Inverse problems with structural prior information

In this paper we propose a method for the regularization of inverse problem s whose solutions are known to exhibit anisotropic characteristics. The met hod is based on the generalized Tikhonov regularization and on the spatial prior information on the underlying solution. We allow the prior informatio n to be only of approximate nature. In the proposed method, the prior infor mation is incorporated into the regularization operator with the aid of a p roperly constructed matrix-valued field. Although the approach is determini stic it also has a clear statistical interpretation that will be discussed from the Bayesian viewpoint. The method is applied to two examples, the fir st is the inversion of a Fredholm integral equation of the first kind and t he second is a case study of electrical impedance tomography (EIT).