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

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 ℓ₁-minimization whatever the sparsity of sparse polynomials is, while the recovery guarantee given in this paper is roughly the same as that of ℓ₁-minimization when the sparsity is less than 93. Finally, the numerical experiments verify the availability of the theoretical results.