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

Inverse Problems and Applications

15 April 15:30 - 16:30


We present recent results on determining anisotropic conductivities from current density and diffusion tensor measurements which can be obtained using Magnetic Resonance Imagers. The mathematical problem is to recover an anisotropic conductivity in a known conformal class from knowledge of one current. 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. This is joint work with Nicholas Hoell and Amir Moradifam. Experimental results are joint work with Weijing Ma, Nahla Elsaid, Michael Joy and Tim DeMonte.