A Direct Reconstruction Method for Anisotropic Electrical Impedance Tomography
This work addresses the challenging problem of anisotropic conductivity reconstruction in EIT, offering a practical and robust approach for medical imaging and geophysics applications.
The paper introduces a novel non-iterative and noise-robust reconstruction method for anisotropic electrical impedance tomography (EIT), bypassing unstable boundary reconstruction steps. The method produces reasonable reconstructions even with unknown boundary shape, paving the way for regularized anisotropic EIT.
A novel computational, non-iterative and noise-robust reconstruction method is introduced for the planar anisotropic inverse conductivity problem. The method is based on bypassing the unstable step of the reconstruction of the values of the isothermal coordinates on the boundary of the domain. Non-uniqueness of the inverse problem is dealt with by recovering the unique isotropic conductivity that can be achieved as a deformation of the measured anisotropic conductivity by \emph{isothermal coordinates}. The method shows how isotropic D-bar reconstruction methods have produced reasonable and informative reconstructions even when used on EIT data known to come from anisotropic media, and when the boundary shape is not known precisely. Furthermore, the results pave the way for regularized anisotropic EIT. Key aspects of the approach involve D-bar methods and inverse scattering theory, complex geometrical optics solutions, and quasi-conformal mapping techniques.