CSpace  > 计算数学与科学工程计算研究所
Phase retrieval from the magnitudes of affine linear measurements
Gao, Bing1; Sun, Qiyu2; Wang, Yang3; Xu, Zhiqiang1,4
2018-02-01
Source PublicationADVANCES IN APPLIED MATHEMATICS
ISSN0196-8858
Volume93Pages:121-141
AbstractIn 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,
KeywordPhase retrieval Frame Sparse signals Algebraic variety
DOI10.1016/j.aam.2017.09.004
Language英语
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000414112800005
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Cited Times:1[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29090
Collection计算数学与科学工程计算研究所
Affiliation1.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
Recommended Citation
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.
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
[Gao, Bing]'s Articles
[Sun, Qiyu]'s Articles
[Wang, Yang]'s Articles
Baidu academic
Similar articles in Baidu academic
[Gao, Bing]'s Articles
[Sun, Qiyu]'s Articles
[Wang, Yang]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Gao, Bing]'s Articles
[Sun, Qiyu]'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.