Reconstruction algorithms for electrical impedance tomography

Electrical Impedance Tomography (EIT) is a new imaging technique which produces the conductivity distribution of material within an object from electrical measurement made at the object's boundary. EIT has applications in biomedical and geophysical engineering and various industrial applications are also under investigation. This thesis is a study of reconstruction algorithm of EIT and involves an examination of nonlinear reconstruction algorithms as well as the mathematical derivation of linear reconstruction techniques. An iterative algorithm is derived using linear network theory and finite element modelling of an continuous object. Relationships and equivalences between a number of iterative algorithms are investigated. The algorithm is tested on both networks and continuous objects, using simulated and measured data. A modified algorithm is then developed to reduce the data errors caused by the finite element modelling and the electrode contact impedance. Meaningful results are obtained from the algorithm. A linear integral equation reconstruction method is developed from a linearized Poisson's equation. Properties of the integral equation are investigated and a numerical algorithm is derived. The relationship between the integral equation method, Radon's back-projection method [Herman and Natterer, 1981] and Barber-Brown's filtered back-projection method [Barber and Brown, 1986] is studied. Useful reconstructions are obtained from simulated and measured data, and problems associated with the integral equation method are discussed. An error analysis of the linearized Poisson's equation is carried out with an emphasis on the applications to EIT. Three types of error are discussed and re-scaling error is found to be dominant. It is also found that the commonly used small perturbation assumption often fails. Case studies and numerical tests agree with the conclusions of the error study.