KMS Of Academy of mathematics and systems sciences, CAS
| Phase retrieval from the magnitudes of affine linear measurements | |
Gao, Bing1; Sun, Qiyu2; Wang, Yang3; Xu, Zhiqiang1,4
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| 2018-02-01 | |
| Source Publication | ADVANCES IN APPLIED MATHEMATICS
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| ISSN | 0196-8858 |
| Volume | 93Pages:121-141 |
| Abstract | 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, |
| Keyword | Phase retrieval Frame Sparse signals Algebraic variety |
| DOI | 10.1016/j.aam.2017.09.004 |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000414112800005 |
| Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/29090 |
| Collection | 计算数学与科学工程计算研究所 |
| Corresponding Author | Xu, Zhiqiang |
| Affiliation | 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 |
| 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. |
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