Generalization of FDK 3D tomographic reconstruction algorithm for an off-centered cone beam geometry

3D reconstruction from 2D cone beam projections obtained along a single circular x-ray source trajectory is commonly performed using an algorithm proposed by Feldkamp, Davis and Kress (FDK) in 1983. This reconstruction algorithm involves the rotation of a source and detector in the same plane which is centered with respect to the volume of interest. Both in industrial and in medical applications, the positioning of the object to be scanned can be bound to strong constraints. A stand, an instrument or the shape of the object, for instance, can prevent the conventional acquisition geometry and introduce an off-centred geometry of the computer tomography (CT) acquisition system. Direct application of FDK algorithm is therefore not adapted. This problem led us to propose a generalization of Feldkamp formula to fit any off-centered geometry. This new formula called α-FDK reduces to original FDK when applied to standard geometry. Reconstructions of simulated phantoms give good results with a limited angle of excentration. We analyse artefacts observed in the Radon space.