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 reconstruction algorithm for application in tomography, which accounts for scanner 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 directed at circular scan paths. The algorithm has been developed for the purpose of reconstructing volume data from projections acquired in an experimental x-ray microtomography (µCT) scanner [Engelke et al., Der Radiologe 39, 203-212 (1999)]. To mathematically model misalignment we use matrix notation with homogeneous coordinates to describe the scanner geometry, its misalignment, and the acquisition process. For convenience analysis is carried out for x-ray CT scanners, but it is applicable to any tomographic modality, where two-dimensional projection acquisition in cone beam geometry takes place, e.g., single photon emission computerized tomography. We derive an algorithm assuming misalignment errors to be small enough to weight and filter original projections and to embed compensation for misalignment in the backprojection. We verify the algorithm on simulations of virtual phantoms and scans of a physical multidisk (Defrise) phantom.