One-Dimensional Phase Retrieval with Additional Interference Intensity Measurements

One-Dimensional Phase Retrieval with Additional Interference Intensity Measurements The one-dimensional phase retrieval problem consists in the recovery of a complex-valued signal from its Fourier intensity. Due to the well-known ambiguousness of this problem, the determination of the original signal within the extensive solution set is challenging and can only be done under suitable a priori assumptions or additional information about the unknown signal. Depending on the application, one has sometimes access to further interference intensity measurements between the unknown signal and a reference signal. Beginning with the reconstruction in the discrete-time setting, we show that each signal can be uniquely recovered from its Fourier intensity and two further interference intensity measurements between the unknown signal and a modulation of the signal itself. Afterwards, we consider the continuous-time problem, where we obtain an equivalent result. Moreover, the unique recovery of a continuous-time signal can also be ensured by using interference intensity measurements with a known or an unknown reference which is unrelated to the unknown signal. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Results in Mathematics Springer Journals

One-Dimensional Phase Retrieval with Additional Interference Intensity Measurements

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Publisher
Springer International Publishing
Copyright
Copyright © 2016 by Springer International Publishing
Subject
Mathematics; Mathematics, general
ISSN
1422-6383
eISSN
1420-9012
D.O.I.
10.1007/s00025-016-0633-9
Publisher site
See Article on Publisher Site

Abstract

The one-dimensional phase retrieval problem consists in the recovery of a complex-valued signal from its Fourier intensity. Due to the well-known ambiguousness of this problem, the determination of the original signal within the extensive solution set is challenging and can only be done under suitable a priori assumptions or additional information about the unknown signal. Depending on the application, one has sometimes access to further interference intensity measurements between the unknown signal and a reference signal. Beginning with the reconstruction in the discrete-time setting, we show that each signal can be uniquely recovered from its Fourier intensity and two further interference intensity measurements between the unknown signal and a modulation of the signal itself. Afterwards, we consider the continuous-time problem, where we obtain an equivalent result. Moreover, the unique recovery of a continuous-time signal can also be ensured by using interference intensity measurements with a known or an unknown reference which is unrelated to the unknown signal.

Journal

Results in MathematicsSpringer Journals

Published: Dec 9, 2016

References

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