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

E. Yu Derevtsov, A. K. Louis, S. V. Maltseva, A. P. Polyakova, I. E. Svetov

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8 Citations (Scopus)

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.

Original languageEnglish
Article number124001
Number of pages17
JournalInverse Problems
Volume33
Issue number12
DOIs
Publication statusPublished - 27 Oct 2017

Keywords

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

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