一种仿射相位恢复的PhaseMax算法  

A PhaseMax Algorithm for Afine Phase Retrieval

作　　者：王凯欣 翟艳丽 庄智涛 WANG Kai-xin;ZHAI Yan-li;ZHUANG Zhi-tao(School of Basic Sciences,Zhengzhou University of Technology,Zhengzhou 450044,China;School of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]郑州工程技术学院基础科学学院,河南郑州450044 [2]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《数学的实践与认识》2024年第9期151-158,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金青年基金(11601152)。

摘　　要：仿射相位恢复是工程数学中的一个重要研究内容,其算法实现更是近几年的一个研究热点.给出了信号能够高概率地仿射相位恢复的一个充要条件,并得到了PhaseMax算法可以成功恢复信号的概率下界.数值实验算例表明,通过谱方法得到合适的初始值后,PhaseMax算法能够有效地求解仿射相位恢复问题.Affine phase retrieval is an important research field in Engineering Mathematics,and its algorithm implementation is a research hotspot in recent years.In this paper,we show a sufficient condition in which a signal from affine phase retrieval could be recovered with high probability,and we get the lower bound for recovering the signal successfully from affine phase retrieval with PhaseMax algorithm.Numerical simulations demonstrate that after obtaining a proper approximation vector from spectral initialization,PhaseMax algorithm can effectively solve the affine phase retrieval problems.

关 键 词：PhaseMax 仿射相位恢复 谱方法 

分 类 号：TN911.7[电子电信—通信与信息系统]