Analysis of orthogonal multi-matching pursuit under restricted isometry property  

作　　者：DAN Wei 

机构地区：[1]School of Mathematics and Statistics,Guangdong University of Finance & Economics

出　　处：《Science China Mathematics》2014年第10期2179-2188,共10页中国科学：数学（英文版）

基　　金：supported by the Science Foundation of Guangdong University of Finance & Economics(Grant No.13GJPY11002);National Natural Science Foundation of China(Grant Nos.11071031,11271060,11290143,U0935004 and U1135003);the Guangdong Natural Science Foundation(Grant No.S2012010010376);the Guangdong University and Colleges Technology Innovation Projects(Grant No.2012KJCX0048)

摘　　要：Orthogonal multi-matching pursuit（OMMP）is a natural extension of orthogonal matching pursuit（OMP）in the sense that N（N≥1）indices are selected per iteration instead of 1.In this paper,the theoretical performance of OMMP under the restricted isometry property（RIP）is presented.We demonstrate that OMMP can exactly recover any K-sparse signal from fewer observations y=φx,provided that the sampling matrixφsatisfiesδKN-N＋1＋√K/NθKN-N＋1,N〈1.Moreover,the performance of OMMP for support recovery from noisy observations is also discussed.It is shown that,for l_2 bounded and l_∞bounded noisy cases,OMMP can recover the true support of any K-sparse signal under conditions on the restricted isometry property of the sampling matrixφand the minimum magnitude of the nonzero components of the signal.Orthogonal multi-matching pursuit(OMMP)is a natural extension of orthogonal matching pursuit(OMP)in the sense that N(N≥1)indices are selected per iteration instead of 1.In this paper,the theoretical performance of OMMP under the restricted isometry property(RIP)is presented.We demonstrate that OMMP can exactly recover any K-sparse signal from fewer observations y=φx,provided that the sampling matrixφsatisfiesδKN-N+1+(K/N)^(1/2)θKN-N+1,N<1.Moreover,the performance of OMMP for support recovery from noisy observations is also discussed.It is shown that,for l_2 bounded and l_∞bounded noisy cases,OMMP can recover the true support of any K-sparse signal under conditions on the restricted isometry property of the sampling matrixφand the minimum magnitude of the nonzero components of the signal.

关 键 词：sparse recovery orthogonal matching pursuit restricted isometry property 

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