Analytic reconstruction approach for parallel translational computed tomography

To develop low-cost and low-dose computed tomography (CT) scanners for developing countries, recently a parallel translational computed tomography (PTCT) is proposed, and the source and detector are translated oppositely with respect to the imaging object without a slip-ring. In this paper, we develop an analytic filtered-backprojection (FBP)-type reconstruction algorithm for two dimensional (2D) fan-beam PTCT and extend it to three dimensional (3D) cone-beam geometry in a Feldkamp-type framework. Particularly, a weighting function is constructed to deal with data redundancy for multiple translations PTCT to eliminate image artifacts. Extensive numerical simulations are performed to validate and evaluate the proposed analytic reconstruction algorithms, and the results confirm their correctness and merits.