On the existence of the solution for one-dimensional discrete phase retrieval problem. Issue 2 (February 2017)

• Record Type: Journal Article
• Authors: Rusu, Corneliu; Astola, Jaakko
• Is Part Of: Signal, image and video processing. Volume 11:Issue 2(2017)
• Page Start: 195
• Page End: 202
• Publication Date: 2017-02
• Subjects: Phase retrieval -- Signal reconstruction -- Discrete Fourier transform -- Positive trigonometric polynomials; Signal processing -- Digital techniques -- Periodicals; Image processing -- Digital techniques -- Periodicals; Digital video -- Periodicals; 621.3822
• DOI: 10.1007/s11760-016-0919-0
• Languages: English
• ISSNs: 1863-1703

Abstract

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.