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Differential Equations and Uniqueness Theorems for the Generalized Attenuated Ray Transforms of Tensor Fields. / Derevtsov, Evgeny Yu; Volkov, Yuriy S.; Schuster, Thomas.

Numerical Computations: Theory and Algorithms - 3rd International Conference, NUMTA 2019, Revised Selected Papers. ред. / Yaroslav D. Sergeyev; Dmitri E. Kvasov; Yaroslav D. Sergeyev; Dmitri E. Kvasov. Springer Gabler, 2020. стр. 97-111 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Том 11974 LNCS).

Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование

Harvard

Derevtsov, EY, Volkov, YS & Schuster, T 2020, Differential Equations and Uniqueness Theorems for the Generalized Attenuated Ray Transforms of Tensor Fields. в YD Sergeyev, DE Kvasov, YD Sergeyev & DE Kvasov (ред.), Numerical Computations: Theory and Algorithms - 3rd International Conference, NUMTA 2019, Revised Selected Papers. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Том. 11974 LNCS, Springer Gabler, стр. 97-111, 3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019, Crotone, Италия, 15.06.2019. https://doi.org/10.1007/978-3-030-40616-5_8

APA

Derevtsov, E. Y., Volkov, Y. S., & Schuster, T. (2020). Differential Equations and Uniqueness Theorems for the Generalized Attenuated Ray Transforms of Tensor Fields. в Y. D. Sergeyev, D. E. Kvasov, Y. D. Sergeyev, & D. E. Kvasov (Ред.), Numerical Computations: Theory and Algorithms - 3rd International Conference, NUMTA 2019, Revised Selected Papers (стр. 97-111). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Том 11974 LNCS). Springer Gabler. https://doi.org/10.1007/978-3-030-40616-5_8

Vancouver

Derevtsov EY, Volkov YS, Schuster T. Differential Equations and Uniqueness Theorems for the Generalized Attenuated Ray Transforms of Tensor Fields. в Sergeyev YD, Kvasov DE, Sergeyev YD, Kvasov DE, Редакторы, Numerical Computations: Theory and Algorithms - 3rd International Conference, NUMTA 2019, Revised Selected Papers. Springer Gabler. 2020. стр. 97-111. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-40616-5_8

Author

Derevtsov, Evgeny Yu ; Volkov, Yuriy S. ; Schuster, Thomas. / Differential Equations and Uniqueness Theorems for the Generalized Attenuated Ray Transforms of Tensor Fields. Numerical Computations: Theory and Algorithms - 3rd International Conference, NUMTA 2019, Revised Selected Papers. Редактор / Yaroslav D. Sergeyev ; Dmitri E. Kvasov ; Yaroslav D. Sergeyev ; Dmitri E. Kvasov. Springer Gabler, 2020. стр. 97-111 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

BibTeX

@inproceedings{8944250baca44e58b092a93b41354772,
title = "Differential Equations and Uniqueness Theorems for the Generalized Attenuated Ray Transforms of Tensor Fields",
abstract = "Properties of operators of generalized attenuated ray transforms (ART) are investigated. Starting with Radon transform in the mathematical model of computer tomography, attenuated ray transform in emission tomography and longitudinal ray transform in tensor tomography, we come to the operators of ART of order k over symmetric m-tensor fields, depending on spatial and temporal variables. The operators of ART of order k over tensor fields contain complex-valued absorption, different weights, and depend on time. Connections between ART of various orders are established by means of application of linear part of transport equation. This connections lead to the inhomogeneous k-th order differential equations for the ART of order k over symmetric m-tensor field. The right hand parts of such equations are m-homogeneous polynomials containing the components of the tensor field as the coefficients. The polynomial variables are the components (formula presented) of direction vector (formula presented) participating in differential part of transport equation. Uniqueness theorems of boundary-value and initial boundary-value problems for the obtained equations are proved, with significant application of Gauss-Ostrogradsky theorem. The connections of specified operators with integral geometry of tensor fields, emission tomography, photometry and wave optics allow to treat the problem of inversion of the ART of order k as the inverse problem of determining the right hand part of certain differential equation.",
keywords = "Attenuated ray transform, Boundary-value problem, Tensor tomography, Transport equation, Uniqueness theorem, DYNAMIC INVERSE PROBLEMS, OPTICAL COHERENCE TOMOGRAPHY, EFFICIENT ALGORITHMS, VECTOR-FIELDS, REGULARIZATION, POLARIZATION",
author = "Derevtsov, {Evgeny Yu} and Volkov, {Yuriy S.} and Thomas Schuster",
year = "2020",
month = jan,
day = "1",
doi = "10.1007/978-3-030-40616-5_8",
language = "English",
isbn = "9783030406158",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Gabler",
pages = "97--111",
editor = "Sergeyev, {Yaroslav D.} and Kvasov, {Dmitri E.} and Sergeyev, {Yaroslav D.} and Kvasov, {Dmitri E.}",
booktitle = "Numerical Computations",
address = "Germany",
note = "3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019 ; Conference date: 15-06-2019 Through 21-06-2019",

