  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.
