Quantification task-optimized estimates from OSEM and FBP reconstructions in single- and multi-subject studies

Task-based selection of image reconstruction methodology in emission tomography is a critically important step when designing a PET protocol. This work concerns optimizing performance for a range of quantification tasks: finding the radioactivity concentration for different sizes of region of interest (ROI) and different group sizes. It is shown that there is a tremendous impact of ROI and group size on the quantitative performance of different algorithms which should be considered when selecting reconstruction parameters. Therefore, a study-specific and space-variant selection rule is proposed that selects a close to optimal estimate from a series of parameter estimates obtained by filtered backprojection (FBP) and different OSEM reconstructions. The optimality criterion is to minimize the approximative mean squared error (MSE), which is estimated from the limited data at hand (single- or multi-subject) using the bootstrap resampling technique. The proposed approach is appropriate for single voxel estimates and ROI estimates in single-and multi-subject studies. An extensive multi-try simulation study using a 2D numerical phantom and relevant count levels shows that the proposed selection rule can produce quantitative estimates that are close to the estimates that minimise the true MSE (that can only normally be obtained from many independent Monte-Carlo realisations with knowledge of the ground truth). This indicates that with the selection rule a truly task-based quantitative parameter estimation is possible not only avoiding the critical step of specifying reconstruction parameters such as OSEM iteration number or the choice between FBP and OSEM, but also providing a close to optimal estimate of the parameter.