Trigonometric Fmn-transform of multi-variable functions and its application to the partial differential equations and image processing

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F22%3AA2302HZG" target="_blank" >RIV/61988987:17610/22:A2302HZG - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00500-022-07481-2" target="_blank" >https://link.springer.com/article/10.1007/s00500-022-07481-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00500-022-07481-2" target="_blank" >10.1007/s00500-022-07481-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Trigonometric Fmn-transform of multi-variable functions and its application to the partial differential equations and image processing

Popis výsledku v původním jazyce

In this study, we focus on the extention of the trigonometric $F$-transform for functions in one variable to: (i) a larger domain; (ii) a higher degree of the $F^m$-transform, and (iii) many-variable functions to improve its approximation properties over the entire domain and especially at its boundaries. In addition, the properties of approximation and convergence of direct and inverse extended and multidimensional trigonometric $F^{m}$-transforms are discussed. Then direct formulas for partial derivatives of functions of several variables are obtained in terms of trigonometric $F^{m}$-transforms, which are used to solve the Cauchy problem for the transport equation. A new image compression method is proposed and compared with well-established compression methods such as JPEG, JPEG 2000 and their less complex variations JPEG(APDCBT), JPEG(APUBT3), APUBT3-NUP, JPEG-FT. We have shown that this $^tbar{F}^ {11 }$-transform image compression method has high accuracy and reasonably low (irredicible) complexity.

Název v anglickém jazyce

Trigonometric Fmn-transform of multi-variable functions and its application to the partial differential equations and image processing

Popis výsledku anglicky

In this study, we focus on the extention of the trigonometric $F$-transform for functions in one variable to: (i) a larger domain; (ii) a higher degree of the $F^m$-transform, and (iii) many-variable functions to improve its approximation properties over the entire domain and especially at its boundaries. In addition, the properties of approximation and convergence of direct and inverse extended and multidimensional trigonometric $F^{m}$-transforms are discussed. Then direct formulas for partial derivatives of functions of several variables are obtained in terms of trigonometric $F^{m}$-transforms, which are used to solve the Cauchy problem for the transport equation. A new image compression method is proposed and compared with well-established compression methods such as JPEG, JPEG 2000 and their less complex variations JPEG(APDCBT), JPEG(APUBT3), APUBT3-NUP, JPEG-FT. We have shown that this $^tbar{F}^ {11 }$-transform image compression method has high accuracy and reasonably low (irredicible) complexity.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/EF17_049%2F0008414" target="_blank" >EF17_049/0008414: Centrum pro výzkum a vývoj metod umělé intelligence v automobilovém průmyslu regionu</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Soft Computing

ISSN

1432-7643

e-ISSN

1433-7479

Svazek periodika

—

Číslo periodika v rámci svazku

10

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

31

Strana od-do

13301-13331

Kód UT WoS článku

000864204500001

EID výsledku v databázi Scopus

2-s2.0-85139173741