A Fully Three-Dimensional Reconstruction Algorithm with the Nonstationary Filter for Improved Single-Orbit Cone Beam SPECT

Conventional single-orbit cone beam tomography presents special problems. They include incomplete sampling and inadequate three-dimensional (3D) reconstruction algorithm. The commonly used Feldkamp reconstruction algorithm simply extends the two-dimensional (2D) fan beam algorithm to 3D cone beam geometry. A truly 3D reconstruction formulation has been derived for the single-orbit cone beam SPECT based on the 3D Fourier slice theorem. In the formulation, a nonstationary filter which depends on the distance from the central plane of the cone beam was derived. The filter is applied to the 2D projection data in directions along and normal to the axis-of-rotation. The 3D reconstruction algorithm with the nonstationary filter was evaluated using both computer simulation and experimental measurements. Significant improvement in image quality was demonstrated in terms of decreased artifacts and distortions in cone beam reconstructed images. However, compared with the Feldkamp algorithm, a five-fold increase in processing time is required. Further improvement in image quality needs complete sampling in frequency space.