The Exact Support Recovery of Sparse Signals With Noise via Orthogonal Matching Pursuit

2013 ◽  
Vol 20 (4) ◽  
pp. 403-406 ◽  
Author(s):  
Rui Wu ◽  
Wei Huang ◽  
Di-Rong Chen
Keyword(s):  
Matching Pursuit ◽  
Orthogonal Matching Pursuit ◽  
Sparse Signals ◽  
Support Recovery

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.

Least Support Orthogonal Matching Pursuit Algorithm With Prior Information

2014 ◽  
Vol 6 (2) ◽  
pp. 111-134 ◽  
Author(s):  
Israa Sh. Tawfic ◽  
Sema Koc Kayhan
Keyword(s):  
Numerical Experiments ◽  
Prior Information ◽  
Matching Pursuit ◽  
Recovery Process ◽  
Orthogonal Matching Pursuit ◽  
Sparse Signal Recovery ◽  
Sparse Signals ◽  
Signal Recovery ◽  
Reconstruction Performance ◽  
Matching Pursuit Algorithm

Abstract This paper proposes a new fast matching pursuit technique named Partially Known Least Support Orthogonal Matching Pursuit (PKLS-OMP) which utilizes partially known support as a prior knowledge to reconstruct sparse signals from a limited number of its linear projections. The PKLS-OMP algorithm chooses optimum least part of the support at each iteration without need to test each candidate independently and incorporates prior signal information in the recovery process. We also derive sufficient condition for stable sparse signal recovery with the partially known support. Result shows that inclusion of prior information weakens the condition on the sensing matrices and needs fewer samples for successful reconstruction. Numerical experiments demonstrate that PKLS-OMP performs well compared to existing algorithms both in terms of reconstruction performance and execution time.

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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