scholarly journals A New Analysis for Support Performance with Block Generalized Orthogonal Matching Pursuit

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
C. Y. Xia ◽  
Z. L. Zhou ◽  
Chun-Bo Guo ◽  
Y. S. Hao ◽  
C. B. Hou
Keyword(s):  
Compressive Sensing ◽  
Matching Pursuit ◽  
Restricted Isometry Property ◽  
Orthogonal Matching Pursuit ◽  
Sparse Signals ◽  
Support Conditions ◽  
Generalized Orthogonal ◽  
Recovery Block ◽  
Block Structures

For recovering block-sparse signals with unknown block structures using compressive sensing, a block orthogonal matching pursuit- (BOMP-) like block generalized orthogonal matching pursuit (BgOMP) algorithm has been proposed recently. This paper focuses on support conditions of recovery of any K -sparse block signals incorporating BgOMP under the framework of restricted isometry property (RIP). The proposed support conditions guarantee that BgOMP can achieve accurate recovery block-sparse signals within k iterations.

scholarly journals A Sharp Bound on RIC in Generalized Orthogonal Matching Pursuit

2018 ◽  
Vol 61 (1) ◽  
pp. 40-54 ◽  
Author(s):  
Wengu Chen ◽  
Huanmin Ge
Keyword(s):  
Matching Pursuit ◽  
Natural Extension ◽  
Orthogonal Matching Pursuit ◽  
Sparse Signal ◽  
Sparse Signals ◽  
Sensing Matrix ◽  
Extra Condition ◽  
Exact Reconstruction ◽  
Restricted Isometry Constant ◽  
Generalized Orthogonal

AbstractThe generalized orthogonal matching pursuit (gOMP) algorithm has received much attention in recent years as a natural extension of the orthogonal matching pursuit (OMP). It is used to recover sparse signals in compressive sensing. In this paper, a new bound is obtained for the exact reconstruction of every K-sparse signal via the gOMP algorithm in the noiseless case. That is, if the restricted isometry constant (RIC) δNK+1 of the sensing matrix A satisfiesthen the gOMP can perfectly recover every K-sparse signal x from y = Ax. Furthermore, the bound is proved to be sharp. In the noisy case, the above bound on RIC combining with an extra condition on the minimum magnitude of the nonzero components of K-sparse signals can guarantee that the gOMP selects all of the support indices of the K-sparse signals.

scholarly journals A Sharp RIP Condition for Orthogonal Matching Pursuit

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Wei Dan
Keyword(s):  
Matching Pursuit ◽  
Restricted Isometry Property ◽  
Orthogonal Matching Pursuit ◽  
Sparse Signal ◽  
Sparse Signals

A restricted isometry property (RIP) conditionδK+KθK,1<1is known to be sufficient for orthogonal matching pursuit (OMP) to exactly recover everyK-sparse signalxfrom measurementsy=Φx. This paper is devoted to demonstrate that this condition is sharp. We construct a specific matrix withδK+KθK,1=1such that OMP cannot exactly recover someK-sparse signals.

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