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 three dimensional
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.