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

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

1 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаанглийский
Название основной публикацииNumerical Computations
Подзаголовок основной публикацииTheory and Algorithms - 3rd International Conference, NUMTA 2019, Revised Selected Papers
РедакторыYaroslav D. Sergeyev, Dmitri E. Kvasov, Yaroslav D. Sergeyev, Dmitri E. Kvasov
ИздательSpringer Gabler
Страницы97-111
Число страниц15
ISBN (печатное издание)9783030406158
DOI
СостояниеОпубликовано - 1 янв 2020
Событие3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019 - Crotone, Италия
Продолжительность: 15 июн 201921 июн 2019

Серия публикаций

НазваниеLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Том11974 LNCS
ISSN (печатное издание)0302-9743
ISSN (электронное издание)1611-3349

Конференция

Конференция3rd Triennial International Conference and Summer School on Numerical Computations: Theory and Algorithms, NUMTA 2019
СтранаИталия
ГородCrotone
Период15.06.201921.06.2019

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