Abstract of the paper ``Variational constraints for electrical impedance tomography'' with Robert V. Kohn

The task of electrical impedance tomography is to invert electrical boundary measurements for the conductivity distribution of a body. This inverse problem can be formulated so the primary data are the measured powers dissipated across injection electrodes. Then, since these powers are minima of the pertinent variational principles (Dirichlet's or Thomson's principle), feasibility constraints can be formulated for the nonlinear inversion problem. These constraints may also be used to stabilize iterative reconstruction algorithms where voltage differences across other electrodes are the primary data and the measured powers are treated only as secondary data. When the powers may be measured accurately, the existence of these dual variational principles implies that an exact solution (if any) must lie at a point of intersection of the two feasibility boundaries.

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