MAP reconstruction from spatially correlated PET data

High sensitivity 3D PET data is often rebinned into 2D data sets in order to reduce the computation time of reconstructions. The need to precorrect the 3D 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 of the rebinned data and 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 2D PET data. The dependence relationship is then incorporated into a novel maximum a posteriori (MAP) 2D reconstruction method. Initial results show that this method is visually superior to traditional EM techniques and offers modest MSE improvements with a reference image over Poisson-based MAP methods.