dc.contributor.author | Railo, Jesse | |
dc.date.accessioned | 2020-08-03T07:12:53Z | |
dc.date.available | 2020-08-03T07:12:53Z | |
dc.date.issued | 2020 | |
dc.identifier.citation | Railo, J. (2020). Fourier Analysis of Periodic Radon Transforms. <i>Journal of Fourier Analysis and Applications</i>, <i>26</i>(4), Article 64. <a href="https://doi.org/10.1007/s00041-020-09775-1" target="_blank">https://doi.org/10.1007/s00041-020-09775-1</a> | |
dc.identifier.other | CONVID_41671248 | |
dc.identifier.uri | https://jyx.jyu.fi/handle/123456789/71312 | |
dc.description.abstract | We study reconstruction of an unknown function from its d-plane Radon transform on the flat torus {\mathbb {T}}^n = {\mathbb {R}}^n /{\mathbb {Z}}^n when 1 \le d \le n-1. We prove new reconstruction formulas and stability results with respect to weighted Bessel potential norms. We solve the associated Tikhonov minimization problem on H^s Sobolev spaces using the properties of the adjoint and normal operators. One of the inversion formulas implies that a compactly supported distribution on the plane with zero average is a weighted sum of its X-ray data. | en |
dc.format.mimetype | application/pdf | |
dc.language | eng | |
dc.language.iso | eng | |
dc.publisher | Springer; Birkhäuser | |
dc.relation.ispartofseries | Journal of Fourier Analysis and Applications | |
dc.rights | CC BY 4.0 | |
dc.subject.other | Radon transform | |
dc.subject.other | Fourier analysis | |
dc.subject.other | periodic distributions | |
dc.subject.other | regularization | |
dc.title | Fourier Analysis of Periodic Radon Transforms | |
dc.type | article | |
dc.identifier.urn | URN:NBN:fi:jyu-202008035460 | |
dc.contributor.laitos | Matematiikan ja tilastotieteen laitos | fi |
dc.contributor.laitos | Department of Mathematics and Statistics | en |
dc.contributor.oppiaine | Matematiikka | fi |
dc.contributor.oppiaine | Inversio-ongelmien huippuyksikkö | fi |
dc.contributor.oppiaine | Mathematics | en |
dc.contributor.oppiaine | Centre of Excellence in Inverse Problems | en |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
dc.type.coar | http://purl.org/coar/resource_type/c_2df8fbb1 | |
dc.description.reviewstatus | peerReviewed | |
dc.relation.issn | 1069-5869 | |
dc.relation.numberinseries | 4 | |
dc.relation.volume | 26 | |
dc.type.version | publishedVersion | |
dc.rights.copyright | © The Author(s) 2020 | |
dc.rights.accesslevel | openAccess | fi |
dc.relation.grantnumber | 284715 HY | |
dc.relation.grantnumber | 309963 | |
dc.format.content | fulltext | |
dc.rights.url | https://creativecommons.org/licenses/by/4.0/ | |
dc.relation.doi | 10.1007/s00041-020-09775-1 | |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Research Council of Finland | en |
dc.relation.funder | Suomen Akatemia | fi |
dc.relation.funder | Suomen Akatemia | fi |
jyx.fundingprogram | Centre of Excellence, AoF | en |
jyx.fundingprogram | Academy Project, AoF | en |
jyx.fundingprogram | Huippuyksikkörahoitus, SA | fi |
jyx.fundingprogram | Akatemiahanke, SA | fi |
jyx.fundinginformation | Open access funding provided by University of Jyväskylä (JYU). This work was supported by the Academy of Finland (Center of Excellence in Inverse Modelling and Imaging, Grant Numbers 284715 and 309963). | |
dc.type.okm | A1 | |