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

Corneliu Rusu, Jaakko Astola

    Research output: Contribution to journalArticleScientificpeer-review

    6 Citations (Scopus)

    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.

    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

    Keywords

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

    Publication forum classification

    • Publication forum level 1

    ASJC Scopus subject areas

    • Electrical and Electronic Engineering
    • Signal Processing

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