Current Density Impedance Imaging of an Anisotropic Conductivity in a Known Conformal Class

Nicholas Hoell; Amir Moradifam; Adrian Nachman

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arXiv · 1302.7044

Current Density Impedance Imaging of an Anisotropic Conductivity in a Known Conformal Class

Nicholas Hoell·Amir Moradifam·Adrian Nachman

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Abstract

We present a procedure for recovering the conformal factor of an anisotropic conductivity matrix in a known conformal class in a domain in Euclidean space of dimension greater than or equal to 2. The method requires one internal measurement, together with a priori knowledge of the conformal class (local orientation) of the conductivity matrix. This problem arises in the coupled-physics medical imaging modality of Current Density Impedance Imaging (CDII) and the assumptions on the data are suitable for measurements determinable from cross-property based couplings of the two imaging modalities CDII and Diffusion Tensor Imaging (DTI). We show that the corresponding electric potential is the unique solution of a constrained minimization problem with respect to a weighted total variation functional defined in terms of the physical data. Further, we show that the associated equipotential surfaces are area minimizing with respect to a Riemannian metric obtained from the data. The results are also extended to allow the presence of perfectly conducting and/or insulating inclusions.

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Nicholas Hoell, Amir Moradifam, Adrian Nachman. 2013-02-28. Current Density Impedance Imaging of an Anisotropic Conductivity in a Known Conformal Class. https://arxiv.org/abs/1302.7044

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