Open AccessClosed-form algorithms for phase retrieval with an additive point signal
Author(s) -
Woo-Shik Kim,
Namhyun Kim
Publication year - 2009
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.17.000528
Subject(s) - phase retrieval , fourier transform , signal (programming language) , algorithm , multidimensional signal processing , signal processing , fractional fourier transform , magnitude (astronomy) , phase (matter) , point (geometry) , signal reconstruction , short time fourier transform , computer science , phase correlation , non uniform discrete fourier transform , harmonic wavelet transform , optics , discrete fourier transform (general) , fourier analysis , mathematics , physics , mathematical analysis , artificial intelligence , digital signal processing , wavelet transform , geometry , wavelet , discrete wavelet transform , astronomy , quantum mechanics , computer hardware , programming language
The phase retrieval problem is a problem of a reconstruction of a signal from the magnitude of its Fourier transform. In this paper, we consider the problem of reconstructing an unknown one-dimensional signal from the magnitude of its Fourier transform and the magnitude of the Fourier transform of another signal that is made by the addition of a point signal at the center of the original signal. After we show that there are exactly two solution signals that satisfy the given condition, we develop a closed-form algorithm that may reconstruct the two solution signals.