Incremental beamwise backprojection using geometrical symmetries for 3D PET reconstruction in a cylindrical scanner geometry

Cho et al have proposed a fast backprojection scheme for parallel beam geometries, the incremental algorithm, which performs backprojection on a ray-by-ray (beam-by-beam) basis as opposed to a pixel-by-pixel approach. We present an extension of this incremental, beamwise, backprojection algorithm to the case of volume reconstruction of data acquired by a cylindrical, multiring positron tomograph. Use is made of geometrical symmetries of the image volume. This method results in a twelve-fold reduction of execution time compared with a straightforward, voxel-driven implementation of the same interpolation equations.