Almost everywhere generalized phase retrieval

doi:10.1016/j.acha.2020.08.002

CSpace

	Almost everywhere generalized phase retrieval
	Huang, Meng 1; Rong, Yi 2; Wang, Yang 2; Xu, Zhiqiang 1,3
	2021
发表期刊	APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
ISSN	1063-5203
卷号	50 页码:16-33
摘要	The aim of generalized phase retrieval is to recover x is an element of F-d from the quadratic measurements xA(1)x, ...,x A(N)x, where A(j) is an element of H-d(F) and F = R or C. In this paper, we study the matrix set A = (Aj)(j=1)(N) which has the almost everywhere phase retrieval property. For the case F = R, we show that N >= d + 1 generic matrices with prescribed ranks have almost everywhere phase retrieval property. We also extend this result to the case where A(1), ..., A(N) are orthogonal matrices and hence establish the almost everywhere phase retrieval property for the fusion frame phase retrieval. For the case where F = C, we obtain similar results under the assumption of N >= 2d. We lower the measurement number d + 1 (resp. 2d) with showing that there exist N = d (resp. 2d - 1) matrices A(1), ..., A(N) is an element of H-d(R) (resp. H-d(C)) which have the almost everywhere phase retrieval property. Our results are an extension of almost everywhere phase retrieval from the standard phase retrieval to the general setting and the proofs are often based on some new ideas about determinant variety. (C) 2020 Elsevier Inc. All rights reserved.
关键词	Frames Phase retrieval
DOI	10.1016/j.acha.2020.08.002
收录类别	SCI
语种	英语
资助项目	Hong Kong Research Grant Council[16306415] ; Beijing Natural Science Foundation[Z180002] ; NSFC[11688101]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000579922900002
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/52311
专题	中国科学院数学与系统科学研究院
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.Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Clear Water Bay, Hong Kong, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Huang, Meng,Rong, Yi,Wang, Yang,et al. Almost everywhere generalized phase retrieval[J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,2021,50:16-33.
APA	Huang, Meng,Rong, Yi,Wang, Yang,&Xu, Zhiqiang.(2021).Almost everywhere generalized phase retrieval.APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,50,16-33.
MLA	Huang, Meng,et al."Almost everywhere generalized phase retrieval".APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 50(2021):16-33.