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)).