Stable recovery of low-rank matrix via nonconvex Schatten p-minimization
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- 作者：WenGu Chen ; YaLing Li
- 关键词：low ; rank matrix recovery ; restricted isometry constant ; Schatten p ; minimization ; 90C26 ; 90C59 ; 65F35
- 刊名：SCIENCE CHINA Mathematics
- 出版年：2015
- 出版时间：December 2015
- 年：2015
- 卷：58
- 期：12
- 页码：2643-2654
- 全文大小：211 KB
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32.Wu R, Chen D R. The improved bounds of restricted isometry constant for recovery - 作者单位：WenGu Chen (1)
YaLing Li (2)
1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China
2. Graduate School, China Academy of Engineering Physics, Beijing, 100088, China - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Chinese Library of Science
Applications of Mathematics - 出版者：Science China Press, co-published with Springer
- ISSN：1869-1862
文摘
In this paper, a sufficient condition is obtained to ensure the stable recovery (? ?0) or exact recovery (? = 0) of all r-rank matrices X ??sup> m×n from \(b = \mathcal{A}(X) + z\) via nonconvex Schatten p-minimization for any \(\delta _{4r} \in \left[ {\frac{{\sqrt 3 }} {2},1} \right)\). Moreover, we determine the range of parameter p with any given δ\(\delta _{4r} \in \left[ {\frac{{\sqrt 3 }} {2},1} \right)\). In fact, for any given \(\delta _{4r} \in \left[ {\frac{{\sqrt 3 }} {2},1} \right)\), p ?(0, 2(1 ?δ4r)] suffices for the stable recovery or exact recovery of all r-rank matrices. Keywords low-rank matrix recovery restricted isometry constant Schatten p-minimization