Sparse Phase Retrieval of One-Dimensional Signals by Prony's Method
Sparse Phase Retrieval of One-Dimensional Signals by Prony's Method
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DOI：
10.3389/fams.2017.00005
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发表时间：
2017-01
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通讯作者：
Robert Beinert;G. Plonka-Hoch
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文献类型：
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作者：
Robert Beinert;G. Plonka-Hoch
本文证明了稀疏信号f（可表示为任意真实的位置的有限数目N个尖峰的线性组合或m阶B样条与任意真实的节点的有限线性组合）几乎可以从O（N2）强度测量值□F[f ]（ω）□2恢复到平凡的模糊度。构造性证明包括两个步骤，其中第一步应用Prony方法恢复自相关函数的所有参数，第二步导出f的参数。此外，我们提出了一个算法来评估f从其傅立叶强度，并说明它在不同的数值例子。
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.