Abstract
The computation of high-order discrete orthogonal moments is very complex and unstable due to fluctuations in numerical polynomial values. In this paper, we will present new algorithms for the stable computation of high-order discrete orthogonal Charlier polynomials and moments. These algorithms are based on the use of modified recurrence relations of Charlier polynomials with respect to the order n and with respect to the variable x, and on the use of the modified Gram-Schmidt orthonormalization process (GSOP). The algorithms in question allow the cancellation of terms that cause the numerical fluctuations of Charlier polynomial values during the recursive calculations. They also preserve the orthogonality property of high-order Charlier polynomials, which enables an efficient analysis of large-size bio-signals and 2D/3D images. Therefore, the simulation results prove the efficiency of the proposed algorithms when it comes to reconstructing large-size bio-signals and images.
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