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Fast recursive computation of Krawtchouk polynomials

Krawtchouk polynomials (KPs) and their moments are used widely in the field of signal processing for their superior discriminatory properties. This study proposes a new fast recursive algorithm to compute Krawtchouk polynomial coefficients (KPCs). This algorithm is based on the symmetry property of...

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Main Authors: Abdulhussain, Sadiq H., Ramli, Abd Rahman, Sy Mohamed, Sy Abd Rahman Al-haddad, Mahmmod, Basheera M., Jassim, Wissam A.
Format: Article
Language:English
Published: Springer 2018
Online Access:http://psasir.upm.edu.my/id/eprint/72738/1/Fast%20recursive%20computation%20of%20Krawtchouk%20polynomials.pdf
http://psasir.upm.edu.my/id/eprint/72738/
https://link.springer.com/article/10.1007/s10851-017-0758-9#citeas
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spelling my.upm.eprints.727382021-01-30T02:02:50Z http://psasir.upm.edu.my/id/eprint/72738/ Fast recursive computation of Krawtchouk polynomials Abdulhussain, Sadiq H. Ramli, Abd Rahman Sy Mohamed, Sy Abd Rahman Al-haddad Mahmmod, Basheera M. Jassim, Wissam A. Krawtchouk polynomials (KPs) and their moments are used widely in the field of signal processing for their superior discriminatory properties. This study proposes a new fast recursive algorithm to compute Krawtchouk polynomial coefficients (KPCs). This algorithm is based on the symmetry property of KPCs along the primary and secondary diagonals of the polynomial array. The n−x plane of the KP array is partitioned into four triangles, which are symmetrical across the primary and secondary diagonals. The proposed algorithm computes the KPCs for only one triangle (partition), while the coefficients of the other three triangles (partitions) can be computed using the derived symmetry properties of the KP. Therefore, only N / 4 recursion times are required. The proposed algorithm can also be used to compute polynomial coefficients for different values of the parameter p in interval (0, 1). The performance of the proposed algorithm is compared with that in previous literature in terms of image reconstruction error, polynomial size, and computation cost. Moreover, the proposed algorithm is applied in a face recognition system to determine the impact of parameter p on feature extraction ability. Simulation results show that the proposed algorithm has a remarkable advantage over other existing algorithms for a wide range of parameters p and polynomial size N, especially in reducing the computation time and the number of operations utilized. Springer 2018 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/72738/1/Fast%20recursive%20computation%20of%20Krawtchouk%20polynomials.pdf Abdulhussain, Sadiq H. and Ramli, Abd Rahman and Sy Mohamed, Sy Abd Rahman Al-haddad and Mahmmod, Basheera M. and Jassim, Wissam A. (2018) Fast recursive computation of Krawtchouk polynomials. Journal of Mathematical Imaging and Vision, 60 (3). 285 - 303. ISSN 0924-9907; ESSN: 1573-7683 https://link.springer.com/article/10.1007/s10851-017-0758-9#citeas 10.1007/s10851-017-0758-9
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description Krawtchouk polynomials (KPs) and their moments are used widely in the field of signal processing for their superior discriminatory properties. This study proposes a new fast recursive algorithm to compute Krawtchouk polynomial coefficients (KPCs). This algorithm is based on the symmetry property of KPCs along the primary and secondary diagonals of the polynomial array. The n−x plane of the KP array is partitioned into four triangles, which are symmetrical across the primary and secondary diagonals. The proposed algorithm computes the KPCs for only one triangle (partition), while the coefficients of the other three triangles (partitions) can be computed using the derived symmetry properties of the KP. Therefore, only N / 4 recursion times are required. The proposed algorithm can also be used to compute polynomial coefficients for different values of the parameter p in interval (0, 1). The performance of the proposed algorithm is compared with that in previous literature in terms of image reconstruction error, polynomial size, and computation cost. Moreover, the proposed algorithm is applied in a face recognition system to determine the impact of parameter p on feature extraction ability. Simulation results show that the proposed algorithm has a remarkable advantage over other existing algorithms for a wide range of parameters p and polynomial size N, especially in reducing the computation time and the number of operations utilized.
format Article
author Abdulhussain, Sadiq H.
Ramli, Abd Rahman
Sy Mohamed, Sy Abd Rahman Al-haddad
Mahmmod, Basheera M.
Jassim, Wissam A.
spellingShingle Abdulhussain, Sadiq H.
Ramli, Abd Rahman
Sy Mohamed, Sy Abd Rahman Al-haddad
Mahmmod, Basheera M.
Jassim, Wissam A.
Fast recursive computation of Krawtchouk polynomials
author_facet Abdulhussain, Sadiq H.
Ramli, Abd Rahman
Sy Mohamed, Sy Abd Rahman Al-haddad
Mahmmod, Basheera M.
Jassim, Wissam A.
author_sort Abdulhussain, Sadiq H.
title Fast recursive computation of Krawtchouk polynomials
title_short Fast recursive computation of Krawtchouk polynomials
title_full Fast recursive computation of Krawtchouk polynomials
title_fullStr Fast recursive computation of Krawtchouk polynomials
title_full_unstemmed Fast recursive computation of Krawtchouk polynomials
title_sort fast recursive computation of krawtchouk polynomials
publisher Springer
publishDate 2018
url http://psasir.upm.edu.my/id/eprint/72738/1/Fast%20recursive%20computation%20of%20Krawtchouk%20polynomials.pdf
http://psasir.upm.edu.my/id/eprint/72738/
https://link.springer.com/article/10.1007/s10851-017-0758-9#citeas
_version_ 1690372575899680768
score 13.211869

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