from 𝒪 (N2) intensity measurements |ℱ[f](ω)| up to trivial ambiguities. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Journal

Proceedings in Applied Mathematics & MechanicsWiley

Published: Jan 1, 2017

References

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