Robust Phase Retrieval Algorithm for Time-Frequency Structured Measurements
Robust Phase Retrieval Algorithm for Time-Frequency Structured Measurements
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DOI：
10.1137/18m1205522
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发表时间：
2019-01-01
影响因子：
2.1
通讯作者：
Salanevich, Palina
中科院分区：
文献类型：
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作者：
Pfander, Goetz E.;Salanevich, Palina
我们解决的问题，信号重建强度测量相对于测量帧。这种非凸逆问题被称为相位恢复。在本文中考虑的情况下，无相测量相对于一个Gabor框架。它在许多实际应用中自然出现，例如衍射成像和语音识别。我们提出了一种重建算法，使用一个接近最佳数量的无相位的时间-频率结构的测量，并讨论其鲁棒性的情况下，当测量被噪声破坏。我们展示了如何测量帧的几何特性与无相重建的鲁棒性有关。
We address the problem of signal reconstruction from intensity measurements with respect to a measurement frame. This nonconvex inverse problem is known as phase retrieval. The case considered in this paper concerns phaseless measurements taken with respect to a Gabor frame. It arises naturally in many practical applications, such as diffraction imaging and speech recognition. We present a reconstruction algorithm that uses a nearly optimal number of phaseless time-frequency structured measurements and discuss its robustness in the case when the measurements are corrupted by noise. We show how geometric properties of the measurement frame are related to the robustness of the phaseless reconstruction.