通过加权维特林格流进行相位恢复

Phase retrieval via reweighted Wirtinger flow.

作者信息

Yuan Ziyang, Wang Hongxia

出版信息

Appl Opt. 2017 Mar 20;56(9):2418-2427. doi: 10.1364/AO.56.002418.

DOI:10.1364/AO.56.002418

Abstract

Phase retrieval (PR) is a kind of ill-condition inverse problem which can be found in various applications. Based on the Wirtinger flow (WF) method, a reweighted Wirtinger flow (RWF) method is proposed to deal with the PR problem. In a nutshell, RWF searches the global optimum by solving a series of sub-PR problems with changing weights. Theoretical analyses illustrate that the RWF has a geometric convergence from a deliberate initialization when the weights are bounded by 1 and 109. Numerical tests also show the RWF has a lower sampling complexity compared with the WF. As an essentially adaptive truncated Wirtinger flow (TWF) method, the RWF performs better than the TWF especially when the ratio between sampling number m and length of signal n is small.

摘要

相位恢复（PR）是一种病态逆问题，在各种应用中都能找到。基于维特林格流（WF）方法，提出了一种重加权维特林格流（RWF）方法来处理PR问题。简而言之，RWF通过求解一系列权重不断变化的子PR问题来搜索全局最优解。理论分析表明，当权重在1和109之间有界时，RWF从精心设计的初始化开始具有几何收敛性。数值测试还表明，与WF相比，RWF具有更低的采样复杂度。作为一种本质上自适应的截断维特林格流（TWF）方法，RWF的性能优于TWF，尤其是当采样数m与信号长度n之比很小时。