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A novel computational, non-iterative and noise-robust reconstruction methodis introduced for the planar anisotropic inverse conductivity problem. Themethod is based on bypassing the unstable step of the reconstruction of thevalues of the isothermal coordinates on the boundary of the domain.Non-uniqueness of the inverse problem is dealt with by recovering the uniqueisotropic conductivity that can be achieved as a deformation of the measuredanisotropic conductivity by \emph{isothermal coordinates}. The method shows howisotropic D-bar reconstruction methods have produced reasonable and informativereconstructions even when used on EIT data known to come from anisotropicmedia, and when the boundary shape is not known precisely. Furthermore, theresults pave the way for regularized anisotropic EIT. Key aspects of theapproach involve D-bar methods and inverse scattering theory, complexgeometrical optics solutions, and quasi-conformal mapping techniques.

A Direct Reconstruction Method for Anisotropic Electrical Impedance Tomography