Spatial inhomogeneity and regularization in EIT

The reconstruction of impedance distribution in electrical impedance tomography (EIT) is a nonlinear ill-posed inverse problem. In order to obtain a stable solution the problem has to be regularized. One of the most common methods for this is the generalized Tikhonov regularization. The regularization matrices that are usually used with the Tikhonov method are more or less ad hoc and the associated implicit assumptions are thus in many cases inappropriate. Here, the authors propose a method with which the prior assumptions on the approximately known spatial inhomogeneity of the impedance distribution can be included in the regularization. The proposed approach is shown to be suitable in the cases in which there are distinct and known jumps in the impedance distribution. Such an example is the imaging of the head in which there are large impedance changes in the scalp-skull and skull-brain interfaces