Almost everywhere generalized phase retrieval

doi:10.1016/j.acha.2020.08.002

	Almost everywhere generalized phase retrieval
	Huang, Meng 2; Rong, Yi 3; Wang, Yang 3; Xu, Zhiqiang 1,2
刊名	APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
	2021
卷号	50 页码:16-33
关键词	Frames Phase retrieval
ISSN号	1063-5203
DOI	10.1016/j.acha.2020.08.002
英文摘要	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.
资助项目	Hong Kong Research Grant Council[16306415] ; Beijing Natural Science Foundation[Z180002] ; NSFC[11688101]
WOS研究方向	Mathematics
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000579922900002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/52310]
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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100190, Peoples R China 3.Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Clear Water Bay, Hong Kong, 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.