Bootstrap Method

Penczek (2002b) developed a method of variance estimation in which multiple reconstructions are created by repeatedly drawing a set of projections at random from the existing pool. In addition to an accurate variance estimation, the method allows estimation of covariances (or correlations) between regions of interest in 3D volume. An application of this method is described in Spahn et al. (2004a).

Specifically, the method is based on the assumption that the number of available projections is large; thus, if we consider the weighted back-projection algorithm we can assume that the weighting function (see chapter 5, section 4.2) will not change significantly with a small change in the number or distribution of projections. Thus, a 3D reconstruction can be considered a weighted sum of projections, with weights being approximately constant. In this case, the variance/covariance can be calculated using a statistical bootstrap technique: given a set of k projections, n different reconstructions are obtained by repeatedly



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