A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calderón's method in the plane. (3rd December 2020)

• Record Type: Journal Article
• Authors: Murthy, Rashmi; Lin, Yi-Hsuan; Shin, Kwancheol; Mueller, Jennifer L
• Is Part Of: Inverse problems. Volume 36:Number 12(2020)
• Publication Date: 2020-12-03
• Subjects: electrical impedance tomograophy -- anisotropy -- quasi-conformal maps -- exponential solutions -- inverse conductivity problem -- Dirichlet-to-Neumann map -- Calderón's problem; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abbe5f
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: A direct reconstruction algorithm based on Calderón'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 Calderón-based approach for anisotropic conductivities. The method is demonstrated on discontinuous radially symmetric conductivities of high and low contrast.