Representation of photon limited data in emission tomography using origin ensembles

Representation and reconstruction of data obtained by emission tomography scanners are challenging due to high noise levels in the data. Typically, images obtained using tomographic measurements are represented using grids. In this work, we define images as sets of origins of events detected during tomographic measurements; we call these origin ensembles (OEs). A state in the ensemble is characterized by a vector of 3N parameters Y, where the parameters are the coordinates of origins of detected events in a three-dimensional space and N is the number of detected events. The 3N-dimensional probability density function (PDF) for that ensemble is derived, and we present an algorithm for OE image estimation from tomographic measurements. A displayable image (e.g. grid based image) is derived from the OE formulation by calculating ensemble expectations based on the PDF using the Markov chain Monte Carlo method. The approach was applied to computer-simulated 3D list-mode positron emission tomography data. The reconstruction errors for a 10 000 000 event acquisition for simulated ranged from 0.1 to 34.8%, depending on object size and sampling density. The method was also applied to experimental data and the results of the OE method were consistent with those obtained by a standard maximum-likelihood approach. The method is a new approach to representation and reconstruction of data obtained by photon-limited emission tomography measurements.