Compton scatter and randoms corrections for origin ensembles 3D PET reconstructions

In this work we develop a novel approach to correction for scatter and randoms in reconstruction of data acquired by 3D positron emission tomography (PET) applicable to tomographic reconstruction done by the origin ensemble (OE) approach. The statistical image reconstruction using OE is based on calculation of expectations of the numbers of emitted events per voxel based on complete-data space. Since the OE estimation is fundamentally different than regular statistical estimators such those based on the maximum likelihoods, the standard methods of implementation of scatter and randoms corrections cannot be used. Based on prompts, scatter, and random rates, each detected event is graded in terms of a probability of being a true event. These grades are utilized by the Markov Chain Monte Carlo (MCMC) algorithm used in OE approach for calculation of the expectation over the complete-data space of the number of emitted events per voxel (OE estimator). We show that the results obtained with the OE are almost identical to results obtained by the maximum likelihood-expectation maximization (ML-EM) algorithm for reconstruction for experimental phantom data acquired using Siemens Biograph mCT 3D PET/CT scanner. The developed correction removes artifacts due to scatter and randoms in investigated 3D PET datasets. (orig.)