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doi:10.22028/D291-36258
Titel: | Generalized attenuated ray transforms and their integral angular moments |
VerfasserIn: | Derevtsov, Evgeny Yu. Volkov, Yuriy S. Schuster, Thomas |
Sprache: | Englisch |
Titel: | Applied mathematics and computation |
Bandnummer: | 409 |
Verlag/Plattform: | Elsevier |
Erscheinungsjahr: | 2021 |
Freie Schlagwörter: | Tomography Attenuated ray transform Transport equation Boundary-value problem Uniqueness theorem Integral angular moment |
DDC-Sachgruppe: | 510 Mathematik |
Dokumenttyp: | Journalartikel / Zeitschriftenartikel |
Abstract: | In this article generalized attenuated ray transforms (ART) and integral angular moments are investigated. Starting from the Radon transform, the attenuated ray transform and the longitudinal ray transform, we derive the concept of ART-operators of order k over functions defined on the phase space and depending on time. The ART-operators are generalized for complex-valued absorption coefficient as well as weight functions of polynomial and exponential type. Connections between ART operators of various orders are established by means of the application of the linear part of a transport equation. These connections lead to inhomogeneous differential equations of order for the ART of order k. Uniqueness theorems for the corresponding boundary-value and initial boundary-value problems are proved. Properties of integral angular moments of order p are considered and connections between the moments of different orders are deduced. A close connection of the considered operators with mathematical models for tomography, physical optics and integral geometry allows to treat the inversion of ART of order k as an inverse problem of determining the right-hand side of a corresponding differential equation. |
DOI der Erstveröffentlichung: | 10.1016/j.amc.2020.125494 |
URL der Erstveröffentlichung: | https://www.sciencedirect.com/science/article/abs/pii/S0096300320304525 |
Link zu diesem Datensatz: | urn:nbn:de:bsz:291--ds-362580 hdl:20.500.11880/33041 http://dx.doi.org/10.22028/D291-36258 |
ISSN: | 0096-3003 |
Datum des Eintrags: | 8-Jun-2022 |
Drittmittel / Förderung: | DFG |
Fördernummer: | SCHU 1978/19-1 |
Fakultät: | MI - Fakultät für Mathematik und Informatik |
Fachrichtung: | MI - Mathematik |
Professur: | MI - Prof. Dr. Thomas Schuster |
Sammlung: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
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