s-Goodness for Low-Rank Matrix Recovery
Joint Authors
Tunçel, Levent
Xiu, Naihua
Kong, Lingchen
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-04-09
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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 ?? 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, γs 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.
American Psychological Association (APA)
Kong, Lingchen& Tunçel, Levent& Xiu, Naihua. 2013. s-Goodness for Low-Rank Matrix Recovery. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-446426
Modern Language Association (MLA)
Kong, Lingchen…[et al.]. s-Goodness for Low-Rank Matrix Recovery. Abstract and Applied Analysis No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-446426
American Medical Association (AMA)
Kong, Lingchen& Tunçel, Levent& Xiu, Naihua. s-Goodness for Low-Rank Matrix Recovery. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-446426
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-446426