On a problem of reconstruction of discontinuities of a function by its attenuated ray transform along geodesics

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

2 Цитирования (Scopus)

Аннотация

A problem of reconstruction of the first kind discontinuities of a given in a unit disk B discontinuous function by its attenuated ray transform is considered. A mathematical model of an inhomogeneous medium includes known Riemannian metric and two positive functions. One of them describes a known absorption factor ϵ of the medium, and the other has the physical meaning of a distribution f of internal sources to be determined. The attenuated ray transform is the integrals of f with the weight depending on ϵ, which are evaluated along all geodesics in B, and are the initial data for the problem. The algorithm of approximate determination of lines of discontinuities of the function f having the discontinuities of the first kind is suggested and realized. The algorithm is investigated numerically. The results of simulation are satisfactory and allow to hope for the further development of the approach.

Язык оригиналаанглийский
Название основной публикацииInternational Conference "Functional Analysis In Interdisciplinary Applications", FAIA 2017
РедакторыT Kalmenov, M Sadybekov
ИздательAmerican Institute of Physics Inc.
Число страниц9
Том1880
ISBN (электронное издание)9780735415607
DOI
СостояниеОпубликовано - 11 сен 2017
СобытиеInternational Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017 - Astana, Казахстан
Продолжительность: 2 окт 20175 окт 2017

Серия публикаций

НазваниеAIP Conference Proceedings
ИздательAMER INST PHYSICS
Том1880
ISSN (печатное издание)0094-243X

Конференция

КонференцияInternational Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017
СтранаКазахстан
ГородAstana
Период02.10.201705.10.2017

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