We discuss the effect of having a finite number of detectors on the es
timation of a bounded linear functional of a PET image. We argue that
the functional should be estimated directly from the detector counts a
nd give an estimate of the effect of the binning of the counts to orde
r D-2, where D is the number of detectors. We then suggest an estimato
r that includes a data determined bias correction reducing the bias to
o(D-2).