Recovering boundary shape and conductivity in electrical impedance tomography
Ville Kolehmainen Matti Lassas Petri Ola Samuli Siltanen
Inverse Problems & Imaging 2013, 7(1): 217-242 doi: 10.3934/ipi.2013.7.217
Electrical impedance tomography (EIT) aims to reconstruct the electric conductivity inside a physical body from current-to-voltage measurements at the boundary of the body. In practical EIT one often lacks exact knowledge of the domain boundary, and inaccurate modeling of the boundary causes artifacts in the reconstructions. A novel method is presented for recovering the boundary shape and an isotropic conductivity from EIT data. The first step is to determine the minimally anisotropic conductivity in a model domain reproducing the measured EIT data. Second, a Beltrami equation is solved, providing shape-deforming reconstruction. The algorithm is applied to simulated noisy data from a realistic electrode model, demonstrating that approximate recovery of the boundary shape and conductivity is feasible.
keywords: conformal deformation. electrical impedance tomography minimally anisotropic conductivity quasiconformal maps Inverse conductivity problem

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