PET statistical reconstruction with modeling of axial effects of FORE

Rebinning methods are often used to simplify the reconstruction of fully 3D PET measurements. These methods result in data sets with first and second order statistics different from conventional 2D collected data. This poses a problem because 2D reconstruction techniques were designed to work with the statistics of conventional 2D data. In this work, we explore how the axial statistics of data rebinned with the commonly used Fourier rebinning (FORE) method deviate from conventional 2D data. FORE essentially interpolates the 3D data into rebinned planes based on frequency content resulting in a blurring and correlating effect amongst planes. We propose an approximation for this effect and describe the conditional mean and covariance of the data. We also present novel methods for incorporating the modified mean and covariance into a 2D iterative reconstruction technique. The method with just the improved second order effect causes little improvement, while the technique with an improved axial mean has strong positive results in terms of contrast.