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


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


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.


  • Discrete Fourier transform, Phase retrieval, Positive trigonometric polynomials, Signal reconstruction

Publication forum classification

Field of science, Statistics Finland