Phase Retrieval with Polarization

被引：86

作者：

Alexeev, Boris ^{[1
]}

Bandeira, Afonso S. ^{[2
]}

Fickus, Matthew ^{[3
]}

Mixon, Dustin G. ^{[3
]}

机构：

[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA

[2] Princeton Univ, PACM, Princeton, NJ 08544 USA

[3] Air Force Inst Technol, Dept Math & Stat, Wright Patterson AFB, OH 45433 USA

来源：

SIAM JOURNAL ON IMAGING SCIENCES | 2014年 / 7卷 / 01期

基金：

美国国家科学基金会;

关键词：

phase retrieval; polarization; expander graph; spectral clustering; angular synchronization; CRYSTALLOGRAPHY; RECONSTRUCTION; INEQUALITIES;

D O I：

10.1137/12089939X

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In this paper, we provide a novel measurement design which is inspired by interferometry and exploits certain properties of expander graphs. We also give an efficient phase retrieval procedure, and use recent results in spectral graph theory to produce a stable performance guarantee which rivals the guarantee for PhaseLift in [Candes, Strohmer, and Voroninski, PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming, preprint, arXiv: 1109.4499, 2011]. We use numerical simulations to illustrate the performance of our phase retrieval procedure, and we compare reconstruction error and runtime with a common alternating-projections-type procedure.

引用

页码：35 / 66

页数：32

共 49 条

[1] Full Spark Frames [J].