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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. et al.

International Conference "Functional Analysis In Interdisciplinary Applications", FAIA 2017. ed. / T Kalmenov; M Sadybekov. Vol. 1880 American Institute of Physics Inc., 2017. 060004 (AIP Conference Proceedings; Vol. 1880).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review

Harvard

Derevtsov, EY, Maltseva, SV, Svetov, IE & Sultanov, MA 2017, On a problem of reconstruction of discontinuities of a function by its attenuated ray transform along geodesics. in T Kalmenov & M Sadybekov (eds), International Conference "Functional Analysis In Interdisciplinary Applications", FAIA 2017. vol. 1880, 060004, AIP Conference Proceedings, vol. 1880, American Institute of Physics Inc., International Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017, Astana, Kazakhstan, 02.10.2017. https://doi.org/10.1063/1.5000658

APA

Derevtsov, E. Y., Maltseva, S. V., Svetov, I. E., & Sultanov, M. A. (2017). On a problem of reconstruction of discontinuities of a function by its attenuated ray transform along geodesics. In T. Kalmenov, & M. Sadybekov (Eds.), International Conference "Functional Analysis In Interdisciplinary Applications", FAIA 2017 (Vol. 1880). [060004] (AIP Conference Proceedings; Vol. 1880). American Institute of Physics Inc.. https://doi.org/10.1063/1.5000658

Vancouver

Derevtsov EY, Maltseva SV, Svetov IE, Sultanov MA. On a problem of reconstruction of discontinuities of a function by its attenuated ray transform along geodesics. In Kalmenov T, Sadybekov M, editors, International Conference "Functional Analysis In Interdisciplinary Applications", FAIA 2017. Vol. 1880. American Institute of Physics Inc. 2017. 060004. (AIP Conference Proceedings). doi: 10.1063/1.5000658

Author

Derevtsov, Evgeny Yu ; Maltseva, Svetlana V. ; Svetov, Ivan E. et al. / On a problem of reconstruction of discontinuities of a function by its attenuated ray transform along geodesics. International Conference "Functional Analysis In Interdisciplinary Applications", FAIA 2017. editor / T Kalmenov ; M Sadybekov. Vol. 1880 American Institute of Physics Inc., 2017. (AIP Conference Proceedings).

BibTeX

@inproceedings{a26fdd3e46eb423bac62102e5ffa3262,
title = "On a problem of reconstruction of discontinuities of a function by its attenuated ray transform along geodesics",
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.",
keywords = "SINGULAR SUPPORT, VECTOR-FIELDS, TOMOGRAPHY",
author = "Derevtsov, {Evgeny Yu} and Maltseva, {Svetlana V.} and Svetov, {Ivan E.} and Sultanov, {Murat A.}",
note = "Publisher Copyright: {\textcopyright} 2017 Author(s).; International Conference on Functional Analysis In Interdisciplinary Applications, FAIA 2017 ; Conference date: 02-10-2017 Through 05-10-2017",
year = "2017",
month = sep,
day = "11",
doi = "10.1063/1.5000658",
language = "English",
volume = "1880",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics Inc.",
editor = "T Kalmenov and M Sadybekov",
booktitle = "International Conference {"}Functional Analysis In Interdisciplinary Applications{"}, FAIA 2017",

}

RIS

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