RECONSTRUCTION FROM INCOMPLETE DATA IN CONE-BEAM TOMOGRAPHY

A method for reconstruction of an object f(x) x=(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 co nvex sets (POCS) for handling the limited (or incomplete) data problem . In cone-beam tomography, one needs to have a complete geometry to co mpletely reconstruct the original three-dimensional object. While comp lete geometries do exist, they are of little use in practical implemen tations. The most common trajectory used in practical scanners is circ ular, which is incomplete. It is, however, possible to recover some of the information of the original signal f(x) based on a priori knowled ge of the nature of f(x). If this knowledge can be posed in a convex s et framework, then POCS can be utilized. In this report, we utilize th is a priori knowledge as convex set constraints to reconstruct f(x) us ing 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. (C) 1996 Soci ety of Photo-Optical instrumentation Engineers.