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reconstruction of sparse polynomialS VIA QUASI-ORTHOGONAL MATCHING PURSUIT METHOD

Journal of Computational Mathematics 2023年第1期41卷 18-38页

作者： Renzhong Feng Aitong Huang Ming-Jun Lai Zhaiming Shen School of Mathematics Science&Key Laboratory of Mathematics Informatics and Behavioral SemanticsMinistry of EducationBeihang UniversityBeijing 100191China Department of Mathematics University of GeorgiaAthensGA 30602U.S.A

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 *** 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 *** results are also extended to general bounded orthogonal system including tensor product of these three univariate orthogonal ***,numerical experiments will be presented to verify the effectiveness of the QOMP method.

关键词： reconstruction of sparse polynomial Compressive sensing Mutual coherence Quasi-orthogonal matching pursuit algorithm

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The Recovery Guarantee for Orthogonal Matching Pursuit Method to Reconstruct sparse polynomials

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Numerical Mathematics(Theory,Methods and Applications) 2022年第3期15卷 793-818页

作者： Aitong Huang Renzhong Feng Sanpeng Zheng School of Mathematics Science&Key Laboratory of Mathematics Informatics and Behavioral SemanticsMinistry of EducationBeihang UniversityBeijingChina

Orthogonal matching pursuit(OMP for short)algorithm is a popular method of sparse signal recovery in compressed *** paper applies OMP to the sparse polynomial reconstruction *** 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 *** results show that the failure probability of OMP given in this paper is exponential small with respect to the number of sampling *** 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 ***,the numerical experiments verify the availability of the theoretical results.

关键词： reconstruction of sparse polynomial uniformly bounded orthogonal system orthogonal matching pursuit method probability of successful reconstruction sub-Gaussian random variable

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