This thesis will discuss the requirements of a software library for tomography and will derive a framework which can be used to realize various applications in cone-beam computed tomography (CBCT). The presented framework is self-contained and is realized using the MATLAB environment in combination with native low-level technologies (C/C++ and CUDA) to improve its computational performance, while providing accessibility and extendability through to use of a scripting language environment. On top of this framework, the realization of Katsevich’s algorithm on multicore hardware will be explained and the resulting implementation will be compared to the Feldkamp, Davis and Kress (FDK) algorithm. It will also be shown that this helical reconstruction method has the potential to reduce the measurement uncertainty. However, misalignment artifacts appear more severe in the helical reconstructions from real data than in the circular ones. Especially for helical CBCT (H-CBCT), this fact suggests that a precise calibration of the computed tomography (CT) system is inevitable. As a consequence, a self-calibration method will be designed that is able to estimate the misalignment parameters from the cone-beam projection data without the need of any additional measurements. The presented method employs a multi-resolution 2D-3D registration technique and a novel volume update scheme in combination with a stochastic reprojection strategy to achieve a reasonable runtime performance. The presented results will show that this method reaches sub-voxel accuracy and can compete with current state-of-the-art online- and offline-calibration approaches. Additionally, for the construction of filters in the area of limited-angle tomography a general scheme which uses the Approximate Inverse (AI) to compute an optimized set of 2D angle-dependent projection filters will be derived. Optimal sets of filters are then precomputed for two angular range setups and will be reused to perform various evaluations on multiple datasets with a filtered backprojection (FBP)-type method. This approach will be compared to the standard FDK algorithm and to the simultaneous iterative reconstruction technique (SIRT). The results of the study show that the introduced filter optimization produces results comparable to those of SIRT with respect to the reduction of reconstruction artifacts, whereby its runtime is comparable to that of the FDK algorithm.
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