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UBC Theses and Dissertations

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UBC Theses and Dissertations

Comparison of algorithms for solving the least squares problem with applications in computed tomography Guenter, Maria


One approach to the image reconstruction problem in Computed Tomography (CT) is to solve a least squares problem. For this application, direct solutions to the least squares problem are ineffective and iterative methods are employed. The current iterative method being used is the Landweber algorithm, however we wish to know if a better algorithm exists. This thesis investigates multiple algorithms for solving the least squares problem, specifically algorithms using superiorization techniques and regularization in order to avoid over fitting. Multiple test problems are investigated using academic image phantoms from the literature as well as clinical image phantoms provided by the 3D Radiation Dosimetry Research Group. Comparison of the algorithms is done using performance pro les on three different performance measures. The results for both the academic and clinical test problems show that there is not one single algorithm outperforming the others, but instead a group of four top algorithms that would all be a suitable choice.

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