On the Constrained Minimal Singular Values for Sparse Signal Recovery

被引:9
作者
Zhang, Hui [1 ]
Cheng, Lizhi [1 ]
机构
[1] Natl Univ Def Technol, Dept Math & Syst Sci, Coll Sci, Changsha 410073, Hunan, Peoples R China
基金
美国国家科学基金会;
关键词
l(1)-constrained minimal singular value; sparse recovery; structured random matrices; width of l(1)-truncated set; CONSTRUCTIONS;
D O I
10.1109/LSP.2012.2203802
中图分类号
TM [电工技术]; TN [电子技术、通信技术];
学科分类号
0808 ; 0809 ;
摘要
The l(1)-constrained minimal singular value (l(1) - CMSV) of the sensing matrix for sparse signal recovery is investigated in this letter. By exploiting certain geometrical properties of the (l(1) - CMSV) we derive new sufficient conditions for the recovery of both exactly and approximately sparse signals. Moreover, we demonstrate that a class of structured random matrices, including the Fourier random matrices and the Hadamard random matrices, can satisfy these sufficient conditions by showing their l(1) - CMSV are bounded away from zero with high probability, as long as the number of measurements is reasonablely large.
引用
收藏
页码:499 / 502
页数:4
相关论文
共 17 条
[1]  
[Anonymous], 2010, Theoretical foundations and numerical methods for sparse recovery, DOI DOI 10.1515/9783110226157.1
[2]   Decay properties of restricted isometry constants [J].
Blanchard, Jeffey D. ;
Cartis, Coralia ;
Tanner, Jared .
IEEE Signal Processing Letters, 2009, 16 (07) :572-575
[3]   Compressed Sensing: How Sharp Is the Restricted Isometry Property? [J].
Blanchard, Jeffrey D. ;
Cartis, Coralia ;
Tanner, Jared .
SIAM REVIEW, 2011, 53 (01) :105-125
[4]   EXPLICIT CONSTRUCTIONS OF RIP MATRICES AND RELATED PROBLEMS [J].
Bourgain, Jean ;
Dilworth, Stephen ;
Ford, Kevin ;
Konyagin, Sergei ;
Kutzarova, Denka .
DUKE MATHEMATICAL JOURNAL, 2011, 159 (01) :145-185
[5]   Stable Recovery of Sparse Signals and an Oracle Inequality [J].
Cai, Tony Tony ;
Wang, Lie ;
Xu, Guangwu .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2010, 56 (07) :3516-3522
[6]  
Candes E. J., 2008, COMPTE RENDUS ACAD S, V346
[7]   Robust uncertainty principles:: Exact signal reconstruction from highly incomplete frequency information [J].
Candès, EJ ;
Romberg, J ;
Tao, T .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (02) :489-509
[8]   Decoding by linear programming [J].
Candes, EJ ;
Tao, T .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2005, 51 (12) :4203-4215
[9]  
Chafai D., 2011, INTERACTIONS BETWEEN
[10]  
Cohen A, 2009, J AM MATH SOC, V22, P211