1. n e abs F square and absolute errors. Reconstructions using RAFDDI and RAFDDI 10 produced higherermsandeabsthan errors resulting from AFDDI but remained lower than the errors resulting from the original FDDI method. Comparisons of the filtered reconstruction errors also show that AFDDI produced the smallest errors for the three error measures but it should be noted that the root mean square errors for the four reconstruction methods are approximately the same (0.1936-0.2092). Visual inspection of the filtered reconstructions in figure 11 shows only small differences in the reconstructed distribution, mainly at the top of the peak and around the base. Loss of the highest gradients due to filtering has caused the reconstruction errors to increase over those of the unfiltered reconstructions.
2. Error measures for cases 2 and 3 were higher than those presented in Tables 1 and 2 however the phantom distributions in cases 2 and 3 are of higher contrast and are more complex than the smoothed top-hat phantom in case 1. ermsvalues ranged from 0.278-0.355 for unfiltered reconstructions in case 2 and 0.297-0.370 for unfiltered reconstructions in case 3. AFDDI produced the lowest root mean square error in case 2 while RAFDDI 10 produced the lowest ermsin case 3. The ability of RAFDDI 10 to lower the root mean square error in case 3 indicates that the refinement of AFDDI is possible but case dependent. The reconstruction methods presented here were developed for reconstruction of smooth distributions of lower gradients than those seen in the phantom distributions studied in this work. The resulting errors for cases 2 and 3 are slightly high but are comparable to those produced by other reconstruction methods in high contrastor complex distributions [2, 10]. Table 1: Error measures for unfiltered reconstructions of the phantom distribution in Figure 10 (case 1).
3. erms eabs emax FDDI 0.1425 0.2136 0.1835 AFDDI 0.0925 0.0982 0.4630