Direct electrical impedance tomography for nonsmooth conductivities
Kari Astala Jennifer L. Mueller Lassi Päivärinta Allan Perämäki Samuli Siltanen
A new reconstruction algorithm is presented for eit in dimension two, based on the constructive uniqueness proof given by Astala and Päivärinta in [Ann. of Math. 163 (2006)]. The method is non-iterative, provides a noise-robust solution of the full nonlinear eit problem, and applies to more general conductivities than previous approaches. In particular, the new algorithm applies to piecewise smooth conductivities. Reconstructions from noisy and non-noisy simulated data from conductivity distributions representing a cross-sections of a chest and a layered medium such as stratified flow in a pipeline are presented. The results suggest that the new method can recover useful and reasonably accurate eit images from data corrupted by realistic amounts of measurement noise. In particular, the dynamic range in medium-contrast conductivities is reconstructed remarkably well.
keywords: Electrical impedance tomography. Nonlinear Fourier transform Complex geometrical optics solution Beltrami equation Conductivity equation Inverse conductivity problem Inverse problem Quasiconformal map Numerical solver

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