Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
On a problem of reconstruction of discontinuities of a function by its attenuated ray transform along geodesics. / Derevtsov, Evgeny Yu; Maltseva, Svetlana V.; Svetov, Ivan E. и др.
International Conference "Functional Analysis In Interdisciplinary Applications", FAIA 2017. ред. / T Kalmenov; M Sadybekov. Том 1880 American Institute of Physics Inc., 2017. 060004 (AIP Conference Proceedings; Том 1880).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
}
TY - GEN
T1 - On a problem of reconstruction of discontinuities of a function by its attenuated ray transform along geodesics
AU - Derevtsov, Evgeny Yu
AU - Maltseva, Svetlana V.
AU - Svetov, Ivan E.
AU - Sultanov, Murat A.
N1 - Publisher Copyright: © 2017 Author(s).
PY - 2017/9/11
Y1 - 2017/9/11
N2 - 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.
AB - 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.
KW - SINGULAR SUPPORT
KW - VECTOR-FIELDS
KW - TOMOGRAPHY
UR - http://www.scopus.com/inward/record.url?scp=85029879117&partnerID=8YFLogxK
U2 - 10.1063/1.5000658
DO - 10.1063/1.5000658
M3 - Conference contribution
AN - SCOPUS:85029879117
VL - 1880
T3 - AIP Conference Proceedings
BT - International Conference "Functional Analysis In Interdisciplinary Applications", FAIA 2017
A2 - Kalmenov, T
A2 - Sadybekov, M
PB - American Institute of Physics Inc.
T2 - International Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017
Y2 - 2 October 2017 through 5 October 2017
ER -
ID: 9905657