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Signal, Image and Video Processing

, Volume 11, Issue 2, pp 195–202 | Cite as

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

  • Corneliu RusuEmail author
  • Jaakko Astola
Original Paper

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

Phase retrieval Signal reconstruction Discrete Fourier transform Positive trigonometric polynomials 

Notes

Acknowledgments

The work of first author has been supported by Grant PAV3M PN-II-PT-PCCA-2013-4-1762.

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Copyright information

© Springer-Verlag London 2016

Authors and Affiliations

  1. 1.Signal Processing Group, Faculty of Electronics, Telecommunications and Information TechnologyTechnical University of Cluj-NapocaCluj-NapocaRomania
  2. 2.Tampere International Center for Signal ProcessingTampere University of TechnologyTampereFinland

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