Implementation of the virtual fan-beam method for 2D region-of-interest reconstruction from truncated data

In the context of two-dimensional (2D) image reconstruction from truncated projections, we describe five implementations, each based on a different formula derived from the virtual fan-beam (VFB) method. Three formulae are already known: (a) and (b) perform the back-projection in the parallel-beam geometry and (c) performs the back-projection in the virtual fan-beam geometry. Two new formulae, (d) and (e), perform the back-projection in the acquisition geometry. Our simulation results using the Shepp-Logan phantom suggest that the best accuracy is obtained from the implementations of formulae (b), (d) and (e).