Fast and efficient recursive algorithm of Meixner polynomials

Abstract

Meixner polynomials (MNPs) and their moments are considered significant feature extraction tools because of their salient representation in signal processing and computer vision. However, the existing recurrence algorithm of MNPs exhibits numerical instabilities of coefficients for high-order polynomials. This paper proposed a new recurrence algorithm to compute the coefficients of MNPs for high-order polynomials. The proposed algorithm is based on a derived identity for MNPs that reduces the number of the utilized recurrence times and the computed number of MNPs coefficients. To minimize the numerical errors, a new form of the recurrence algorithm is presented. The proposed algorithm computes $$\sim $$ 50% of the MNP coefficients. A comparison with different state-of-the-art algorithms is performed to evaluate the performance of the proposed recurrence algorithm in terms of computational cost and reconstruction error. In addition, an investigation is performed to find the maximum generated size. The results show that the proposed algorithm remarkably reduces the computational cost and increases the generated size of the MNPs. The proposed algorithm shows an average improvement of $$\sim $$ 77% in terms of computation cost. In addition, the proposed algorithm exhibits an improvement of $$\sim $$ 1269% in terms of generated size.