MAP reconstruction from spatially correlated PET data

High sensitivity 3-D PET data is often rebinned into 2-D data sets in order to reduce the computation time of reconstructions. The need to precorrect the 3-D data for attenuation, accidentals, scatter, and deadtime effects before rebinning along with the rebinning process itself changes the statistics of the data. This paper presents an approach for finding and using the statistics of Fourier rebinned (FORE) data. In particular, utilizing a space domain representation of FORE, we find the approximate covariance matrix. We also derive an improved estimate of the mean of the rebinned data with a 2-D forward projector that more accurately represents the effect of FORE on the original 3-D PET measurements. In order to incorporate dependent information, we model the data conditioned on the image as a low-order Markov field. This model is based on a quadratic approximation of the log-likelihood of dependent 2-D PET data. The dependence relationship is then incorporated into a novel maximum a posteriori (MAP) 2-D reconstruction method. Initial results show that this method offers modest MSE improvements with a reference image over Poisson-based MAP methods. Results also reveal that the use of only the improved mean leads to significant improvements in reconstructions from FORE data.