Erratum: An Inverse Backscatter Problem for Electric Impedance Tomography
We fix an incorrect statement from our paper [M. Hanke, N. Hyvonen, and S. Reusswig, SIAM J. Math. Anal., 41 (2009), pp. 1948–1966] claiming that two different perfectly conducting inclusions necessarily have different backscatter in impedance tomography. We also present a counterexample to show that this kind of nonuniqueness does indeed occur.
A regularized Newton method for locating thin tubular conductivity inhomogeneities
We consider the inverse problem of determining the position and shape of a thin tubular object, such as for instance a wire, a thin channel or a curve-like crack, embedded in some three-dimensional homogeneous body from a single measurement of electrostatic currents and potentials on the boundary of the body. Using an asymptotic model describing perturbations of electrostatic potentials caused by such thin objects, we reformulate the inverse problem as a nonlinear operator equation. We establish Frechet differentiability of the corresponding operator, compute its Frechet derivative and set up a regularized Newton scheme to solve the inverse problem numerically. We discuss our implementation…
Justification of point electrode models in electrical impedance tomography
The most accurate model for real-life electrical impedance tomography is the complete electrode model, which takes into account electrode shapes and (usually unknown) contact impedances at electrode-object interfaces. When the electrodes are small, however, it is tempting to formally replace them by point sources. This simplifies the model considerably and completely eliminates the effect of contact impedance. In this work we rigorously justify such a point electrode model for the important case of having difference measurements ("relative data") as data for the reconstruction problem. We do this by deriving the asymptotic limit of the complete model for vanishing electrode size. This is s…