Assessment of bootstrap resampling accuracy for PET data

Bootstrap resampling has been successfully used in estimating statistical properties of PET images by generating a set of statistically equivalent datasets based on one or more original datasets. However, the bootstrap resampling is only valid when the original dataset well represents the underlying distribution. The purpose of this work is to assess the validity of nonparametric bootstrap resampling using a long acquisition of a planar brain phantom, ensuring a good representation of the underlying distribution of all possible events. The assessment is carried out in two stages corresponding to the two `worlds´: i) the real world-generation of K reference list-mode datasets with five statistical levels (0.01%, 0.1%, 1%, 10% and 20% of the original dataset) using resampling with replacement of the statistically very rich original dataset playing the role of the population; and ii) the bootstrap world-generation of equivalent K bootstrap replicates using five resampled dataset from stage i) for each of the five statistical levels. The distributions from the two stages or worlds are then compared using the metric of Jensen-Shannon (J-S) divergence to quantify the similarity of the two distributions from stages i) and ii). In order to apply the J-S divergence two different histogramming methods are used: i) with constant and ii) adaptable binning. The bootstrap distributions are found to be constantly different to the real world distributions regardless of the data size and binning method. However when statistics are very low (for single voxels and 0.01% datasets) the comparison fails as the distributions are limited by the non-negativity constraint.