On the theory of function-valued mappings and its application to the processing of hyperspectral images

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dc.contributor.authorOtero, Daniel
dc.contributor.authorLa Torre, Davide
dc.contributor.authorMichailovich, Oleg
dc.contributor.authorVrscay, Edward R.
dc.creatorDaniel, Otero
dc.date.accessioned2017-12-20T09:19:03Z
dc.date.available2017-12-20T09:19:03Z
dc.date.issued2017-05-01
dc.description.abstractAbstract The concept of a mapping, which takes its values in an infinite-dimensional functional space, has been studied by the mathematical community since the third decade of the last century. This effort has produced a range of important contributions, many of which have already made their way to applied sciences, where they have been successfully used to facilitate numerous practical applications across various fields. Surprisingly enough, one particular field, which could have benefited from the above contributions to a much greater extent, still relies on finite-dimensional models and approximations, thus missing out on numerous advantages offered through adopting a more general framework. This field is image processing, which is in the focus of this study. In particular, in this paper, we introduce an alternative approach to the analysis of multidimensional imagery data based on the mathematical theory of function-valued mappings. In addition to extending various tools of standard functional calculus, we generalize the notions of Fourier and fractal transforms, followed by their application to processing of multispectral imaging data. Some applications and future extensions of this work are discussed as well.en_US
dc.identifierDOI:10.1016/j.sigpro.2016.12.014
dc.identifier.citationDaniel Otero, Davide La Torre, Oleg Michailovich, Edward R. Vrscay, On the theory of function-valued mappings and its application to the processing of hyperspectral images, In Signal Processing, Volume 134, 2017, Pages 185-196en_US
dc.identifier.issn01651684
dc.identifier.urihttps://www.sciencedirect.com/science/article/pii/S0165168416303565
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/2970
dc.language.isoenen_US
dc.publisherSignal Processingen_US
dc.relation.ispartofSignal Processing
dc.rights.license© 2016 Elsevier B.V. All rights reserved.
dc.subjectFunction-valued functionsen_US
dc.subjectImage processingen_US
dc.subjectBanach spacesen_US
dc.subjectFourier transformen_US
dc.subjectAnd fractal transformen_US
dc.titleOn the theory of function-valued mappings and its application to the processing of hyperspectral imagesen_US
dc.typeArticleen_US
elsevier.aggregationtypeJournal
elsevier.coverdate2017-05-01
elsevier.coverdisplaydateMay 2017
elsevier.endingpage196
elsevier.identifier.doi10.1016/j.sigpro.2016.12.014
elsevier.identifier.eid1-s2.0-S0165168416303565
elsevier.identifier.piiS0165-1684(16)30356-5
elsevier.identifier.scopusid85007390155
elsevier.openaccess0
elsevier.openaccessarticlefalse
elsevier.openarchivearticlefalse
elsevier.startingpage185
elsevier.teaserThe concept of a mapping, which takes its values in an infinite-dimensional functional space, has been studied by the mathematical community since the third decade of the last century. This effort has...
elsevier.volume134
workflow.import.sourcescience

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