On computation of test dipoles for factorization method

Abstract

In electrical impedance tomography, one tries to recover the spatial conductivity distribution inside a body from boundary measurements of current and voltage. In many important situations, the examined object has known background conductivity but is contaminated by inhomogeneities. The factorization method of Kirsch provides a tool for locating such inclusions. The computational attractiveness of the factorization technique relies heavily on efficient computation of Dirichlet boundary values of potentials created by dipole sources located inside the examined object and corresponding to the homogeneous Neumann boundary condition and to the known background conductivity. In certain simple situations, these test potentials can be written down explicitly or given with the help of suitable analytic maps, but, in general, they must be computed numerically. This work introduces an inexpensive algorithm for approximating the test potentials in the framework of real-life electrode measurements and analyzes how well this technique can be imbedded in the factorization method. The performance of the resulting fast reconstruction algorithm is tested in two spatial dimensions.