Three-dimensional forward and back projection methods

A projector or back-projector system having a non-transitory computer readable medium encoded with an executable program for image reconstruction, said projector or back-projector system comprising:

• a computational system using computational operations occurring separately in axial and transaxial directions that exploit the separability of approximation of a footprint function, said computational operations comprising:
• computing projected coordinates of a plurality of 3D voxels on a detector surface;
• approximating 2D footprints of said plurality of voxels as separable functions, said separable functions being a computational product of a 1D axial footprint function and a 1D transaxial footprint function;
• approximating 2D detector blur as a computational product of a 1D axial blur function and a 1D transaxial blur function;
• and
• determining the contribution of said plurality of voxels to detector cells or vice versa using computational sums and products of said 1D axial footprint function, said 1D transaxial footprint function, said 1D axial blur function, and said 1D transaxial blur function in accordance with said projected coordinates.