Collimator optimization in SPECT using different tasks involving detection and localization

We use task-driven measures of image quality to optimize collimator properties in SPECT. We apply ideal observers to the following tasks: detection and localization, detection with signal location known, detection with signal location unknown and detection performance averaged over known signal locations. The ideal observer yields the best performance amongst other observers for the chosen task. The ideal observer is applied to the raw data, the sinogram, rather than the reconstructed image. We consider an ideal observer for the task of joint-detection and localization and compare its performance to that of the other three tasks on a family of collimators indexed by a resolution/sensitivity parameter. We compare this performance curve to that obtained using a detection only signal-known-exactly (SKE) and a SKEV task in which SKE performance is averaged over location. We also compare this performance curve to that obtained using detection-only task in which the signal location is unknown. It is interesting to compare the respective performance vs resolution/sensitivity parameter curves. The ideal LROC observer results in a sharply peaked curve, preferring one collimator, and the SKE and SKEV curves result in broad flat curves much less sensitive to the resolution/sensitivity parameter. The ideal collimator selected by the more realistic detection+location task differs from these selected by the other three tasks. We conclude that for the object class of this experiment, the ideal detection and localization observer should be used since it represents a more realistic task and leads to a different collimator.