Recovery of Low Rank Symmetric Matrices via Schatten p Norm Minimization

Li Cui; Lu Liu; Di Rong Chen; Jian Feng Xie

doi:10.1142/S0217595916500032

Recovery of Low Rank Symmetric Matrices via Schatten p Norm Minimization

Li Cui
, Lu Liu^*
, Di Rong Chen
, Jian Feng Xie

^*此作品的通讯作者

数学科学学院

Beihang University
Beijing Institute of Remote Sensing Information
Qian Xuesen Laboratory of Space Technology

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

In this paper, we give an application of the perturbation inequality to the low rank matrix recovery problem and provide a condition on the linear map of underdetermined linear system that every minimal rank symmetric matrix X ε ^m×n can be exactly recovered from the linear measurement b = (X) εℝ^q via some Schatten p0 norm minimization. Moreover it is shown that the explicit bound on exponent p0 in the Schatten p0 norm minimization can be exactly extracted.

源语言	英语
文章编号	1650003
期刊	Asia-Pacific Journal of Operational Research
卷	33
期	1
DOI	https://doi.org/10.1142/S0217595916500032
出版状态	已出版 - 1 2月 2016

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title = "Recovery of Low Rank Symmetric Matrices via Schatten p Norm Minimization",

abstract = "In this paper, we give an application of the perturbation inequality to the low rank matrix recovery problem and provide a condition on the linear map of underdetermined linear system that every minimal rank symmetric matrix X ε m×n can be exactly recovered from the linear measurement b = (X) εℝq via some Schatten p0 norm minimization. Moreover it is shown that the explicit bound on exponent p0 in the Schatten p0 norm minimization can be exactly extracted.",

keywords = "Rank minimization problem, Schatten p norm minimization, null space property, restricted isometry property, singular value decomposition",

author = "Li Cui and Lu Liu and Chen, \{Di Rong\} and Xie, \{Jian Feng\}",

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AU - Cui, Li

AU - Liu, Lu

AU - Chen, Di Rong

AU - Xie, Jian Feng

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Y1 - 2016/2/1

N2 - In this paper, we give an application of the perturbation inequality to the low rank matrix recovery problem and provide a condition on the linear map of underdetermined linear system that every minimal rank symmetric matrix X ε m×n can be exactly recovered from the linear measurement b = (X) εℝq via some Schatten p0 norm minimization. Moreover it is shown that the explicit bound on exponent p0 in the Schatten p0 norm minimization can be exactly extracted.

AB - In this paper, we give an application of the perturbation inequality to the low rank matrix recovery problem and provide a condition on the linear map of underdetermined linear system that every minimal rank symmetric matrix X ε m×n can be exactly recovered from the linear measurement b = (X) εℝq via some Schatten p0 norm minimization. Moreover it is shown that the explicit bound on exponent p0 in the Schatten p0 norm minimization can be exactly extracted.

KW - Rank minimization problem

KW - Schatten p norm minimization

KW - null space property

KW - restricted isometry property

KW - singular value decomposition

UR - https://www.scopus.com/pages/publications/84960441075

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DO - 10.1142/S0217595916500032

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JO - Asia-Pacific Journal of Operational Research

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M1 - 1650003

ER -

Recovery of Low Rank Symmetric Matrices via Schatten p Norm Minimization

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