Generalized Fuzzy Transform and Non-Local Laplace Operator
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Generalized Fuzzy Transform and Non-Local Laplace Operator
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GF24-10177L" target="_blank" >GF24-10177L: Fractional and fuzzy-fractional transport in disordered environments</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IEEE T FUZZY SYST
ISSN
1063-6706
e-ISSN
1941-0034
Volume of the periodical
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Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
13
Pages from-to
717-729
UT code for WoS article
001416196300003
EID of the result in the Scopus database
2-s2.0-85208372668