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

Frontiers in Applied Mathematics and Statistics

Beinert, Robert¹  Plonka, Gerlind² 

[1] Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universitär Numerische und Angewandte Mathematik, Georg-August-Universität Göt Graz, Graz, Austria;ttingen, Göttingen, Germany

关键词: Sparse phase retrieval;    Sparse signals;    non-uniform spline functions;    finite support;    Prony';    s method;   

DOI  :  10.3389/fams.2017.00005

学科分类：数学（综合）

来源: Frontiers

【 摘 要 】

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.

【 授权许可】

CC BY