Task-oriented quantitative image reconstruction in emission tomography for single- and multi-subject studies

Task-based selection of image reconstruction methodology in emission tomography is a critically important step when designing a PET study. This paper concerns optimizing, given the measured data of the study only, reconstruction performance for a range of quantification tasks: finding the mean radioactivity concentration for different regions of interests (ROIs), different ROI sizes and different group sizes (i.e. the number of subjects in the PET study). At present, the variability of quantification performance of different reconstruction methods, according to both the ROI and group sizes, is largely ignored. In this paper, it is shown that both the ROI and group size have a tremendous impact on the error of the estimator for the task of ROI quantification. A study-specific, task-oriented and space-variant selection rule is proposed that selects a close to optimal estimate drawn from a series of estimates obtained by filtered backprojection (FBP) and different OSEM (ordered subset expectation maximization) iterations. The optimality criterion is to minimize an estimated mean square error (MSE), where the MSE is estimated from the data in the study using the bootstrap resampling technique. The proposed approach is appropriate for both pixel-level estimates and ROI estimates in single- and multi-subject studies. An extensive multi-trial 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 minimize the true MSE (where the true MSE can only be obtained from many independent Monte-Carlo realizations with knowledge of the ground truth). This indicates that with the proposed selection rule one can obtain a close to optimal estimate while avoiding the critical step of selecting user-defined reconstruction settings (such as an OSEM iteration number or the choice between FBP and OSEM). In this initial 2D study, only FBP and OSEM reconstruction methods are considered but the proposed selection rule should readily generalize to different estimators (i.e. different reconstruction algorithms) and 3D imaging.