Positron Range Correction in PET Using an Alternating EM Algorithm

In Positron Emission Tomography (PET), positrons travel a short distance before annihilating with an electron resulting in blurred reconstructed imaged because of the difference between the positions of the emitted positrons and their annihilation points. For radionuclides which have a long mean positron range, this results in a significant loss in spatial resolution. This blurring occurs in the image space and is independent of the tomographic imaging process. In this paper we propose a reconstruction algorithm that models the PET imaging problem as a two step process positron emission followed by annihilations which are detected by the imaging system. Within the first step of this approach, the standard EM algorithm for PET is viewed as reconstructing an annihilation distribution rather than the actual activity distribution. Second, the annihilation distribution is then viewed as a blurred version of the activity distribution which can be recovered by image deconvolution with a density dependant positron range kernel. Our proposed algorithm is expressed as an alternating maximization algorithm that maximizes the likelihood of the annihilation and activity distributions given the data.