TY - JOUR
T1 - The Recovery Guarantee for Orthogonal Matching Pursuit Method to Reconstruct Sparse Polynomials
AU - Huang , Aitong
AU - Feng , Renzhong
AU - Zheng , Sanpeng
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 793
EP - 818
PY - 2022
DA - 2022/07
SN - 15
DO - http://doi.org/10.4208/nmtma.OA-2022-0015
UR - https://global-sci.org/intro/article_detail/nmtma/20816.html
KW - Reconstruction of sparse polynomial, uniformly bounded orthogonal system, orthogonal matching pursuit method, probability of successful reconstruction, sub-Gaussian random variable.
AB - <p style="text-align: justify;">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.</p>