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.
SIAM J. Imaging Sci.