}

RIS

TY - GEN

T1 - Differential Equations and Uniqueness Theorems for the Generalized Attenuated Ray Transforms of Tensor Fields

AU - Derevtsov, Evgeny Yu

AU - Volkov, Yuriy S.

AU - Schuster, Thomas

PY - 2020/1/1

Y1 - 2020/1/1

N2 - Properties of operators of generalized attenuated ray transforms (ART) are investigated. Starting with Radon transform in the mathematical model of computer tomography, attenuated ray transform in emission tomography and longitudinal ray transform in tensor tomography, we come to the operators of ART of order k over symmetric m-tensor fields, depending on spatial and temporal variables. The operators of ART of order k over tensor fields contain complex-valued absorption, different weights, and depend on time. Connections between ART of various orders are established by means of application of linear part of transport equation. This connections lead to the inhomogeneous k-th order differential equations for the ART of order k over symmetric m-tensor field. The right hand parts of such equations are m-homogeneous polynomials containing the components of the tensor field as the coefficients. The polynomial variables are the components (formula presented) of direction vector (formula presented) participating in differential part of transport equation. Uniqueness theorems of boundary-value and initial boundary-value problems for the obtained equations are proved, with significant application of Gauss-Ostrogradsky theorem. The connections of specified operators with integral geometry of tensor fields, emission tomography, photometry and wave optics allow to treat the problem of inversion of the ART of order k as the inverse problem of determining the right hand part of certain differential equation.

AB - Properties of operators of generalized attenuated ray transforms (ART) are investigated. Starting with Radon transform in the mathematical model of computer tomography, attenuated ray transform in emission tomography and longitudinal ray transform in tensor tomography, we come to the operators of ART of order k over symmetric m-tensor fields, depending on spatial and temporal variables. The operators of ART of order k over tensor fields contain complex-valued absorption, different weights, and depend on time. Connections between ART of various orders are established by means of application of linear part of transport equation. This connections lead to the inhomogeneous k-th order differential equations for the ART of order k over symmetric m-tensor field. The right hand parts of such equations are m-homogeneous polynomials containing the components of the tensor field as the coefficients. The polynomial variables are the components (formula presented) of direction vector (formula presented) participating in differential part of transport equation. Uniqueness theorems of boundary-value and initial boundary-value problems for the obtained equations are proved, with significant application of Gauss-Ostrogradsky theorem. The connections of specified operators with integral geometry of tensor fields, emission tomography, photometry and wave optics allow to treat the problem of inversion of the ART of order k as the inverse problem of determining the right hand part of certain differential equation.

KW - Attenuated ray transform

KW - Boundary-value problem

KW - Tensor tomography

KW - Transport equation

KW - Uniqueness theorem

KW - DYNAMIC INVERSE PROBLEMS

KW - OPTICAL COHERENCE TOMOGRAPHY

KW - EFFICIENT ALGORITHMS

KW - VECTOR-FIELDS

KW - REGULARIZATION

KW - POLARIZATION

UR - http://www.scopus.com/inward/record.url?scp=85080901810&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-40616-5_8

DO - 10.1007/978-3-030-40616-5_8

M3 - Conference contribution

AN - SCOPUS:85080901810

SN - 9783030406158

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 97

EP - 111

BT - Numerical Computations

A2 - Sergeyev, Yaroslav D.

A2 - Kvasov, Dmitri E.

A2 - Sergeyev, Yaroslav D.

A2 - Kvasov, Dmitri E.

PB - Springer Gabler

T2 - 3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019

Y2 - 15 June 2019 through 21 June 2019

ER -

ID: 23738286