Complete electrode model of electrical impedance tomography: Approximation properties and characterization of inclusions

In electrical impedance tomography one tries to recover the spatial admittance distribution inside a body from boundary measurements. In theoretical considerations it is usually assumed that the boundary data consists of the Neumann-to-Dirichlet map; when conducting real-world measurements, the obtainable data is a linear finite-dimensional operator mapping electrode currents onto electrode potentials. In this paper it is shown that when using the complete electrode model to handle electrode measurements, the corresponding current-to-voltage map can be seen as a discrete approximation of the traditional Neumann-to-Dirichlet operator. This approximating link is utilized further in the special case of constant background conductivity with inhomogeneities: It is demonstrated how inclusions with strictly higher or lower conductivities can be characterized by the limit behavior of the range of a boundary operator, determined through electrode measurements, when the electrodes get in finitely small and cover all of the object boundary.