Phase Retrieval of Real-Valued Signals in a Shift-Invariant Space
Phase Retrieval of Real-Valued Signals in a Shift-Invariant Space
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DOI：
10.1016/j.acha.2018.11.002
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发表时间：
2016-03
期刊：
影响因子：
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通讯作者：
Yang Chen;Cheng Cheng-Cheng;Qiyu Sun;Haichao Wang
中科院分区：
文献类型：
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作者：
Yang Chen;Cheng Cheng-Cheng;Qiyu Sun;Haichao Wang
在这篇文章中，我们考虑了一个无限维位相恢复问题，该问题从实值信号的全线或有限采样密度的离散集上采集的无相位样本中重建存在于平移不变空间的实值信号。我们利用实值移位不变空间中所有的相位可恢复信号的不可分性来刻画它们。对于支撑长度为L的函数所产生的不可分离信号，我们证明了在采样密度为2 L−1的离散集上采集的含有噪声的无相样本可以很好地逼近到符号。本文还提出了一个具有线性计算复杂度的算法，可以从被有界噪声污染的无相样本重构移位不变空间中的不可分信号。
In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living in a shift-invariant space from their phaseless samples taken either on the whole line or on a discrete set with finite sampling density. We characterize all phase retrievable signals in a real-valued shift-invariant space using their nonseparability. For nonseparable signals generated by some function with support length L, we show that they can be well approximated, up to a sign, from their noisy phaseless samples taken on a discrete set with sampling density 2 L− 1. In this paper, we also propose an algorithm with linear computational complexity to reconstruct nonseparable signals in a shift-invariant space from their phaseless samples corrupted by bounded noises.