A geometric inverse problem identification procedure for detection of cavities

In this paper the inverse problem of electrical impedance tomography (EIT) in a three dimensional environment is considered. In this technique, electrodes are placed on the external boundary of the body and electrical current is injected by sequentially activating pairs of them while the corresponding potentials are measured. Usually such measures are used in order to solve the nonlinear inverse problem of achieving a two-dimensional image of the conductivity distribution over the cross section of the body. In the problem studied here the goal is to determine the size and position of an existing cavity within a homogeneous medium. The geometrical parameters that describe the cavities are the unknowns of the resulting 3D inverse problem, which is solved by the Levenberg–Marquardt method. Two shapes of geometrical cavities are here considered: spherical and spheroidal. Due to its accuracy and simplicity of mesh generation, the Boundary Element Method (BEM) is used in the solution of the direct problem. In order to evaluate the proposed strategy, numerical experiments are presented varying the position and the shape of the cavity and also the injection-measure protocol used. Since measured data are not currently available, boundary potential measurements have been obtained computationally also using BEM. The sensitivity of the present method in the presence of measurement noise has also been estimated through numerical experiments.