Almost everywhere generalized phase retrieval
Huang, Meng1; Rong, Yi2; Wang, Yang2; Xu, Zhiqiang1,3
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
Indexed BySCI
Funding ProjectHong Kong Research Grant Council[16306415] ; Beijing Natural Science Foundation[Z180002] ; NSFC[11688101]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000579922900002
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Document Type期刊论文
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.
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