Comparison of 3D PET data bootstrap resampling methods for numerical observer studies

Bootstrap methods have been proposed to estimate the statistical properties of PET and SPECT images by generating multiple statistically equivalent data sets from few data samples. Bootstrap methods might be very helpful for detection performance studies, whose aim is to evaluate detectability based on large series of statistically equivalent images. However, previous reports regarding bootstrap approaches suggest different results. The goal of this work was to compare the accuracy of three bootstrap methods, namely the list-mode based method used by Dahlbom and the parametric and non-parametric sinogram-based methods proposed by Haynor and by Buvat respectively, for predicting the moments of order 1 and 2 (mean and variance) of reconstructed images in 3D PET. We used simulated data generated with the GATE simulation tool and compared the mean and variance images estimated from 100 repeated scans and from series of 100 bootstrap resampled data generated with the three bootstrap methods. Results indicate that the non-parametric bootstrap method by Buvat based on a small number of statistically equivalent data samples seems to correctly estimate the mean of reconstructed images unlike the other two methods based on one original scan only. The comparison of variance images also indicates significant discrepancies between the method by Buvat and the other two bootstrap methods. However, the variance image from the 100 repeated scans, which served as a gold standard, was too noisy to allow us to determine which bootstrap method was the most accurate.