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Generalized phase retrieval: Measurement number, matrix recovery and beyond

文献类型：期刊论文

作者Wang, Yang2; Xu, Zhiqiang1
刊名APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
出版日期2019-09-01
卷号47期号:2页码:423-446
关键词Phase retrieval Frames Fusion frames Fourier transform Measurement number Low rank matrix recovery Bilinear form Embedding
ISSN号1063-5203
DOI10.1016/j.acha.2017.09.003
英文摘要In this paper, we develop a framework of generalized phase retrieval in which one aims to reconstruct a vector x in R-d or C-d through quadratic samples x*A(1)x, ..., x*A(N)x. The generalized phase retrieval includes as special cases the standard phase retrieval as well as the phase retrieval by orthogonal projections. We first explore the connections among generalized phase retrieval, low-rank matrix recovery and nonsingular bilinear form. Motivated by the connections, we present results on the minimal measurement number needed for recovering a matrix that lies in a set W is an element of C-dxd. Applying the results to phase retrieval, we show that generic d x d matrices A(1), ..., A(N) have the phase retrieval property if N >= 2d - 1 in the real case and N >= 4d - 4 in the complex case for very general classes of A(1), ..., A(N), e.g. matrices with prescribed ranks or orthogonal projections. We also give lower bounds on the minimal measurement number required for generalized phase retrieval. For several classes of dimensions d we obtain the precise values of the minimal measurement number. Our work unifies and enhances results from the standard phase retrieval, phase retrieval by projections and low-rank matrix recovery. (C) 2017 Elsevier Inc. All rights reserved.
资助项目Hong Kong Research Grant Council[16306415] ; Hong Kong Research Grant Council[16317416] ; NSFC[11171336] ; NSFC[11422113] ; NSFC[11021101] ; NSFC[11331012] ; National Basic Research Program of China (973 Program)[2015CB856000]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000477689000006
出版者ACADEMIC PRESS INC ELSEVIER SCIENCE
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/35303]  
专题计算数学与科学工程计算研究所
通讯作者Wang, Yang
作者单位1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, Peoples R China
2.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		 Wang, Yang,Xu, Zhiqiang. Generalized phase retrieval: Measurement number, matrix recovery and beyond[J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,2019,47(2):423-446.
APA Wang, Yang,&Xu, Zhiqiang.(2019).Generalized phase retrieval: Measurement number, matrix recovery and beyond.APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,47(2),423-446.
MLA Wang, Yang,et al."Generalized phase retrieval: Measurement number, matrix recovery and beyond".APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 47.2(2019):423-446.

入库方式： OAI收割

来源：数学与系统科学研究院

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