MIT image reconstruction based on edge-preserving regularization

Tikhonov regularization has been widely used in electrical tomography to deal with the ill-posedness of the inverse problem. However, due to the fact that discontinuities are strongly penalized, this approach tends to produce blurred images. Recently, a lot of interest has been devoted to methods with edge-preserving properties, such as those related to total variation, wavelets and half-quadratic regularization. In the present work, the performance of an edge-preserving regularization method, called ARTUR, is evaluated in the context of magnetic induction tomography (MIT). ARTUR is a deterministic method based on half-quadratic regularization, where complementary a priori information may be introduced in the reconstruction algorithm by the use of a nonnegativity constraint. The method is first tested using an MIT analytical model that generates projection data given the position, the radius and the magnetic permeability of a single nonconductive cylindrical object. It is shown that even in the presence of strong Gaussian additive noise, it is still able to recover the main features of the object. Secondly, reconstructions based on real data for different configurations of conductive nonmagnetic cylindrical objects are presented and some of their parameters estimated.