A Geometric Model to Characterize Annihilation Positions Associated With Scattered Coincidences in PET: A Simulation-Based Study

Abstract

If high energy resolution detectors are available, activity and electron density can be reconstructed in positron emission tomography (PET) using single scattered coincidences. In 2-D, each scattered coincidence can be represented by two circular arcs (TCA) that encompass the annihilation position. This geometric relationship enables PET images to be reconstructed using only scattered coincidences and in conjunction with trues, the image quality is improved. In the current generalized scatter reconstruction algorithm, a uniform distribution of activity is assumed within the arcs. The presence of multiple scatter and nonideal detector energy resolution blurs the image and further algorithmic improvements are required for clinical implementation. This work uses Monte-Carlo simulation of a PET system with ideal (0.1%) energy resolution detectors to develop and evaluate a geometric model that uses a normalized coordinate system to describe the distribution of the annihilation positions within the TCA associated with the scattered coincidences. The proposed model was able to describe and constrain the distribution of the annihilation positions as a function of the activity location and the size of the scanned object using a normalized co-ordinate system. The geometric model compares well with the simulation data and is insensitive to the actual activity distribution and shape of the patient, needing only the maximum dimension of the phantom. Building this distribution of annihilation positions into the scattering reconstruction algorithm improves the contrast and noise of the reconstructed images by 6% and 4%, respectively.