Planar tomosynthesis reconstruction in a parallel-beam framework via virtual object reconstruction

A framework for image reconstruction from planar tomosynthesis trajectories (i.e. all source positions reside in a single plane) is presented. The parallel beam geometry is a convenient starting point in deriving reconstruction algorithms, both analytic and iterative, as the relation between frequency space and image space is well known. We present a method for utilizing parallel beam reconstruction algorithms in an internally consistent manner. The concept of a virtual image object is utilized. This virtual image object has the property that cone-beam projections through the real object are directly related to parallel-beam projections of the virtual object. The virtual object may then be reconstructed using any algorithm derived for parallel beam projections. Finally, an affine transform may be applied to the virtual image object in order to generate the reconstruction result. In the implementation described here the backprojection operation is performed such that the real image object is reconstructed without introducing a rebinning in image space. Image reconstruction comparisons are given for a standard filtered backprojection (FBP) type algorithm where parallel projections were assumed in the algorithm derivation. Numerical simulations were performed for a C-arm type geometry and parallel beam FBP reconstructions using the virtual object are compared with the standard backprojection algorithm. Finally, a comparison was made between the new parallel beam reconstruction and the standard approximation where the cone-beams are assumed to be approximately parallel beams and a cone-beam backprojection is employed. A reduction in streaking artifacts was observed using the new algorithm compared with the standard approximation.