TY - JOUR
T1 - Reconstruction of Sparse Polynomials via Quasi-Orthogonal Matching Pursuit Method
AU - Feng , Renzhong
AU - Huang , Aitong
AU - Lai , Ming-Jun
AU - Shen , Zhaiming
JO - Journal of Computational Mathematics
VL - 1
SP - 18
EP - 38
PY - 2022
DA - 2022/11
SN - 41
DO - http://doi.org/10.4208/jcm.2104-m2020-0250
UR - https://global-sci.org/intro/article_detail/jcm/21168.html
KW - Reconstruction of sparse polynomial, Compressive sensing, Mutual coherence, Quasi-orthogonal matching pursuit algorithm.
AB - <p style="text-align: justify;">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&nbsp; the QOMP algorithm which can reconstruct $s$-sparse Legendre polynomials, Chebyshev polynomials and&nbsp; 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.</p>