scholarly journals A Sharp Condition for Exact Support Recovery With Orthogonal Matching Pursuit

2017 ◽  
Vol 65 (6) ◽  
pp. 1370-1382 ◽  
Author(s):  
Jinming Wen ◽  
Zhengchun Zhou ◽  
Jian Wang ◽  
Xiaohu Tang ◽  
Qun Mo
Keyword(s):  
Matching Pursuit ◽  
Orthogonal Matching Pursuit ◽  
Sharp Condition ◽  
Support Recovery

scholarly journals On Probability of Support Recovery for Orthogonal Matching Pursuit Using Mutual Coherence

2017 ◽  
Vol 24 (11) ◽  
pp. 1646-1650 ◽  
Author(s):  
Ehsan Miandji ◽  
Mohammad Emadi ◽  
Jonas Unger ◽  
Ehsan Afshari
Keyword(s):  
Matching Pursuit ◽  
Orthogonal Matching Pursuit ◽  
Mutual Coherence ◽  
Support Recovery

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.

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