Implementation of a cone-beam reconstruction algorithm for the single-circle source orbit with embedded misalignment correction using homogeneous coordinates

We present an efficient implementation of an approximate cone-beam image re construction algorithm for application in tomography, which accounts for sc anner mechanical misalignment. The implementation is based on the algorithm proposed by Feldkamp et al [J. Opt. Soc. Am. A 6, 612-619 (1984)] and is d irected at circular scan paths. The algorithm has been developed for the pu rpose of reconstructing volume data from projections acquired in an experim ental x-ray microtomography (mu CT) scanner [Engelke et al., Der Radiologe 39,2103-212 (1999)]. To mathematically model misalignment we use matrix not ation with homogeneous coordinates to describe the scanner geometry, its mi salignment, and the acquisition process. For convenience analysis is carrie d out for x-ray CT scanners, but it is applicable to any tomographic modali ty, where two-dimensional projection acquisition in cone beam geometry take s place, e.g., single photon emission computerized tomography. We derive an algorithm assuming misalignment errors to be small enough to weight and fi lter original projections and to embed compensation for misalignment in the back-projection. We verify the algorithm on simulations of virtual phantom s and scans of a physical multidisk (Defrise) phantom. (C) 2001 American As sociation of Physicists in Medicine.