robustnesspropertiesofdimensionalityreductionwithgaussianrandommatrices

	robustnesspropertiesofdimensionalityreductionwithgaussianrandommatrices
	Han Bin 1; Xu Zhiqiang2
	2017
Source Publication	sciencechinamathematics
ISSN	1674-7283
Volume	60 Issue:10 Pages:1753
Abstract	Abstract In 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.
Language	英语
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/44788
Collection	计算数学与科学工程计算研究所
Affiliation	1.阿尔伯塔大学 2.中国科学院数学与系统科学研究院
Recommended Citation GB/T 7714	Han Bin,Xu Zhiqiang. robustnesspropertiesofdimensionalityreductionwithgaussianrandommatrices[J]. sciencechinamathematics,2017,60(10):1753.
APA	Han Bin,&Xu Zhiqiang.(2017).robustnesspropertiesofdimensionalityreductionwithgaussianrandommatrices.sciencechinamathematics,60(10),1753.
MLA	Han Bin,et al."robustnesspropertiesofdimensionalityreductionwithgaussianrandommatrices".sciencechinamathematics 60.10(2017):1753.

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