Fast and accurate detector module crystal blur and mis-position error modeling for PET imaging

We propose a new method for modeling the detector module crystal positioning-blur and mis-positioning errors based on the detector modules' flood histograms (crystal position map) and crystal segmentation maps and use simulations for validation. First, a statistical simulation tool is used to simulate signal pathways from gamma photons in crystals to photo-multiplier tube pulses and then to digitized data for flood histograms. Next, a mixture of generalized 2D skewed Gaussian functions is used to model the simulated flood histogram for each crystal. A fitted flood histogram is generated with the estimated parameters from the simulated flood histogram. By applying the crystal segmentation map to the results of the fit, a crystal crosstalk matrix is calculated to characterize the probability distribution of the detector module crystal positioning-blur and mis-position error. The crystal crosstalk is then used to generate the probability distribution function (pdf) of the crystal blur and mis-position error for each detector module. To evaluate our method, we applied the pdf on GATE-simulated singles and/or paired list-mode data for point sources at various locations without considering crystal blur and mis-position error. The FWHM of each point in the reconstructed images was evaluated and compared to that of those reconstructed without applying the model. Preliminary results show that the method could efficiently model the resolution degradation. The advantage of the proposed method is that it can use real measurement data and can potentially include all resolution degradation effects in the detector module and detecting electronics. It is also fast and feasible for multiple repeated studies because it does not require time-consuming photon-tracking simulations. This approach is suitable both for accurate data generation after photon tracking through the phantom/patient and also for real detector PSF modeling inside image reconstruction algorithms.