Asymptotic Consistency of the Maximum Likelihood Estimate in Positron Emission Tomography and Applications

Abstract

This paper indicates that a minor modification of the maximum likelihood estimate of Vardi, Shepp and Kaufman can be regarded as a step in the standard nonparametric MLE by the method of sieves and establishes the asymptotic consistency for it. This method of sieves suggests that the number of pixels needs to be in line with the number of detectors in order to avoid poor image reconstructions. A simulation study is also presented to support this suggestion.