Numerical solvers based on the method of approximate inverse for 2D vector and 2-tensor tomography problems

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Numerical solvers based on the method of approximate inverse for 2D vector and 2-tensor tomography problems. / Derevtsov, E. Yu; Louis, A. K.; Maltseva, S. V. et al.

In: Inverse Problems, Vol. 33, No. 12, 124001, 27.10.2017.

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

BibTeX

@article{4c04c44ced334ab4bb64e5f675538d89,

title = "Numerical solvers based on the method of approximate inverse for 2D vector and 2-tensor tomography problems",

abstract = "A problem of reconstruction of 2D vector or symmetric 2-tensor fields by their known ray transforms is considered. Two numerical approaches based on the method of approximate inverse are suggested for solving the problem. The first method allows to recover components of a vector or tensor field, and the second reconstructs its potentials in the sense of feature reconstruction, where the observation operator assigns to a field its potential. Numerical simulations show good results of reconstruction of the sought-for fields or their solenoidal or potential parts from its ray transforms.",

keywords = "method of approximate inverse, ray transform, tensor tomography, DESIGN, RAY TRANSFORMS, FIELD TOMOGRAPHY",

author = "Derevtsov, {E. Yu} and Louis, {A. K.} and Maltseva, {S. V.} and Polyakova, {A. P.} and Svetov, {I. E.}",

note = "Publisher Copyright: {\textcopyright} 2017 IOP Publishing Ltd.",

year = "2017",

month = oct,

day = "27",

doi = "10.1088/1361-6420/aa8f5a",

language = "English",

volume = "33",

journal = "Inverse Problems",

issn = "0266-5611",

publisher = "IOP Publishing Ltd.",

number = "12",

}

RIS

TY - JOUR

T1 - Numerical solvers based on the method of approximate inverse for 2D vector and 2-tensor tomography problems

AU - Derevtsov, E. Yu

AU - Louis, A. K.

AU - Maltseva, S. V.

AU - Polyakova, A. P.

AU - Svetov, I. E.

PY - 2017/10/27

Y1 - 2017/10/27

N2 - A problem of reconstruction of 2D vector or symmetric 2-tensor fields by their known ray transforms is considered. Two numerical approaches based on the method of approximate inverse are suggested for solving the problem. The first method allows to recover components of a vector or tensor field, and the second reconstructs its potentials in the sense of feature reconstruction, where the observation operator assigns to a field its potential. Numerical simulations show good results of reconstruction of the sought-for fields or their solenoidal or potential parts from its ray transforms.

AB - A problem of reconstruction of 2D vector or symmetric 2-tensor fields by their known ray transforms is considered. Two numerical approaches based on the method of approximate inverse are suggested for solving the problem. The first method allows to recover components of a vector or tensor field, and the second reconstructs its potentials in the sense of feature reconstruction, where the observation operator assigns to a field its potential. Numerical simulations show good results of reconstruction of the sought-for fields or their solenoidal or potential parts from its ray transforms.

KW - method of approximate inverse

KW - ray transform

KW - tensor tomography

KW - DESIGN

KW - RAY TRANSFORMS

KW - FIELD TOMOGRAPHY

UR - http://www.scopus.com/inward/record.url?scp=85038426418&partnerID=8YFLogxK

U2 - 10.1088/1361-6420/aa8f5a

DO - 10.1088/1361-6420/aa8f5a

M3 - Article

AN - SCOPUS:85038426418

VL - 33

JO - Inverse Problems

JF - Inverse Problems

SN - 0266-5611

IS - 12

M1 - 124001

ER -

ID: 9645173