Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F23%3A00576213" target="_blank" >RIV/67985556:_____/23:00576213 - isvavai.cz</a>

Result on the web

<a href="https://ieeexplore.ieee.org/document/10271275" target="_blank" >https://ieeexplore.ieee.org/document/10271275</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/ACCESS.2023.3321969" target="_blank" >10.1109/ACCESS.2023.3321969</a>

Result language

angličtina

Original language name

Accelerated and Improved Stabilization for High Order Moments of Racah Polynomials

Original language description

Discrete Racah polynomials (DRPs) are highly efficient orthogonal polynomials widely used in various scientific fields for signal representation. They find applications in disciplines like image processing and computer vision. Racah polynomials were originally introduced by Wilson and later modified by Zhu to be orthogonal on a discrete set of samples. However, when the degree of the polynomial is high, it encounters numerical instability issues. In this paper, we propose a novel algorithm called Improved Stabilization (ImSt) for computing DRP coefficients. The algorithm partitions the DRP plane into asymmetric parts based on the polynomial size and DRP parameters. We have optimized the use of stabilizing conditions in these partitions. To compute the initial values, we employ the logarithmic gamma function along with a new formula. This combination enables us to compute the initial values efficiently for a wide range of DRP parameter values and large polynomial sizes. Additionally, we have derived a symmetry relation for the case when the Racah polynomial parameters are zero ($a=0$, $alpha=0$, $beta=0$). This symmetry makes the Racah polynomials symmetric, and we present a different algorithm for this specific scenario. We have demonstrated that the ImSt algorithm works for a broader range of parameters and higher degrees compared to existing algorithms. A comprehensive comparison between ImSt and the existing algorithms has been conducted, considering the maximum polynomial degree, computation time, restriction error analysis, and reconstruction error. The results of the comparison indicate that ImSt outperforms the existing algorithms for various values of Racah polynomial parameters.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

20201 - Electrical and electronic engineering

Project

<a href="/en/project/GA21-03921S" target="_blank" >GA21-03921S: Inverse problems in image processing</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

IEEE Access

ISSN

2169-3536

e-ISSN

2169-3536

Volume of the periodical

11

Issue of the periodical within the volume

1

Country of publishing house

AU - AUSTRALIA

Number of pages

20

Pages from-to

110502-110521

UT code for WoS article

001094808500001

EID of the result in the Scopus database

2-s2.0-85174839455