Collimator design optimization using Monte Carlo simulation and Bayesian parameter estimation

A Bayesian estimator has been implemented to serve as a paradigm for human observer performance in detecting lesions of unknown size and activity in a uniform noisy background of unknown amplitude. The Bayesian observer used knowledge of the possible range of lesion sizes as a prior. The results of a six-observer ROC study were well predicted by the performance of the Bayesian estimator. A calculation of the Cramer-Rao bound on the variance of lesion activity estimates (which included the same prior) was then used to optimize the geometric parameters of a two-layer tungsten collimator being constructed from crossed grids for a new imaging detector. A Monte Carlo program was used to estimate all contributions to the radial point-spread function for collimators of differing tungsten contents and spatial resolutions, imaging 140-keV photons emitted from the center of a 15-cm-diameter, water-filled cylinder. The optimal collimator design for detecting small lesions with unknown diameters in the range 2.5-7.5 mm provided a geometric collimator efficiency of 1.21×10^-4 and a single-septum penetration probability of 1%