论文标题
部分相干观测的相位检索
Phase Retrieval for Partially Coherent Observations
论文作者
论文摘要
相位检索通常是一个非凸面和非线性任务，相应的算法与局部最小值的问题斗争。我们考虑的情况是，通常在非常小且断开的子集中相互连接的测量样品相互关联 - 这是我们天线测量目标的合理假设。讨论了两类的测量设置，可以提供此类额外的信息：具有多个参考信号的多探针系统和全息测量。我们提出了相应阶段检索问题的几种表述。这些配方中最简单的方程式是类似于特征值问题的线性系统，其中需要找到独特的非平凡空空间矢量。因此，通过可靠的解决方案过程和解决方案质量的判断，可以进行部分相干观测的准确相重建。在理想的无噪声条件下，所需的采样密度小于未知数的两倍。噪声和其他观察错误略微增加了该值。 Simulations for Gaussian random matrices and for antenna measurement scenarios demonstrate that reliable phase reconstruction is possible with the presented approach.
Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets are coherently linked to each other - which is a reasonable assumption for our objective of antenna measurements. Two classes of measurement setups are discussed which can provide this kind of extra information: multi-probe systems and holographic measurements with multiple reference signals. We propose several formulations of the corresponding phase retrieval problem. The simplest of these formulations poses a linear system of equations similar to an eigenvalue problem where a unique non-trivial null-space vector needs to be found. Accurate phase reconstruction for partially coherent observations is, thus, possible by a reliable solution process and with judgment of the solution quality. Under ideal, noise-free conditions, the required sampling density is less than two times the number of unknowns. Noise and other observation errors increase this value slightly. Simulations for Gaussian random matrices and for antenna measurement scenarios demonstrate that reliable phase reconstruction is possible with the presented approach.
