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Anisotropic Polarization Tensors and Detection of an Anisotropic Inclusion

We introduce the notion of (generalized) anisotropic polarization tensors and prove that they are symmetric and positive-definite. We also estimate the eigenvalues of the anisotropic polarization tensor in terms of the volume of the given domain. We apply these properties to an electrical impedance tomography problem to detect a single anisotropic inhomogeneity of small size. The goal is to detect an unknown inclusion when anisotropic conductivities of the background and the inclusion are known. Three results of computational experiments for the detection of an inclusion are given. One experiment is to assure the validity of the algorithm, while the other two are to see how anisotropy plays a role in the detection procedure.