Combination of butterworth and variable conductance diffusion approach for filtered back-projection reconstructions

This study investigates the differences in both image texture and numerical performance among various filtering methods used in filtered back-projection reconstructions, including Butterworth, variable conductance diffusion (VCD), and a combination approach of the two. A χ² Butterworth method is proposed to be used for 2-D prefiltering on the projection data and a 3-D VCD method is then applied post-reconstruction. The combination approach has the smooth boundaries a VCD method can not normally obtain while minimizing the severe ringings normally incurred by a Butterworth with low cut-off. Use of χ² criterion in Butterworth provides a reasonably good starting point for VCD, which then only needs a few iterations to reach a desirable degree of smoothness. The use of Butterworth filtering before VCD also results in less noisy estimates of the parameters which control VCD. Thus, the combination of global smoothing with the Butterworth, and local smoothing with VCD is much faster than VCD alone and preserves the desirable properties of each.