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Papadimitriou Katerina. MSc, Computer Science Department, University of Ioannina, Greece. June, 2015. Tomographic image reconstruction with spatially varying mixture models. Thesis Supervisor: Christophoros Nikou. Image reconstruction is a mathematical process through which an accurate image of an object is reconstructed from multiple projections. Tomographic reconstruction strategies have gained tremendous attention in the last decades, due to their crucial role in noninvasive visualization of the interior of objects such as the human body. Applications of these methods are, among others, radiology, geophysics and material science. Although, several approaches have been proposed for solving the tomographic reconstruction problem, such as analytical reconstruction techniques, the main research tendencies are centered on iterative image reconstruction. This approximation inevitably requires repeated projection and back projection procedures, signifying that the estimated image is progressively re ned in a repetitive calculation. The basic problem of tomographic reconstruction is the estimation of the attenuation coe cient, which leads to noisy data. This assumption is based on the knowledge that, because of its blurring e ect, the system (projection) matrix suppresses image detail. Therefore any such detail present in the reconstructed image is more probably to have been caused from noise. A regular method for addressing the problem of noise propagation is the Bayesian maximum a posteriori (MAP) algorithm, which imposes a prior probability on the image to be reconstructed and usually aims to encourage the image to be smooth, so as to suppress the e ect of noise. The purpose of this study is the e ective noise elimination and the preservation of region boundaries in the reconstructed image. To this end, we present four models which are based on maximum a posteriori estimation and use two di erent priors: a Gaussian mixture prior and a Gamma mixture prior. Simultaneously, in order to account for the modeling of edges between image segments, appropriate MRF smoothness priors, which are based on Student's t-distribution and Bernoulli distributions formalized as a line process, on the contextual mixing proportions are employed, which model the existence or not of boundaries. The overall algorithm consists of two alternating steps. At rst, the mixture model parameters are automatically estimated from the image and then the vi reconstructed image is estimated by optimizing the MAP criterion using the one-steplate-EM (OSL-EM) or the preconditioned conjugate gradient (PCG) algorithms.