Tampere University of Technology

TUTCRIS Research Portal

On the existence of the solution for one-dimensional discrete phase retrieval problem

Research output: Contribution to journalArticleScientificpeer-review

Standard

On the existence of the solution for one-dimensional discrete phase retrieval problem. / Rusu, Corneliu; Astola, Jaakko.

In: Signal, Image and Video Processing, Vol. 11, No. 2, 2017, p. 195–202.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

Rusu, C & Astola, J 2017, 'On the existence of the solution for one-dimensional discrete phase retrieval problem', Signal, Image and Video Processing, vol. 11, no. 2, pp. 195–202. https://doi.org/10.1007/s11760-016-0919-0

APA

Rusu, C., & Astola, J. (2017). On the existence of the solution for one-dimensional discrete phase retrieval problem. Signal, Image and Video Processing, 11(2), 195–202. https://doi.org/10.1007/s11760-016-0919-0

Vancouver

Author

Rusu, Corneliu ; Astola, Jaakko. / On the existence of the solution for one-dimensional discrete phase retrieval problem. In: Signal, Image and Video Processing. 2017 ; Vol. 11, No. 2. pp. 195–202.

Bibtex - Download

@article{e0a7bf34ecac4807b54293c4bf4ead4a,
title = "On the existence of the solution for one-dimensional discrete phase retrieval problem",
abstract = "We consider the discrete form of the one-dimensional phase retrieval (1-D DPhR) problem from the point of view of input magnitude data. The direct method can provide a solution to the 1-D DPhR problem if certain conditions are satisfied by the input magnitude data, namely the corresponding trigonometric polynomial must be nonnegative. To test positivity of a trigonometric polynomial a novel DFT-based criterion is proposed. We use this DFT criterion for different sets of input magnitude data to evaluate whether the direct method applied to the 1-D DPhR problem leads to a solution in all explored cases.",
keywords = "Discrete Fourier transform, Phase retrieval, Positive trigonometric polynomials, Signal reconstruction",
author = "Corneliu Rusu and Jaakko Astola",
note = "EXT={"}Rusu, Corneliu{"}",
year = "2017",
doi = "10.1007/s11760-016-0919-0",
language = "English",
volume = "11",
pages = "195–202",
journal = "Signal, Image and Video Processing",
issn = "1863-1703",
publisher = "Springer Verlag",
number = "2",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - On the existence of the solution for one-dimensional discrete phase retrieval problem

AU - Rusu, Corneliu

AU - Astola, Jaakko

N1 - EXT="Rusu, Corneliu"

PY - 2017

Y1 - 2017

N2 - We consider the discrete form of the one-dimensional phase retrieval (1-D DPhR) problem from the point of view of input magnitude data. The direct method can provide a solution to the 1-D DPhR problem if certain conditions are satisfied by the input magnitude data, namely the corresponding trigonometric polynomial must be nonnegative. To test positivity of a trigonometric polynomial a novel DFT-based criterion is proposed. We use this DFT criterion for different sets of input magnitude data to evaluate whether the direct method applied to the 1-D DPhR problem leads to a solution in all explored cases.

AB - We consider the discrete form of the one-dimensional phase retrieval (1-D DPhR) problem from the point of view of input magnitude data. The direct method can provide a solution to the 1-D DPhR problem if certain conditions are satisfied by the input magnitude data, namely the corresponding trigonometric polynomial must be nonnegative. To test positivity of a trigonometric polynomial a novel DFT-based criterion is proposed. We use this DFT criterion for different sets of input magnitude data to evaluate whether the direct method applied to the 1-D DPhR problem leads to a solution in all explored cases.

KW - Discrete Fourier transform

KW - Phase retrieval

KW - Positive trigonometric polynomials

KW - Signal reconstruction

U2 - 10.1007/s11760-016-0919-0

DO - 10.1007/s11760-016-0919-0

M3 - Article

VL - 11

SP - 195

EP - 202

JO - Signal, Image and Video Processing

JF - Signal, Image and Video Processing

SN - 1863-1703

IS - 2

ER -