A cone-beam projection of some object is a collection of ray-sums through the object, where all the rays converge on a single "vertex point" in space. Usually this vertex point is outside the object, and it is often assumed that from each vertex point, every non-zero ray-sum through the object is available. If some of these ray-sums are not available, the cone-beam projection is called a truncated projection.

Several algorithms are available to reconstruct the object from its cone-beam projections, under the assumptions that the vertex point travels along a suitable path in space and that no projection is truncated. There has been progress recently on algorithms that relax these assumptions. Effective algorithms for handling certain kinds of truncated data will be discussed, and an algorithm that is able to reconstruct from a discrete, unordered set of vertex points (but with no truncated projections) will be presented.

Images obtained from these algorithms will be presented for the cases of computer-simulated data, and for data taken from a large-area CT scanner.

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1996-1997 Mathematics in High Performance Computing