Recovery of Low Rank Symmetric Matrices via Schatten p Norm Minimization

Li Cui, Lu Liu, Di-Rong Chen () and Jian-Feng Xie ()
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Li Cui: Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100191, P. R. China2Beijing Institute of Remote Sensing Information, Beijing 100192, P. R. China
Lu Liu: Qian Xuesen Laboratory of Space Technology, No. 104 Youyi Road, Haidian District, Beijing 100094, P. R. China
Di-Rong Chen: Department of Mathematics, Beijing University of Aeronautics and Astronautics, Beijing 100191, P. R. China
Jian-Feng Xie: Beijing Institute of Remote Sensing Information, Beijing 100192, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2016, vol. 33, issue 01, 1-11

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 ∈ ℝm×n can be exactly recovered from the linear measurement b = 𝒜(X) ∈ ℝq 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; singular value decomposition; restricted isometry property; null space property (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0217595916500032

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