Reconstruction of Sparse Polynomials via Quasi-Orthogonal Matching Pursuit Method

Reconstruction of Sparse Polynomials via Quasi-Orthogonal Matching Pursuit Method

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.

Author Details

Renzhong Feng

Aitong Huang

Ming-Jun Lai

Zhaiming Shen