COMPUTER-AIDED TOMOGRAPHIC IMAGING FROM CONE-BEAM DATA

The principle issue addressed in this dissertation is generalized tomographic reconstruction from fan-beam and cone-beam data. One consequence of the generalized tomographic reconstruction method developed in this dissertation is that it allows one to collect fan-beam data along a more general path than previously developed methods that require collecting the data along a circular path about the object. The lack of knowledge concerning reconstruction from cone-beam data has hindered the development of exact closed-form convolution-backprojection reconstruction methods for cone-beam data. In this dissertation necessary and sufficient conditions for reconstructing from cone-beam data are derived and exact convolution-backprojection reconstruction methods are developed. The most efficient of these methods require a stringent condition on the path of source points. A search is made for paths which satisfy the requirements of the most efficient method. Additionally, the most efficient method is compared with that of Feldkamp et al. and found equivalent when the path of source points is a circle