Tomographic image reconstruction is an inverse problem, where unknown parameters describing an internal volume are estimated from a set of known measurements (observations). Tomographic images are increasingly used in diagnostic applications in medicine and other industries, such as seismology and non-destructive testing. In many biomedical applications, the underlying anatomy contains sharp interfaces between the different organs and tissue types. Classical linear formulations of tomographic image reconstruction tend to smooth these sharp interfaces and produce blurred, low contrast images. Alternatives to these linear image reconstruction algorithms are edge-preserving image reconstruction methods (EPIRM) which preserve the sharp interfaces by non-linear parameterizations. The main aim of this thesis is to develop novel EPIRMs applied to reconstruct high contrast, edge-preserving images which are robust against noise and data outliers. This thesis proposes three novel variants of the EPIRM and evaluates the robustness of the proposed EPIRMs against measurement errors. This thesis proposes an evaluation framework to qualitatively and quantitatively compare the performance of four competing methods (iterative Gauss-Newton (GN) with Tikhonov regularization term, GN with NOSER algorithm, Total Variation (TV), and an L1 norm based inverse problem solved using the Primal-Dual Interior Point Method (hereinafter referred to as the PDIPM) against that of the proposed EPIRMs over Electrical Impedance Tomography (EIT) simulated data. The simulation results show that the proposed EPIRMs offer the highest accuracy in the reconstruction of two low conductive inclusions with an overall average accuracy score of 2.57 (out of 3), vs. 1.78 for TV as the second best performing method. Moreover, the results show that the proposed EPIRM with the sum of absolute values (L1 norm) on the image and data terms of the inverse problem offers the highest robustness against measurement errors with an average robustness score of 3 (out of 3), averaged over three different measurement conditions. The PDIPM with the L1 norms on its inverse problem terms offers an average robustness score of 1.33 and is the second robust method in dealing with the uncertainties
