Determination of Discontinuities of a Function in a Domain with Refraction from Its Attenuated Ray Transform

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Determination of Discontinuities of a Function in a Domain with Refraction from Its Attenuated Ray Transform. / Derevtsov, E. Yu; Maltseva, S. V.; Svetov, I. E.

In: Journal of Applied and Industrial Mathematics, Vol. 12, No. 4, 01.10.2018, p. 619-641.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{0e8814b4e9274673bd4d6b2a12978a3e,

title = "Determination of Discontinuities of a Function in a Domain with Refraction from Its Attenuated Ray Transform",

abstract = "Some results of numerical investigations are presented for the problem of determination of discontinuities of an unknown function that has the meaning of the internal source distribution and is given in a domain with absorption and refraction, on using the attenuated ray transform of the function. The refraction and the absorption coefficient are assumed to be given. The behavior of the available and newly constructed discontinuity indicator operators is investigated in some numerical tests. Some modification of discontinuity indicators was carried out for the purpose of applying them in the model of refractive tomography with absorption. Numerical methods are applied to investigate the possibility of using the operators of this kind for solving the problem of finding the discontinuities of a function from its attenuated ray transform; the degree is investigated of the influence on the recovery quality of such factors as the level of the noise introduced into the generated data, the parameters of metrics, the magnitude and variation of the absorption coefficient.",

keywords = "absorption, attenuated ray transform, back-projection, discontinuity indicator, discontinuous function, internal source, refraction, tomography",

author = "Derevtsov, {E. Yu} and Maltseva, {S. V.} and Svetov, {I. E.}",

note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd.",

year = "2018",

month = oct,

day = "1",

doi = "10.1134/S1990478918040038",

language = "English",

volume = "12",

pages = "619--641",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "4",

}

RIS

TY - JOUR

T1 - Determination of Discontinuities of a Function in a Domain with Refraction from Its Attenuated Ray Transform

AU - Derevtsov, E. Yu

AU - Maltseva, S. V.

AU - Svetov, I. E.

PY - 2018/10/1

Y1 - 2018/10/1

N2 - Some results of numerical investigations are presented for the problem of determination of discontinuities of an unknown function that has the meaning of the internal source distribution and is given in a domain with absorption and refraction, on using the attenuated ray transform of the function. The refraction and the absorption coefficient are assumed to be given. The behavior of the available and newly constructed discontinuity indicator operators is investigated in some numerical tests. Some modification of discontinuity indicators was carried out for the purpose of applying them in the model of refractive tomography with absorption. Numerical methods are applied to investigate the possibility of using the operators of this kind for solving the problem of finding the discontinuities of a function from its attenuated ray transform; the degree is investigated of the influence on the recovery quality of such factors as the level of the noise introduced into the generated data, the parameters of metrics, the magnitude and variation of the absorption coefficient.

AB - Some results of numerical investigations are presented for the problem of determination of discontinuities of an unknown function that has the meaning of the internal source distribution and is given in a domain with absorption and refraction, on using the attenuated ray transform of the function. The refraction and the absorption coefficient are assumed to be given. The behavior of the available and newly constructed discontinuity indicator operators is investigated in some numerical tests. Some modification of discontinuity indicators was carried out for the purpose of applying them in the model of refractive tomography with absorption. Numerical methods are applied to investigate the possibility of using the operators of this kind for solving the problem of finding the discontinuities of a function from its attenuated ray transform; the degree is investigated of the influence on the recovery quality of such factors as the level of the noise introduced into the generated data, the parameters of metrics, the magnitude and variation of the absorption coefficient.

KW - absorption

KW - attenuated ray transform

KW - back-projection

KW - discontinuity indicator

KW - discontinuous function

KW - internal source

KW - refraction

KW - tomography

UR - http://www.scopus.com/inward/record.url?scp=85058109537&partnerID=8YFLogxK

U2 - 10.1134/S1990478918040038

DO - 10.1134/S1990478918040038

M3 - Article

AN - SCOPUS:85058109537

VL - 12

SP - 619

EP - 641

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 4

ER -

ID: 17831716