Cone-Beam Reconstruction Using Filtered Backprojection

Sammanfattning: The art of medical computed tomography is constantly evolving and the last years have seen new ground breaking systems with multi-row detectors. These tomographs 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 generations of tomographs with even more detector rows than found in currentmultirow systems.The first practical algorithm for three-dimensional reconstruction from conebeamprojections acquired from a circular source trajectory is the FDKmethod. 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 algorithms, 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.