Assessment of bootstrap resampling performance for PET data

Bootstrap resampling has been successfully used for estimation of statistical uncertainty of parameters such as tissue metabolism, blood flow or displacement fields for image registration. The performance of bootstrap resampling as applied to PET list-mode data of the human brain and dedicated phantoms is assessed in a novel and systematic way such that: (1) the assessment is carried out in two resampling stages: the 'real world' stage where multiple reference datasets of varying statistical level are generated and the 'bootstrap world' stage where corresponding bootstrap replicates are generated from the reference datasets. (2) All resampled datasets were reconstructed yielding images from which multiple voxel and regions of interest (ROI) values were extracted to form corresponding distributions between the two stages. (3) The difference between the distributions from both stages was quantified using the Jensen-Shannon divergence and the first four moments. It was found that the bootstrap distributions are consistently different to the real world distributions across the statistical levels. The difference was explained by a shift in the mean (up to 33% for voxels and 14% for ROIs) being proportional to the inverse square root of the statistical level (number of counts). Other moments were well replicated by the bootstrap although for very low statistical levels the estimation of the variance was poor. Therefore, the bootstrap method should be used with care when estimating systematic errors (bias) and variance when very low statistical levels are present such as in early time frames of dynamic acquisitions, when the underlying population may not be sufficiently represented.