PET reconstruction from deconvolved FORE data

Fully 3D PET data is often rebinned into 2D data sets in order to avoid time consuming fully 3D reconstruction. Then, conventional 2D reconstruction techniques are employed to obtain images from the rebinned data. In a common scenario, 2D filtered back projection (FBP) is applied to Fourier rebinned (FORE) data. This approach is suboptimal because FBP is based on an idealized mathematical model of the data. Specifically, FBP cannot account fully for variations in the system and the statistical structure of the data and noise. FORE data contains some blur in all 3 dimensions in comparison to conventional 2D PET data. In this work, we propose methods for approximating this blur due to FORE through its point spread function (PSF). We also explore simple methods for deconvolving the rebinned data with this PSF to restore it to a more ideal state prior to FBP. Our results show that deconvolution of the approximate transaxial PSF yields little improvement, while deconvolution of the axial PSF leads to significant gains in contrast levels.