Year: 2023
Author: Renzhong Feng, Aitong Huang, Ming-Jun Lai, Zhaiming Shen
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 1 : pp. 18–38
Abstract
In this paper, we propose a Quasi-Orthogonal Matching Pursuit (QOMP) algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal polynomials. For the two kinds of sampled data, data with noises and without noises, we apply the mutual coherence of measurement matrix to establish the convergence of the QOMP algorithm which can reconstruct $s$-sparse Legendre polynomials, Chebyshev polynomials and trigonometric polynomials in $s$ step iterations. The results are also extended to general bounded orthogonal system including tensor product of these three univariate orthogonal polynomials. Finally, numerical experiments will be presented to verify the effectiveness of the QOMP method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2104-m2020-0250
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 1 : pp. 18–38
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Reconstruction of sparse polynomial Compressive sensing Mutual coherence Quasi-orthogonal matching pursuit algorithm.