CSpace
Almost everywhere generalized phase retrieval
Huang, Meng1; Rong, Yi2; Wang, Yang2; Xu, Zhiqiang1,3
2021
Source PublicationAPPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
ISSN1063-5203
Volume50Pages:16-33
AbstractThe aim of generalized phase retrieval is to recover x is an element of F-d from the quadratic measurements x*A(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.
KeywordFrames Phase retrieval
DOI10.1016/j.acha.2020.08.002
Indexed BySCI
Language英语
Funding ProjectHong Kong Research Grant Council[16306415] ; Beijing Natural Science Foundation[Z180002] ; NSFC[11688101]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000579922900002
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/52311
Collection中国科学院数学与系统科学研究院
Corresponding AuthorXu, Zhiqiang
Affiliation1.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
Recommended Citation
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.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Huang, Meng]'s Articles
[Rong, Yi]'s Articles
[Wang, Yang]'s Articles
Baidu academic
Similar articles in Baidu academic
[Huang, Meng]'s Articles
[Rong, Yi]'s Articles
[Wang, Yang]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Huang, Meng]'s Articles
[Rong, Yi]'s Articles
[Wang, Yang]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.