FRECHET DERIVATIVE WITH RESPECT TO THE SHAPE OF AN INTERNAL ELECTRODE IN ELECTRICAL IMPEDANCE TOMOGRAPHY

Electrical impedance tomography is a noninvasive imaging technique for recovering the admittance distribution inside a body from boundary measurements of current and voltage. In this work, we consider application of impedance tomography to nondestructive testing of reinforced concrete: The aim is to estimate the thickness of the concrete layer on top of the reinforcing bars in order to assess the risk of corrosion. This problem is tackled by introducing the Frechet derivative of the boundary measurement map with respect to the shape of the bars, and then building a Newton-type output least squares algorithm for locating them. The measurements are modeled with the complete electrode model, which is in good agreement with real-life electrode measurements. A special characteristic of our measurement setting is that some reinforcing bars may be used as internal electrodes with unknown shapes; i.e., one may be able to apply currents and measure voltages on the bars. According to our numerical studies based on simulated data, this makes the reconstruction process considerably less ill-posed.