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

Evgeny Yu Derevtsov, Svetlana V. Maltseva, Ivan E. Svetov, Murat A. Sultanov

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationInternational Conference "Functional Analysis In Interdisciplinary Applications", FAIA 2017
EditorsT Kalmenov, M Sadybekov
PublisherAmerican Institute of Physics Inc.
Number of pages9
Volume1880
ISBN (Electronic)9780735415607
DOIs
Publication statusPublished - 11 Sep 2017
EventInternational Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017 - Astana, Kazakhstan
Duration: 2 Oct 20175 Oct 2017

Publication series

NameAIP Conference Proceedings
PublisherAMER INST PHYSICS
Volume1880
ISSN (Print)0094-243X

Conference

ConferenceInternational Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017
CountryKazakhstan
CityAstana
Period02.10.201705.10.2017

Keywords

  • SINGULAR SUPPORT
  • VECTOR-FIELDS
  • TOMOGRAPHY

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