A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calderón's method in the plane

Rashmi Murthy*, Yi Hsuan Lin, Kwancheol Shin, Jennifer L. Mueller

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

A direct reconstruction algorithm based on Calder'on's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic inverse conductivity problem, the entries of the unperturbed anisotropic tensors are assumed known a priori, and it remains to reconstruct the multiplicative scalar field. The quasi-conformal map in the plane facilitates the Calder'on-based approach for anisotropic conductivities. The method is demonstrated on discontinuous radially symmetric conductivities of high and low contrast.

Original languageEnglish
Article number125008
JournalInverse Problems
Volume36
Issue number12
DOIs
StatePublished - Dec 2020

Keywords

  • Anisotropy
  • Calder'on's problem
  • Dirichlet-to-Neumann map
  • Electrical impedance tomograophy
  • Exponential solutions
  • Inverse conductivity problem
  • Quasi-conformal maps

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