Fast methods for shape reconstruction in Electrical Resistance Tomography

Electrical Resistance Tomography (ERT) is a body of methods and techniques aimed to reconstruct the spatial distribution of the conductivity of a material starting from the knowledge of boundary measurements such as, for instance, the Neumann-to-Dirichlet map. This inverse problem is ill-posed and nonlinear and, therefore, its solution require a considerable computational effort. In this paper we present a comparison between three fast non-iterative reconstruction methods for locating inclusions in an otherwise homogeneous material (for both 2D and 3D geometries). These methods, potentially, are candidate for real-time applications.