The efficiency of using Orthogonal Matching Pursuit in compressed sensing

被引：0
作者：
Ye, Peixin
Wei, Xiujie
机构：
[1] Nankai Univ, Sch Math, Tianjin, Peoples R China
[2] Nankai Univ, LPMC, Tianjin, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING | 2015年 / 15卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Orthogonal Matching Pursuit; Restricted Isometry Property (RIP); compressed sensing; K-sparse signal;
D O I：
10.3233/JCM-150558
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
We investigate the efficiency of compressed sensing by using Orthogonal Matching Pursuit. We prove that if the sampling Matrix phi has coherence less than 1/20K0.8 and satisfies the Restricted Isometry Property (RIP) of order [CK1.2] with constant delta = cK(-0.2), then every K-sparse signal x can be recovered from measure values y = Phi(x) via Orthogonal Matching Pursuit in at most optimal approximation on the first [CK1.2] iterations.
引用
收藏
页码：459 / 466
页数：8
相关论文
共 19 条
[1]   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
[2]  
Candes EJ, 2006, P INT C MATHEMATICIA, V3, P1433, DOI DOI 10.4171/022-3/69
[3]   Analysis of Orthogonal Matching Pursuit Using the Restricted Isometry Property [J].
Davenport, Mark A. ;
Wakin, Michael B. .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2010, 56 (09) :4395-4401
[4]   Some remarks on greedy algorithms [J].
DeVore, RA ;
Temlyakov, VN .
ADVANCES IN COMPUTATIONAL MATHEMATICS, 1996, 5 (2-3) :173-187
[5]   On Lebesgue-type inequalities for greedy approximation [J].
Donoho, D. L. ;
Elad, M. ;
Temlyakov, V. N. .
JOURNAL OF APPROXIMATION THEORY, 2007, 147 (02) :185-195
[6]   Sparse Solution of Underdetermined Systems of Linear Equations by Stagewise Orthogonal Matching Pursuit [J].
Donoho, David L. ;
Tsaig, Yaakov ;
Drori, Iddo ;
Starck, Jean-Luc .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2012, 58 (02) :1094-1121
[7]   Compressed sensing [J].
Donoho, DL .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (04) :1289-1306
[8]   Stable recovery of sparse overcomplete representations in the presence of noise [J].
Donoho, DL ;
Elad, M ;
Temlyakov, VN .
IEEE TRANSACTIONS ON INFORMATION THEORY, 2006, 52 (01) :6-18
[9]  
Gilbert AC, 2003, SIAM PROC S, P243
[10]   DIAMETERS OF SOME FINITE-DIMENSIONAL SETS AND CLASSES OF SMOOTH FUNCTIONS [J].
KASIN, BS .
MATHEMATICS OF THE USSR-IZVESTIYA, 1977, 11 (02) :317-333
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