Analysis of Spectral Methods for Phase Retrieval With Random Orthogonal Matrices
Analysis of Spectral Methods for Phase Retrieval With Random Orthogonal Matrices
复制标题
随机正交矩阵相位检索谱方法分析
DOI：
10.1109/tit.2020.2981910
复制
发表时间：
2019
影响因子：
2.5
通讯作者：
A. Maleki
中科院分区：
文献类型：
--
作者：
Rishabh Dudeja;Milad Bakhshizadeh;Junjie Ma;A. Maleki
相位恢复是指用于从其无相测量恢复信号的算法方法。最近有兴趣了解的性能，直接对非凸制定的问题的局部搜索算法。由于问题的非凸性，这些局部搜索算法的成功在很大程度上取决于它们的起点。最广泛使用的初始化方案是谱方法，其中使用数据相关矩阵的首特征向量作为起始点。最近，对于具有独立同分布项的测量矩阵，谱初始化的性能得到了准确的表征。本文的目的是获得相同水平的知识各向同性随机列正交矩阵，这是实际相位恢复系统的更好的模型。为了实现这一目标，我们考虑的渐近设置，其中测量的数量<inline-formula><tex-math notation="LaTeX">$m$</tex-math></inline-formula>，和信号的维数，<inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>，发散到无穷大与<inline-formula><tex-math notation="LaTeX">$m/n = \delta \in（1，\infty）$</tex-math></inline-formula>，并获得一个简单的表达式的频谱估计和真实的信号向量之间的重叠。
Phase retrieval refers to algorithmic methods for recovering a signal from its phaseless measurements. There has been recent interest in understanding the performance of local search algorithms that work directly on the non-convex formulation of the problem. Due to the non-convexity of the problem, the success of these local search algorithms depends heavily on their starting points. The most widely used initialization scheme is the spectral method, in which the leading eigenvector of a data-dependent matrix is used as a starting point. Recently, the performance of the spectral initialization was characterized accurately for measurement matrices with independent and identically distributed entries. This paper aims to obtain the same level of knowledge for isotropically random column-orthogonal matrices, which are substantially better models for practical phase retrieval systems. Towards this goal, we consider the asymptotic setting in which the number of measurements <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula>, and the dimension of the signal, <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>, diverge to infinity with <inline-formula> <tex-math notation="LaTeX">$m/n = \delta \in (1,\infty )$ </tex-math></inline-formula>, and obtain a simple expression for the overlap between the spectral estimator and the true signal vector.
影响因子：
5.4
作者：
Luo, Wangyu;Alghamdi, Wael;Lu, Yue M.
通讯作者：
Lu, Yue M.
影响因子：
3
作者：
Mondelli, Marco;Montanari, Andrea
通讯作者：
Montanari, Andrea