6533b859fe1ef96bd12b7f3d

RESEARCH PRODUCT

Explicit Characterization of Inclusions in Electrical Impedance Tomography

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In electrical impedance tomography one seeks to recover the spatial conductivity distribution inside a body from knowledge of the Neumann--Dirichlet map. In many practically relevant situations the conductivity is smooth apart from some inhomogeneities where the conductivity jumps to a higher or lower value. An explicit characterization of these inclusions is developed in this paper. To this end a class of dipole-like indicator functions is introduced, for which one has to check whether their boundary values are contained in the range of an operator determined by the measured Neumann--Dirichlet map. It is shown that this holds true if and only if the dipole singularity lies inside the inhomogeneity. This procedure is conceptually similar to a recent method proposed by Kirsch in inverse scattering theory.