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In electrical impedance tomography (EIT) images of the object are formed based on passive electrical properties of the interior structures. In EIT an array of electrodes is attached around the object and small alternating currents are injected via these electrodes and the resulting voltages are measured. Using di erent current injections and voltage measurements, an approximation for the spatial distribution of impedance (or resistivity) within the object can be reconstructed. Mathematically the EIT reconstruction problem is a nonlinear ill-posed inverse problem, the solution of which necessitates the use of regularization methods. In this thesis new approaches of EIT image reconstrution are proposed. Three novel methods are developed, all of which exploit available prior information. The rst one, the basis constraint method, is based on a learning process from which a few basis images are obtained and the solution is forced to be a linear combination of these few images. In the learning process the available prior information that is based on the object properties is e ectively utilized. Due to the parameter reduction the reconstruction procedure becomes fast. However, the method still enables the modelling of small changes in the interior structures. It was found that if the actual resistivity distribution is in accordance with the prior this method gives good results, but if it is not, misleading results are obtained. The second proposed method is a modi cation of the rst one and it is based on the Tikhonov regularization technique. In this method the solution is drawn towards the assumed solution, that is, towards the linear combination of the basis images with the aid of properly constructed regularization matrix. This method gives good resistivity estimates when the actual resistivity distribution is in accordance with the prior but even if it is not, the resistivity distribution can be quite well reconstructed. The third method is based on the state space representation of the EIT reconstruction problem. The method is applicable to such cases in which the resistivity distribution can not be assumed to be time-invariant within one measurement cycle. With this method fast resistivity changes can be tracked. National Library of Medicine Classi cation: WN 180, WN 206, QT 36 AMS Subject Classi cation: 65R30, 35R30, 65N30, 92C55, 93E12 INSPEC Thesaurus: electric impedance imaging; inverse problems; nite element analysis; Bayes methods; Kalman lters