Figure 15. The Lower-Value, Backprojection and Hybrid Backprojection/Lower-Value Reconstruction Algorithms.

In these three panels, the stacked plots show reconstructions by the three methods of a plane extracted from the (3,2)-D HNCO of GB1. Four projections were used, at the angles 0°, 45°, 90° and 135°. The reconstructions have been normalized to allow for the comparison of signal and noise levels. The diagrams at top illustrate how each method calculates an output given the four inputs A, B, C and D, representing the four projections. (a) In the lower-value (LV) algorithm, the value assigned to a point in the spectrum is the minimum of the corresponding values found on the projections. The resulting reconstruction shows the two peaks found on this plane. (b) In backprojection (BP) reconstruction, the value assigned to a point in the spectrum is the sum of the corresponding values found on all of the projections. This produces reconstructions with backprojection ridges. The two true peaks are formed in locations where the ridges intersect; there are additional intersection points between ridges, however, which lead to spurious peaks of various heights. The signal level is eight times higher in this reconstruction than in the lower-value reconstruction, because of the additive nature of the backprojection process. (c) The hybrid (HBLV) method involves computing the sums of all possible combinations of k projections, and then assigning to the reconstruction point the smallest value encountered from among the set of sums. For four projections and a bin size k = 2, there are six combinations to be compared, which are shown in the diagram at top. The resulting spectrum shows stronger signals than in lower-value reconstruction, reflecting the partially additive nature of the process, without introducing artifacts. Reprinted, with permission, from [72]. © 2005 American Chemical Society.