基于掩蔽信号功率谱的相位恢复
Phase retrieval from power spectra of masked signals
摘要：
在衍射成像中，人们的任务是从信号的功率谱重建信号。为了解决这个逆问题中的模糊性，人们可能会调用有关信号的先验知识，但在这种情况下，相位恢复算法已经取得了有限的成功。一种替代方案是通过多次照射信号来在测量过程中产生冗余，每次使用不同的掩模使信号失真。尽管最近在相位恢复方面取得了一些进展，但该社区尚未构建一个唯一确定所有信号并承认有效重建算法的掩模集合。在本文中，我们利用最近提出的偏振方法来构建这样的合奏。我们还提出了数值模拟，以说明在这种情况下的偏振方法的稳定性。在一个国家的最先进的相位恢复算法称为PhaseLift相比，我们发现，偏振速度快得多，具有可比的稳定性。
英文摘要：
In diffraction imaging, one is tasked with reconstructing a signal from its power spectrum. To resolve the ambiguity in this inverse problem, one might invoke prior knowledge about the signal, but phase retrieval algorithms in this vein have found limited success. One alternative is to create redundancy in the measurement process by illuminating the signal multiple times, distorting the signal each time with a different mask. Despite several recent advances in phase retrieval, the community has yet to construct an ensemble of masks which uniquely determines all signals and admits an efficient reconstruction algorithm. In this paper, we leverage the recently proposed polarization method to construct such an ensemble. We also present numerical simulations to illustrate the stability of the polarization method in this setting. In comparison to a state-of-the-art phase retrieval algorithm known as PhaseLift, we find that polarization is much faster with comparable stability.
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