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.

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 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.

A perturbation analysis based on group sparse representation with orthogonal matching pursuit

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Chunyan Liu ◽  
Feng Zhang ◽  
Wei Qiu ◽  
Chuan Li ◽  
Zhenbei Leng
Keyword(s):  
Numerical Study ◽  
Matching Pursuit ◽  
Sufficient Conditions ◽  
Schur Complement ◽  
Orthogonal Matching Pursuit ◽  
Sparse Signal ◽  
Sparse Signals ◽  
Actual Performance ◽  
Sharp Condition ◽  
Total Noise

AbstractIn this paper, by exploiting orthogonal projection matrix and block Schur complement, we extend the study to a complete perturbation model. Based on the block-restricted isometry property (BRIP), we establish some sufficient conditions for recovering the support of the block 𝐾-sparse signals via block orthogonal matching pursuit (BOMP) algorithm. Under some constraints on the minimum magnitude of the nonzero elements of the block 𝐾-sparse signals, we prove that the support of the block 𝐾-sparse signals can be exactly recovered by the BOMP algorithm in the case of \ell_{2} and \ell_{2}/\ell_{\infty} bounded total noise if 𝑨 satisfies the BRIP of order K+1 with\delta_{K+1}<\frac{1}{\sqrt{K+1}(1+\epsilon_{\boldsymbol{A}}^{(K+1)})^{2}}+\frac{1}{(1+\epsilon_{\boldsymbol{A}}^{(K+1)})^{2}}-1.In addition, we also show that this is a sharp condition for exactly recovering any block 𝐾-sparse signal with the BOMP algorithm. Moreover, we also give the reconstruction upper bound of the error between the recovered block-sparse signal and the original block-sparse signal. In the noiseless and perturbed case, we also prove that the BOMP algorithm can exactly recover the block 𝐾-sparse signal under some constraints on the block 𝐾-sparse signal and\delta_{K+1}<\frac{2+\sqrt{2}}{2(1+\epsilon_{\boldsymbol{A}}^{(K+1)})^{2}}-1.Finally, we compare the actual performance of perturbed OMP and perturbed BOMP algorithm in the numerical study. We also present some numerical experiments to verify the main theorem by using the completely perturbed BOMP algorithm.

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.

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