Estimating linear functionals of a PET image

The authors discuss the effect of having a finite number of detectors on the estimation of a bounded linear functional of a PET image. They argue that the functional should be estimated directly from the detector counts and give an estimate of the effect of the binning of the counts to order D^-2, where D is the number of detectors. The authors then suggest an estimator that includes a data determined bias correction reducing the bias to o(D^-2)