AUTHOR=Beinert Robert , Plonka Gerlind 

TITLE=Sparse Phase Retrieval of One-Dimensional Signals by Prony's Method

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 3 - 2017

YEAR=2017

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2017.00005

DOI=10.3389/fams.2017.00005

ISSN=2297-4687

ABSTRACT=In this paper, we show that sparse signals f representable as a linear combination of a finite number N of spikes at arbitrary real locations or as a finite linear combination of B-splines of order m with arbitrary real knots can be almost surely recovered from O (N 2 ) intensity mea- surements □□□□F[f ](ω)□□□□2 up to trivial ambiguities. The constructive proof consists of two steps, where in the first step the Prony method is applied to recover all parameters of the autocorre- lation function and in the second step the parameters of f are derived. Moreover, we present an algorithm to evaluate f from its Fourier intensities and illustrate it at different numerical examples.