Analytical methods of three-dimensional image reconstruction

This paper describes the theory and practice of analytical methods of three-dimensional (3D) image reconstruction for PET and SPECT. In 3D PET, the 3D image is reconstructed from parallel-beam projections taken at various slant angles. The main topics are '3D filtered backprojection method' for a constant acceptance angle of projections, '3D reprojection method' used in practical 3D PET scanners, and 'rebinning methods' as the fast approximate reconstruction methods. This paper also describes a sufficiency condition for 3D image reconstruction from cone-beam projection data obtained with cone-beam SPECT, and gives a fundamental reconstruction method on the basis of Radon transform and some practical algorithms. Principle of rotating slant-hole SPECT and its recent topics are mentioned briefly. (author)