Noise Reduction as an Inverse Problem in F-Transform Modelling

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F22%3AA2302G3M" target="_blank" >RIV/61988987:17610/22:A2302G3M - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/content/pdf/10.1007/978-3-031-08974-9_32.pdf" target="_blank" >https://link.springer.com/content/pdf/10.1007/978-3-031-08974-9_32.pdf</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-031-08974-9_32" target="_blank" >10.1007/978-3-031-08974-9_32</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Noise Reduction as an Inverse Problem in F-Transform Modelling

Popis výsledku v původním jazyce

In this paper, we discuss a special type of fuzzy partitioned space generated by a fuzzy set that is used to enrich the data domain with a notion of closeness. We utilize this notion to sketch the solution to the denoising problem in the discrete, now only 1-D setting, where the Nyquist-Shannon-Kotelnikov sampling theorem in not applicable. The finite-dimensional space with closeness is described by a closeness matrix that transforms discrete one-dimensional signals (considered as functions defined on the space and identified with high-dimensional vectors) into a lower-dimensional vectors. On the basis of this and the corresponding pseudo-inverse transformation, we characterize the signal denoising problem as a type of inverse problem. This opens a new perspective on discrete data processing involving algebraic tools and singular value matrix decomposition. As there are many degrees of freedom in initializing parameters of the chosen model, we restrict ourselves on some special cases. The link between the generating function of the fuzzy partition and a fundamental subspace of the closeness matrix is expressed in terms of Euclidean orthogonality. The theoretical background as well as solutions in particular settings are illustrated by numerical examples.

Název v anglickém jazyce

Noise Reduction as an Inverse Problem in F-Transform Modelling

Popis výsledku anglicky

In this paper, we discuss a special type of fuzzy partitioned space generated by a fuzzy set that is used to enrich the data domain with a notion of closeness. We utilize this notion to sketch the solution to the denoising problem in the discrete, now only 1-D setting, where the Nyquist-Shannon-Kotelnikov sampling theorem in not applicable. The finite-dimensional space with closeness is described by a closeness matrix that transforms discrete one-dimensional signals (considered as functions defined on the space and identified with high-dimensional vectors) into a lower-dimensional vectors. On the basis of this and the corresponding pseudo-inverse transformation, we characterize the signal denoising problem as a type of inverse problem. This opens a new perspective on discrete data processing involving algebraic tools and singular value matrix decomposition. As there are many degrees of freedom in initializing parameters of the chosen model, we restrict ourselves on some special cases. The link between the generating function of the fuzzy partition and a fundamental subspace of the closeness matrix is expressed in terms of Euclidean orthogonality. The theoretical background as well as solutions in particular settings are illustrated by numerical examples.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název statě ve sborníku

Information Processing and Management of Uncertainty in Knowledge-Based Systems

ISBN

978-3-031-08973-2

ISSN

1865-0929

e-ISSN

1865-0937

Počet stran výsledku

13

Strana od-do

405-417

Název nakladatele

Springer Nature Switzerland AG

Místo vydání

Cham

Místo konání akce

Milan, Italy

Datum konání akce

11. 7. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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