Parallel Computational Experiments in Electrical Impedance Tomography

In this work we present a parallel method for the solution of the inverse problem associated to Electrical Impedance Tomography (EIT). This technique tries to recover the spa-tial distribution of electrical conductivity in the interior of a body from electric potential measurements taken on the ex-ternal boundary of the body. The problem we address in this work consists in estimating the shape and position of cav-ities inside a two-dimensional domain. In the present ap-proach a parametric representation of the geometry of the internal cavities is used and the problem is formulated as an optimization one, where the objective function is the fit between simulated and measured electrical potentials. The simulated electric potentials are numerically obtained by casting the Poison’s Equation and applying the Boundary Element Method (BEM) for discretization. As experimen-tal data was not available, the BEM is also used to gener-ate synthetic sets of measured electric potentials. The op-timization strategy is based on a hybrid method that uses a Genetic Algorithm (GA) as a localization tool and a clas-sical derivative free mathematical programming routine to enhance the spatial precision achieved by the GA. Since the GA dominates computation time, this part of the method is parallelized in a master-slave fashion. Results showing the performance of the proposed parallel strategy are presented for the standard problem of identifying cylindrical cavities with the influence of noise in the synthetic measurements.