Rapid Optimization of SPECT Scatter Correction Using Model LROC Observers

The problem we address is the optimization and comparison of window-based scatter correction (SC) methods in SPECT for maximum a posteriori reconstructions. While sophisticated reconstruction-based SC methods are available, the commonly used window-based SC methods are fast, easy to use, and perform reasonably well. Rather than subtracting a scatter estimate from the measured sinogram and then reconstructing, we use an ensemble approach and model the mean scatter sinogram in the likelihood function. This mean scatter sinogram estimate, computed from satellite window data, is itself inexact (noisy). Therefore two sources of noise, that due to Poisson noise of unscattered photons and that due to the model error in the scatter estimate, are propagated into the reconstruction. The optimization and comparison is driven by a figure of merit, the area under the LROC curve (ALROC) that gauges performance in a signal detection plus localization task. We use model observers to perform the task. This usually entails laborious generation of many sample reconstructions, but in this work, we instead develop a theoretical approach that allows one to rapidly compute ALROC given known information about the imaging system and the scatter correction scheme. A critical step in the theory approach is to predict additional (above that due to to the propagated Poisson noise of the primary photons) contributions to the reconstructed image covariance due to scatter (model error) noise. Simulations show that our theory method yields, for a range of search tolerances, LROC curves and ALROC values in close agreement to that obtained using model observer responses obtained from sample reconstruction methods. This opens the door to rapid comparison of different window-based SC methods and to optimizing the parameters (including window placement and size, scatter sinogram smoothing kernel) of the SC method.