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Fast and efficient computation of high‐order Tchebichef polynomials

Abdulhussain, SH, Mahmmod, BM, Baker, T and Al‐Jumeily, D (2022) Fast and efficient computation of high‐order Tchebichef polynomials. Concurrency and Computation: Practice and Experience. ISSN 1532-0626

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Discrete Tchebichef polynomials (DTPs) and their moments are effectively utilized in different fields such as video and image coding due to their remarkable performance. However, when the moments order becomes large (high), DTPs prone to exhibit numerical instabilities. In this paper, a computationally efficient and numerically stable recurrence algorithm is proposed for high order. The proposed algorithm is based on combining two recurrence algorithms. In addition, an adaptive threshold is used to stabilize the generation of the DTP coefficients. The designed algorithm can generate the DTP coefficients for high order and large signal size. To evaluate the performance of the proposed algorithm, a comparison study is performed with state-of-the-art algorithms in terms of computational cost and capability of generating DTPs with large size and high order. The results show that the proposed algorithm has a remarkable low computation cost and numerically stable compared to other algorithms. The improvement shows that the computation of the polynomial for a limited order is 27x times faster than the efficient algorithm.

Item Type: Article
Additional Information: This is the peer reviewed version of the following article: Abdulhussain SH, Mahmmod BM, Baker T, Al-Jumeily D. Fast and accurate computation of high-order Tchebichef polynomials. Concurrency Computat Pract Exper. 2022;e7311. doi: 10.1002/cpe.7311, which has been published in final form at 10.1002/cpe.7311. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.
Uncontrolled Keywords: Distributed Computing; 0801 Artificial Intelligence and Image Processing; 0803 Computer Software; 0805 Distributed Computing
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Computer Science & Mathematics
Publisher: Wiley
SWORD Depositor: A Symplectic
Date Deposited: 20 Sep 2022 08:40
Last Modified: 14 Feb 2024 10:45
DOI or ID number: 10.1002/cpe.7311
URI: https://researchonline.ljmu.ac.uk/id/eprint/17598
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