Rapid computation of LROC figures of merit using numerical observers (for SPECT/PET reconstruction)

The assessment of PET and SPECT image reconstructions by image quality metrics is typically time consuming, even if model observers and sample methods are used to replace human testing. We consider a detection task where the background is known exactly and the signal is known except for location. We develop theoretical formulae to rapidly evaluate relevant figures of merit, the area under the LROC curve and the probability of correct localization. The formulae can accomodate different forms of model observer. The theory hinges on the fact that we are able to rapidly compute the mean and covariance of the reconstruction. For two forms of model observer, the theoretical expressions are validated by Monte Carlo studies. The theory method affords a 10²-10³ speedup relative to methods in which model observers are applied to sample reconstructions.