High fidelity imaging in electrical impedance tomography

Abstract

This thesis addresses the computational reconstruction of images using Electrical Impedance Tomography (EIT). EIT is an imaging method, in which electrical currents are injected through electrodes into a conducting volume and the resulting potential distribution is measured at surface electrodes. From these potentials, an image of the electrical conductivity can be obtained using numerical reconstruction techniques. This non-linear reconstruction is mathematically difficult and computationally intensive. Most applications in medicine and industry rely upon a fast and accurate image acquisition. The aim of this investigation is to find methods which improve the speed and accuracy of EIT by a range of improvements to the numerical methods used in the forward solution and inverse reconstruction. We investigate the impact of the finite element discretization on the performance of computing the electric field forward solution. We derive an a posteriori error estimate on the finite element mesh and implement 2D adaptive mesh refinement techniques in an optimised forward solver. Our results of this novel approach show that a speed-up of approximately an order of magnitude can be obtained. We extend the developed iterative Newton-Raphson algorithm to include image smoothness constraints and adaptive mesh refinement based on conductivity gradients in the image. The results show that the image resolution can be made independent of the underlying numerical discretization and therefore is limited only by the level of noise present in the measurements. An additional benefit of this new technique is the automatic focus of available computational resources on key regions for forward solution and inverse reconstruction. As 3D impedance imaging becomes computationally too expensive for the Newton-Raphson method, we develop a novel non-linear conjugate gradient algorithm incorporating 3D adaptive mesh refinement routines, and present results showing the decrease of memory requirements and the increase in image reconstruction performance. In addition, a Matlab software package containing optimised routines for the finite element-based computations in EIT has been developed as part of this work. Finally, we outline a method for obtaining a map for the determination of the reconstruction reliability and image correlation of an EIT algorithm. With the improvements to reconstruction accuracy and speed investigated in this thesis, we conclude that efficient non-linear 3D impedance imaging is feasible

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