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Complete electrode model of electrical impedance tomography: approximation properties and characterization of inclusions. (English) Zbl 1059.35168

Summary: 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 infinitely small and cover all of the object boundary.

MSC:

35R30 Inverse problems for PDEs
35J25 Boundary value problems for second-order elliptic equations
35Q60 PDEs in connection with optics and electromagnetic theory
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
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