A survey of algebraic algorithms in computerized tomography
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X-ray computed tomography (CT) is a medical imaging framework. It takes measured projections of X-rays through two-dimensional cross-sections of an object from multiple angles and incorporates algorithms in building a sequence of two-dimensional reconstructions of the interior structure. This thesis comprises a review of the different types of algebraic algorithms used in X-ray CT. Using simulated test data, I evaluate the viability of algorithmic alternatives that could potentially reduce overexposure to radiation, as this is seen as a major health concern and the limiting factor in the advancement of CT [36, 34]. Most of the current evaluations in the literature [31, 39, 11] deal with low-resolution reconstructions and the results are impressive, however, modern CT applications demand very high-resolution imaging. Consequently, I selected ve of the fundamental algebraic reconstruction algorithms (ART, SART, Cimmino's Method, CAV, DROP) for extensive testing and the results are reported in this thesis. The quantitative numerical results obtained in this study, con rm the qualitative suggestion that algebraic techniques are not yet adequate for practical use. However, as algebraic techniques can actually produce an image from corrupt and/or missing data, I conclude that further re nement of algebraic techniques may ultimately lead to a breakthrough in CT.