Phaseless Sampling and Reconstruction of Real-Valued Signals in Shift-Invariant Spaces
Phaseless Sampling and Reconstruction of Real-Valued Signals in Shift-Invariant Spaces
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DOI：
10.1007/s00041-018-9639-x
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发表时间：
2017-02
影响因子：
1.2
通讯作者：
Cheng Cheng-Cheng;Junzheng Jiang;Qiyu Sun
中科院分区：
文献类型：
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作者：
Cheng Cheng-Cheng;Junzheng Jiang;Qiyu Sun
平移不变空间采样是平滑频谱信号的一种现实模型。在本文中，我们考虑的无相位采样和重建的实值信号在一个高维的移位不变的空间从他们的幅度测量整个欧几里德空间和从他们的无相位采样的离散集有限的采样密度。在移位不变空间中的信号的确定，直到一个符号，通过它在整个欧几里得空间上的幅度测量已经在文献中被证明是等价于它的不可分性。在本文中，我们引入了一个无向图与移位不变空间中的信号，并使用图的连通性来表征信号的不可分离性。在移位不变空间的局部互补性假设下，我们找到一个具有有限采样密度的离散集，使得移位不变空间中的不可分信号可以从该集合上的无相位样本以稳定的方式重构。在本文中，我们还提出了一种重建算法，它提供了一个近似的原始信号时，其嘈杂的无相位样本是唯一可用的。最后，数值模拟表明，该算法的鲁棒性，从他们的噪声无相位样本重建盒样条信号。
Sampling in shift-invariant spaces is a realistic model for signals with smooth spectrum. In this paper, we consider phaseless sampling and reconstruction of real-valued signals in a high-dimensional shift-invariant space from their magnitude measurements on the whole Euclidean space and from their phaseless samples taken on a discrete set with finite sampling density. The determination of a signal in a shift-invariant space, up to a sign, by its magnitude measurements on the whole Euclidean space has been shown in the literature to be equivalent to its nonseparability. In this paper, we introduce an undirected graph associated with the signal in a shift-invariant space and use connectivity of the graph to characterize nonseparability of the signal. Under the local complement property assumption on a shift-invariant space, we find a discrete set with finite sampling density such that nonseparable signals in the shift-invariant space can be reconstructed in a stable way from their phaseless samples taken on that set. In this paper, we also propose a reconstruction algorithm which provides an approximation to the original signal when its noisy phaseless samples are available only. Finally, numerical simulations are performed to demonstrate the robustness of the proposed algorithm to reconstruct box spline signals from their noisy phaseless samples.