Computed Tomography (CT) is an imaging technique that is used to calculate the interior of an object using X-rays under multiple projection angles. A well-known application is medical imaging with... Show moreComputed Tomography (CT) is an imaging technique that is used to calculate the interior of an object using X-rays under multiple projection angles. A well-known application is medical imaging with a CT-scanner. The reconstruction methods can roughly be divided into two categories: analytical reconstruction methods and algebraic reconstruction methods (ARMs). An example of an algorithm from the first category is Filtered Backprojection (FBP). This method has a high computational efficiency and it performs well in cases with many equiangularly distributed projection angles and high signal-to-noise ratio. ARMs require in general more computation time. They are more robust with respect to noise and can handle few projection angles or a limited angular range better. In this dissertation, the new algorithm Algebraic filter – Filtered Backprojection (AF-FBP) is introduced, which uses an ARM to create filters that can be used in FBP. The reconstruction quality of AF-FBP approximates that of the corresponding (locally) linear ARM, while the reconstructions are obtained with the computational efficiency of FBP. In cases with a small number of different scanning geometries, using AF-FBP enables the reconstruction of images of relatively high quality for few projection angles, limited angular range, or low signal-to-noise ratio. Show less
In X-ray tomography, a three-dimensional image of the interior of an object is computed from multiple X-ray images, acquired over a range of angles. Two types of methods are commonly used to... Show moreIn X-ray tomography, a three-dimensional image of the interior of an object is computed from multiple X-ray images, acquired over a range of angles. Two types of methods are commonly used to compute such an image: analytical methods and iterative methods. Analytical methods are computationally efficient, but in many applications, they produce reconstructions that are not accurate enough for further analysis. More accurate reconstructions can be obtained by using (regularized) iterative methods, but these can have computational costs that are too high to be used in practice. In this thesis, new reconstruction methods are developed that combine the analytical and algebraic approaches, resulting in methods that are as computationally efficient as analytical methods, but with a reconstruction accuracy of iterative methods. Analytical methods allow for changing their filter without increasing the needed computation time. We use this freedom in filter choice to develop new filter-based reconstruction methods, which are based on the analytical FBP method with specific filters. The filters can be defined and computed in different ways, and can depend on the acquisition geometry, the scanned object, and/or a separate pre-computing step. Several filter-based methods are introduced in this thesis and reconstruction results are compared with other popular methods. Show less
