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dc.contributor.authorBrander, Tommi
dc.contributor.authorIlmavirta, Joonas
dc.contributor.authorPiiroinen, Petteri
dc.contributor.authorTyni, Teemu
dc.date.accessioned2020-12-15T14:16:42Z
dc.date.available2020-12-15T14:16:42Z
dc.date.issued2020
dc.identifier.citationBrander, T., Ilmavirta, J., Piiroinen, P., & Tyni, T. (2020). Optimal recovery of a radiating source with multiple frequencies along one line. <i>Inverse Problems and Imaging</i>, <i>14</i>(6), 967-983. <a href="https://doi.org/10.3934/ipi.2020044" target="_blank">https://doi.org/10.3934/ipi.2020044</a>
dc.identifier.otherCONVID_47332741
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/73223
dc.description.abstractWe study an inverse problem where an unknown radiating source is observed with collimated detectors along a single line and the medium has a known attenuation. The research is motivated by applications in SPECT and beam hardening. If measurements are carried out with frequencies ranging in an open set, we show that the source density is uniquely determined by these measurements up to averaging over levelsets of the integrated attenuation. This leads to a generalized Laplace transform. We also discuss some numerical approaches and demonstrate the results with several examples.en
dc.format.mimetypeapplication/pdf
dc.languageeng
dc.language.isoeng
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)
dc.relation.ispartofseriesInverse Problems and Imaging
dc.rightsIn Copyright
dc.subject.otherinverse source problem
dc.subject.othermultispectral
dc.subject.otherSPECT
dc.subject.otherLaplace transform
dc.subject.otherbeam hardening
dc.subject.othermultiplicative system theorem
dc.subject.otherattenuated Radon transform
dc.subject.otheruniqueness theorem
dc.subject.otherPET
dc.subject.otheremission computed tomography
dc.subject.othernuclear medicine.
dc.titleOptimal recovery of a radiating source with multiple frequencies along one line
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202012157168
dc.contributor.laitosMatematiikan ja tilastotieteen laitosfi
dc.contributor.laitosDepartment of Mathematics and Statisticsen
dc.contributor.oppiaineMatematiikkafi
dc.contributor.oppiaineInversio-ongelmien huippuyksikköfi
dc.contributor.oppiaineMathematicsen
dc.contributor.oppiaineCentre of Excellence in Inverse Problemsen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.type.coarhttp://purl.org/coar/resource_type/c_2df8fbb1
dc.description.reviewstatuspeerReviewed
dc.format.pagerange967-983
dc.relation.issn1930-8345
dc.relation.numberinseries6
dc.relation.volume14
dc.type.versionacceptedVersion
dc.rights.copyright© 2020 American Institute of Mathematical Sciences
dc.rights.accesslevelopenAccessfi
dc.relation.grantnumber295853
dc.subject.ysoinversio-ongelmat
dc.subject.ysotietokonetomografia
dc.subject.ysonumeerinen analyysi
dc.subject.ysokuvantaminen
dc.subject.ysosovellettu matematiikka
dc.subject.ysopositroniemissiotomografia
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p27912
jyx.subject.urihttp://www.yso.fi/onto/yso/p20535
jyx.subject.urihttp://www.yso.fi/onto/yso/p15833
jyx.subject.urihttp://www.yso.fi/onto/yso/p3532
jyx.subject.urihttp://www.yso.fi/onto/yso/p38113
jyx.subject.urihttp://www.yso.fi/onto/yso/p19539
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.3934/ipi.2020044
dc.relation.funderResearch Council of Finlanden
dc.relation.funderSuomen Akatemiafi
jyx.fundingprogramPostdoctoral Researcher, AoFen
jyx.fundingprogramTutkijatohtori, SAfi
jyx.fundinginformationT.B. was partially funded by grant no. 4002-00123 from the Danish Council for Independent Research | Natural Sciences and partially by the Research Council of Norway through the FRIPRO Toppforsk project "Waves and nonlinear phenomena". J.I. was supported by the Academy of Finland (decision 295853). T.T. was supported by the Academy of Finland (application number 312123, Centre of Excellence of Inverse Modelling and Imaging 2018–2025).
dc.type.okmA1


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