Year: 2022
Author: Sanpeng Zheng, Aitong Huang, Renzhong Feng, Sanpeng Zheng
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 3 : pp. 793–818
Abstract
Orthogonal matching pursuit (OMP for short) algorithm is a popular method of sparse signal recovery in compressed sensing. This paper applies OMP to the sparse polynomial reconstruction problem. Distinguishing from classical research methods using mutual coherence or restricted isometry property of the measurement matrix, the recovery guarantee and the success probability of OMP are obtained directly by the greedy selection ratio and the probability theory. The results show that the failure probability of OMP given in this paper is exponential small with respect to the number of sampling points. In addition, the recovery guarantee of OMP obtained through classical methods is lager than that of $ℓ_1$-minimization whatever the sparsity of sparse polynomials is, while the recovery guarantee given in this paper is roughly the same as that of $ℓ_1$-minimization when the sparsity is less than 93. Finally, the numerical experiments verify the availability of the theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2022-0015
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 3 : pp. 793–818
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Reconstruction of sparse polynomial uniformly bounded orthogonal system orthogonal matching pursuit method probability of successful reconstruction sub-Gaussian random variable.
Author Details
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The Sufficient Conditions for Orthogonal Matching Pursuit to Exactly Reconstruct Sparse Polynomials
Huang, Aitong
Feng, Renzhong
Wang, Andong
Mathematics, Vol. 10 (2022), Iss. 19 P.3703
https://doi.org/10.3390/math10193703 [Citations: 1]