APPROXIMATING IDEALIZED BOUNDARY DATA OF ELECTRIC IMPEDANCE TOMOGRAPHY BY ELECTRODE MEASUREMENTS

In electric impedance tomography, one tries to recover the spatial admittance distribution inside a body from boundary measurements of current and voltage. In theoretical considerations, it is usually assumed that the available data is the in finite-dimensional Neumann-to-Dirichlet map, i.e. one assumes to be able to use any boundary current and measure the corresponding potential everywhere on the object boundary. However, in practice, the data consists of a finite-dimensional operator mapping the electrode currents onto the corresponding electrode potentials. What is more, the measurements are affected by the contact impedance at the electrode-object interfaces. In this paper, we show that the introduction of a suitable nonorthogonal projection operator makes it possible to approximate the Neumann-to-Dirichlet map by its electrode counterpart in the topology of bounded linear operators on square integrable functions, with the discrepancy depending linearly on the distance between centers of adjacent electrodes. In particular, convergence is proved without assuming that the electrodes cover all of the object boundary. The theoretical results are complemented by two-dimensional numerical experiments.