|TOPOLOGICAL DERIVATIVE IN IMPEDANCE TOMOGRAPHY|
The aim of this article is to develop new numerical methods and algorithms in the field of impedance tomography based on the concept of the topological derivative for the two-dimensional situation. We use a modification of the topological derivative definition in which we calculate topological derivative for inclusions in the interior of the geometrical domain as opposite to small holes. The topological derivative provides the information on the infinitesimal variation of the shape functional if a small hole is created in the domain. Object is modelled as the best possible numerical solution as a ''real object''. The topological derivative in the shape optimization for tentative localization of variation of the equation coefficient is compared with the classical method of computing inverse problems. The comparison criteria are: accuracy of the method, time of calculations, perturbations tolerance. It is also shown how important is the choice of the shape functional in the topological derivative to get most accurate results.
|Key Words:||topological derivative, impedance tomography, shape optimisation, inverse problem.|