Cone-beam tomography: recent advances and a tutorial review

Cone-beam tomography is the science of forming images by inverting three-dimensional divergent cone-beam ray-sum data sets. The impetus for its application is its three-dimensional data collection abilities, which result in (1) significant reduction in the time needed to collect a sufficient number of data to produce a three-dimensional image and (2) elimination of the inaccuracy due to misalignment of cross sectional images. On the other hand, the divergence of cone-beam data has hindered its application. Because of the divergence, the theory that has been developed for fan-beam and parallel two- and three-dimensional tomography does not provide a totally adequate means for analyzing or inverting cone-beam data. Consider the following: In practice, as the data are collected, the vertex of the cone is movedalong some path about the object. Which paths, if any, provide enough information to make an inversion possible? Suppose by some means enough information has been obtained. How does one derive an exact formula for inverting this data? To answer these questions a new theory that takes into account the threedimensional divergence of cone-beam data needs to be developed. In 1985, a paper was published in which several advances in the theory of cone-beam tomography were made. A tutorial review of the results given in the 1985 paper B. D. Smith, "Image reconstruction from cone-beam projections: necessary and sufficient conditions and reconstruction methods," IEEE Trans. Med Imag. MI-4, 14-28 (1985) will be given here. This review will include the advances that have been made since that time. Additionally, a brief review of the contributions made by a number of other researchers will be given.