Phase retrieval from the magnitudes of affine linear measurements

doi:10.1016/j.aam.2017.09.004

	Phase retrieval from the magnitudes of affine linear measurements
	Gao, Bing 1; Sun, Qiyu 2; Wang, Yang 3; Xu, Zhiqiang1,4
	2018-02-01
发表期刊	ADVANCES IN APPLIED MATHEMATICS
ISSN	0196-8858
卷号	93 页码:121-141
摘要	In this paper, we consider the affine phase retrieval problem in which one aims to recover a signal from the magnitudes of affine measurements. Let {a(j)}(m)(j=1) subset of H-d and b = (b(1),...,b(m))(T) is an element of H-m, where H = R or C. We say {a(j)}(m)(j=1) and b are affine phase retrievable for H-d if any x is an element of H-d can be recovered from the magnitudes of the affine measurements {vertical bar < a(j), x) + b(j)>, 1 <= j <= m}. We develop general framework for affine phase retrieval and prove necessary and sufficient conditions for {a(j)}(m)(j=1) and b to be affine phase retrievable. We establish results on minimal measurements and generic measurements for affine phase retrieval as well as on sparse affine phase retrieval. In particular, we also highlight some notable differences between affine phase retrieval and the standard phase retrieval in which one aims to recover a signal x from the magnitudes of its linear measurements. In standard phase retrieval, one can only recover x up to a unimodular constant,
关键词	Phase retrieval Frame Sparse signals Algebraic variety
DOI	10.1016/j.aam.2017.09.004
语种	英语
资助项目	National Science Foundation[DMS-1412413] ; Hong Kong Research Grant Council grant[16306415] ; Hong Kong Research Grant Council grant[16317416] ; AFOSR grant[FA9550-12-1-0455] ; NSFC[11422113] ; NSFC[91630203] ; NSFC[11331012] ; National Basic Research Program of China (973 Program)[201503856000]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000414112800005
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29090
专题	计算数学与科学工程计算研究所
通讯作者	Xu, Zhiqiang
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100190, Peoples R China 2.Univ Cent Florida, Dept Math, Orlando, FL 32816 USA 3.Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Hong Kong, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Gao, Bing,Sun, Qiyu,Wang, Yang,et al. Phase retrieval from the magnitudes of affine linear measurements[J]. ADVANCES IN APPLIED MATHEMATICS,2018,93:121-141.
APA	Gao, Bing,Sun, Qiyu,Wang, Yang,&Xu, Zhiqiang.(2018).Phase retrieval from the magnitudes of affine linear measurements.ADVANCES IN APPLIED MATHEMATICS,93,121-141.
MLA	Gao, Bing,et al."Phase retrieval from the magnitudes of affine linear measurements".ADVANCES IN APPLIED MATHEMATICS 93(2018):121-141.