A method for reconstruction of an object f (x) x5(x ,y ,z ) from
a limited set of cone-beam projection data has been developed. This
method uses a modified form of convolution back-projection and projection
onto convex sets (POCS) for handling the limited (or incomplete)
data problem. In cone-beam tomography, one needs to have a complete
geometry to completely reconstruct the original three-dimensional object.
While complete geometries do exist, they are of little use in practical
implementations. The most common trajectory used in practical scanners
is circular, which is incomplete. It is, however, possible to recover
some of the information of the original signal f (x) based on a priori
knowledge of the nature of f (x). If this knowledge can be posed in a
convex set framework, then POCS can be utilized. In this report, we
utilize this a priori knowledge as convex set constraints to reconstruct
f (x) using POCS. While we demonstrate the effectiveness of our algorithm
for circular trajectories, it is essentially geometry independent and
will be useful in any limited-view cone-beam reconstruction.