中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
首页 机构 成果 学者
  
  1. CAS IR Grid
  2. 数学与系统科学研究院
  3. 中国科学院数学与系统科学研究院
  4. 计算数学与科学工程计算研究所
Phase retrieval from the magnitudes of affine linear measurements

文献类型：期刊论文

作者Gao, Bing1; Sun, Qiyu2; Wang, Yang3; Xu, Zhiqiang1,4
刊名ADVANCES IN APPLIED MATHEMATICS
出版日期2018-02-01
卷号93页码:121-141
关键词Phase retrieval Frame Sparse signals Algebraic variety
ISSN号0196-8858
DOI10.1016/j.aam.2017.09.004
英文摘要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,
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
语种英语
WOS记录号WOS:000414112800005
出版者ACADEMIC PRESS INC ELSEVIER SCIENCE
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/29089]  
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.

入库方式： OAI收割

来源：数学与系统科学研究院

浏览0
下载0
收藏0
其他版本

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。