The Recovery Guarantee for Orthogonal Matching Pursuit Method to Reconstruct Sparse Polynomials  

作　　者：Aitong Huang Renzhong Feng Sanpeng Zheng 

机构地区：[1]School of Mathematics Science&Key Laboratory of Mathematics,Informatics and Behavioral Semantics,Ministry of Education,Beihang University,Beijing,China

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2022年第3期793-818,共26页高等学校计算数学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant No.12071019).

摘　　要：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.

关 键 词：Reconstruction of sparse polynomial uniformly bounded orthogonal system orthogonal matching pursuit method probability of successful reconstruction sub-Gaussian random variable 

分 类 号：O17[理学—数学]