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2013 s -Goodness for Low-Rank Matrix Recovery
Lingchen Kong, Levent Tunçel, Naihua Xiu
Abstr. Appl. Anal. 2013(SI07): 1-9 (2013). DOI: 10.1155/2013/101974


Low-rank matrix recovery (LMR) is a rank minimization problem subject to linear equality constraints, and it arises in many fields such as signal and image processing, statistics, computer vision, and system identification and control. This class of optimization problems is generally 𝒩 𝒫 hard. A popular approach replaces the rank function with the nuclear norm of the matrix variable. In this paper, we extend and characterize the concept of s -goodness for a sensing matrix in sparse signal recovery (proposed by Juditsky and Nemirovski (Math Program, 2011)) to linear transformations in LMR. Using the two characteristic s -goodness constants, γ s and γ ^ s , of a linear transformation, we derive necessary and sufficient conditions for a linear transformation to be s -good. Moreover, we establish the equivalence of s -goodness and the null space properties. Therefore, s -goodness is a necessary and sufficient condition for exact s -rank matrix recovery via the nuclear norm minimization.


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Lingchen Kong. Levent Tunçel. Naihua Xiu. " s -Goodness for Low-Rank Matrix Recovery." Abstr. Appl. Anal. 2013 (SI07) 1 - 9, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1317.94027
MathSciNet: MR3044901
Digital Object Identifier: 10.1155/2013/101974

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI07 • 2013
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