A D-Bar Algorithm with A Priori Information for 2-Dimensional Electrical Impedance Tomography

A method for including a priori information in the 2-dimensional D-bar algorithm is presented. It is shown that this method also constitutes a nonlinear regularization strategy for the D-bar method that converges to the true conductivity as the noise level tends to zero in the case of a correct prior. An explicit rate of convergence in the appropriate Banach space is derived. Two methods of assigning conductivity values to the prior are presented, each corresponding to a different scenario in applications. The method is tested on several numerical examples with and without noise and is demonstrated to be highly effective in improving the spatial resolution of the D-bar method.