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

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Details

Original languageEnglish
Pages (from-to)195–202
Number of pages8
JournalSignal, Image and Video Processing
Volume11
Issue number2
DOIs
Publication statusPublished - 2017
Publication typeA1 Journal article-refereed

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

Publication forum classification

Field of science, Statistics Finland