Generalized Fuzzy Transform and Non-Local Laplace Operator

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F24%3AA25038Z1" target="_blank" >RIV/61988987:17610/24:A25038Z1 - isvavai.cz</a>

Výsledek na webu

<a href="https://ieeexplore.ieee.org/document/10740054/" target="_blank" >https://ieeexplore.ieee.org/document/10740054/</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/tfuzz.2024.3489227" target="_blank" >10.1109/tfuzz.2024.3489227</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Generalized Fuzzy Transform and Non-Local Laplace Operator

Popis výsledku v původním jazyce

The F-transform has proven to be effective in various applications such as time series analysis, numerical solutions of differential equations, and signal or image processing. The most important parameter of the F-transform is a fuzzy partition initially introduced for one-dimensional spaces, with a few generalizations to higher-dimensional spaces. However, these generalizations have a limited application to signals defined on domains with arbitrary geometry. To overcome this limitation, we propose using non-separable membership functions induced by kernels, allowing the application of the F-transform to more general domains. We introduce a universal concept of a fuzzy partition that includes a kernel representation, a fuzzy partition, and the corresponding F-transform. Additionally, we discuss the main properties of this generalized F-transform and characterize the non-local Laplace operator in terms of the F-transform. We also discuss image denoising as the main application and compare our results with state-of-the-art methods and different noise types and intensities.

Název v anglickém jazyce

Generalized Fuzzy Transform and Non-Local Laplace Operator

Popis výsledku anglicky

The F-transform has proven to be effective in various applications such as time series analysis, numerical solutions of differential equations, and signal or image processing. The most important parameter of the F-transform is a fuzzy partition initially introduced for one-dimensional spaces, with a few generalizations to higher-dimensional spaces. However, these generalizations have a limited application to signals defined on domains with arbitrary geometry. To overcome this limitation, we propose using non-separable membership functions induced by kernels, allowing the application of the F-transform to more general domains. We introduce a universal concept of a fuzzy partition that includes a kernel representation, a fuzzy partition, and the corresponding F-transform. Additionally, we discuss the main properties of this generalized F-transform and characterize the non-local Laplace operator in terms of the F-transform. We also discuss image denoising as the main application and compare our results with state-of-the-art methods and different noise types and intensities.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GF24-10177L" target="_blank" >GF24-10177L: Frakční a fuzzy-frakční transport v neuspořádaném prostředí</a><br>

Návaznosti

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

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

IEEE T FUZZY SYST

ISSN

1063-6706

e-ISSN

1941-0034

Svazek periodika

—

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

717-729

Kód UT WoS článku

001416196300003

EID výsledku v databázi Scopus

2-s2.0-85208372668