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Robustness properties of dimensionality reduction with Gaussian random matrices
Han, Bin1; Xu, ZhiQiang2,3
2017-10-01
Source PublicationSCIENCE CHINA-MATHEMATICS
ISSN1674-7283
Volume60Issue:10Pages:1753-1778
AbstractIn this paper, motivated by the results in compressive phase retrieval, we study the robustness properties of dimensionality reduction with Gaussian random matrices having arbitrarily erased rows. We first study the robustness property against erasure for the almost norm preservation property of Gaussian random matrices by obtaining the optimal estimate of the erasure ratio for a small given norm distortion rate. As a consequence, we establish the robustness property of Johnson-Lindenstrauss lemma and the robustness property of restricted isometry property with corruption for Gaussian random matrices. Secondly, we obtain a sharp estimate for the optimal lower and upper bounds of norm distortion rates of Gaussian random matrices under a given erasure ratio. This allows us to establish the strong restricted isometry property with the almost optimal restricted isometry property (RIP) constants, which plays a central role in the study of phaseless compressed sensing. As a byproduct of our results, we also establish the robustness property of Gaussian random finite frames under erasure.
Keywordphase retrieval finite frames sparse approximation restricted isometry property Johnson-Lindenstrauss lemma
DOI10.1007/s11425-016-9018-x
Language英语
Funding ProjectNatural Sciences and Engineering Research Council of Canada[05865] ; National Natural Science Foundation of China[11422113] ; National Natural Science Foundation of China[91630203] ; National Natural Science Foundation of China[11021101] ; National Natural Science Foundation of China[11331012] ; National Basic Research Program of China (973 Program)[2015CB856000]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000410823100002
PublisherSCIENCE PRESS
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26582
Collection计算数学与科学工程计算研究所
Affiliation1.Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada
2.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Han, Bin,Xu, ZhiQiang. Robustness properties of dimensionality reduction with Gaussian random matrices[J]. SCIENCE CHINA-MATHEMATICS,2017,60(10):1753-1778.
APA Han, Bin,&Xu, ZhiQiang.(2017).Robustness properties of dimensionality reduction with Gaussian random matrices.SCIENCE CHINA-MATHEMATICS,60(10),1753-1778.
MLA Han, Bin,et al."Robustness properties of dimensionality reduction with Gaussian random matrices".SCIENCE CHINA-MATHEMATICS 60.10(2017):1753-1778.
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