Fast angular synchronization for phase retrieval via incomplete information
Fast angular synchronization for phase retrieval via incomplete information
复制标题
通过不完整信息进行相位检索的快速角同步
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
M. Iwen
中科院分区：
文献类型：
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作者：
A. Viswanathan;M. Iwen
我们考虑未知向量x∈ℂd的相位恢复问题，给定(归一化)形式为xjxk*/|xjxk*|，j，k∈{1，...，d}的相位差测量，其中xj*表示xj的复共轭。这个问题有时被称为角同步问题。本文分析了一种基于特征向量线性时间的角同步算法，并研究了它在一类高度不完整和可能有噪声的相位差测量中的理论和数值性能。给出了理想(无噪声)测量的理论结果，并通过数值仿真验证了该方法对测量噪声的鲁棒性。最后，我们证明了这个角同步问题和所考虑的不完全相位差测量的具体形式出现在相位恢复问题中--我们从无相位(或幅度)测量中恢复未知的复矢量。
We consider the problem of recovering the phase of an unknown vector, x ∈ ℂd, given (normalized) phase difference measurements of the form xjxk*/|xjxk*|, j,k ∈ {1,...,d}, and where xj* denotes the complex conjugate of xj. This problem is sometimes referred to as the angular synchronization problem. This paper analyzes a linear-time-in-d eigenvector-based angular synchronization algorithm and studies its theoretical and numerical performance when applied to a particular class of highly incomplete and possibly noisy phase difference measurements. Theoretical results are provided for perfect (noiseless) measurements, while numerical simulations demonstrate the robustness of the method to measurement noise. Finally, we show that this angular synchronization problem and the specific form of incomplete phase difference measurements considered arise in the phase retrieval problem - where we recover an unknown complex vector from phaseless (or magnitude) measurements.
影响因子：
2.5
作者：
Singer, A.
通讯作者：
Singer, A.