Noise Reduction as an Inverse Problem in F-Transform Modelling

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Noise Reduction as an Inverse Problem in F-Transform Modelling
Original language description
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.
Czech name
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Czech description
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Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Information Processing and Management of Uncertainty in Knowledge-Based Systems
ISBN
978-3-031-08973-2
ISSN
1865-0929
e-ISSN
1865-0937
Number of pages
13
Pages from-to
405-417
Publisher name
Springer Nature Switzerland AG
Place of publication
Cham
Event location
Milan, Italy
Event date
Jul 11, 2022
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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