Convergence issues of non-linear 3D reconstruction in EIT

Abstract

The convergence of non-linear reconstruction algorithms for Electrical Impedance Tomography (EIT) depends on many factors, such as the noise of the measurement system, the numerical discretization of the object and the starting value of the iterative approximation. We have shown previously that the result can be made independent of the underlying numerical discretization of the object when adaptive mesh refinement methods are used in combination with a logarithmic image smoothness constraint. The non-linear nature of EIT reconstruction and the unavoidable measurement noise, however, cause several differing solutions in the image space to satisfy the conditions for a 'best-fit' conductivity distribution. A verification of the correctness of an obtained image can only be carried out if the true distribution is known. This, however, is not possible when in-vivo measurements are made and hence we need to establish a measure of similarity between the reconstructed result and a simulated object to characterize the algorithmic behaviour for real experiments. By distributing and reconstructing a large number of initial 3D conductivity estimates on a commodity cluster of PCs, we can determine the quality of the final images and correlate the results with the true images within a short time-span. This gives an indication of the quality of image and provides a measure of convergence properties of the tested algorithms. In this paper, we present results from these investigations into the characteristics and efficient reconstruction of the final image and comment on the clinical importance of choice of starting valu