Cone-Beam Reconstruction Using Filtered Backprojection. Linkoeping studies in science and technology (Linkoeping University

To my parents The art of medical computed tomography is constantly evolving and the last years have seen new ground breaking systems with multi-row detectors. These tomo-graphs are able to increase both scanning speed and image quality compared to the single-row systems more commonly found in hospitals today. This thesis deals with three-dimensional image reconstruction algorithms to be used in future gen-erations of tomographs with even more detector rows than found in current multi-row systems. The first practical algorithm for three-dimensional reconstruction from cone-beam projections acquired from a circular source trajectory is the FDK method. We present a novel version of this algorithm that produces images of higher quality. We also formulate a version of the FDK method that performs the backprojection in O(N3 logN) steps instead of the O(N4) steps traditionally required. An efficient way to acquire volumetric patient data is to use a helical source trajectory together with a multi-row detector. We present an overview of existing reconstruction algorithms for this geometry. We also present a new family of algo-rithms, the PI methods, which seem to surpass other proposals in simplicity while delivering images of high quality. The detector used in the PI methods is limited to a window that exactly fits the cylindrical section between two consecutive turns of the helical source path. A rebinning to oblique parallel beams yields a geometry with many attractive properties. The key property behind the simplicity of the PI methods is that each object point to be reconstructed is illuminated by the source during a rotation of exactly half a turn. This allows for fast and simple reconstruction.