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

被引：11

作者：

Derevtsov, E. Yu ^{[1
,2
]}

Louis, A. K. ^{[3
]}

Maltseva, S. V. ^{[1
,2
,4
]}

Polyakova, A. P. ^{[1
,2
]}

Svetov, I. E. ^{[1
,2
]}

机构：

[1] SB RAS, Sobolev Inst Math, Acad Koptyug Av 4, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Pirogova Str 2, Novosibirsk 630090, Russia

[3] Saarland Univ, Dept Math, D-66041 Saarbrucken, Germany

[4] Lavrentyev Inst Hydrodynam, Acad Lavrentyev Av 15, Novosibirsk 630090, Russia

来源：

INVERSE PROBLEMS | 2017年 / 33卷 / 12期

关键词：

tensor tomography; ray transform; method of approximate inverse; FIELD TOMOGRAPHY; RAY TRANSFORMS; DESIGN;

D O I：

10.1088/1361-6420/aa8f5a

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：17

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