LROC Model Observers for Emission Tomographic Reconstruction

Detection and localization performance with signal location uncertainty may be summarized by Figures of Merit (FOM’s) obtained from the LROC curve. We consider model observers that may be used to compute the two LROC FOM’s: ALROC and PCL, for emission tomographic MAP reconstruction. We address the case background-known-exactly (BKE) and signal known except for location. Model observers may be used, for instance, to rapidly prototype studies that use human observers. Our FOM calculation is an ensemble method (no samples of reconstructions needed) that makes use of theoretical expressions for the mean and covariance of the reconstruction. An affine local observer computes a response at each location, and the maximum of these is used as the global observer the response needed by the LROC curve. In previous work, we had assumed the local observers to be independent and normally distributed, which allowed the use of closed form expressions to compute the FOM’s. Here, we relax the independence assumption and make the approximation that the local observer responses are jointly normal. We demonstrate a fast theoretical method to compute the mean and covariance of this joint distribution (for the signal absent and present cases) given the theoretical expressions for the reconstruction mean and covariance. We can then generate samples from this joint distribution and rapidly (since no reconstructions need be computed) compute the LROC FOM’s. We validate the results of the procedure by comparison to FOM’s obtained using a gold-standard Monte Carlo method employing a large set of reconstructed noise trials.