Analytical reconstruction of deconvolved Fourier rebinned PET sinograms

Fully 3D PET data are often rebinned into 2D data sets in order to avoid computationally intensive 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 and cannot account for the statistical structure of data and noise. FORE data contain some blur in all three dimensions in comparison to conventional 2D PET data. In this work, we propose methods for approximating this blur in the sinogram domain 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 no improvement. When low image noise levels are required for detection tasks, the deconvolution of the axial PSF does not provide adequate resolution or quantitative benefits to justify its application. When accurate quantitation is required and higher noise levels are acceptable, the deconvolution of the axial PSF leads to considerable gains (30%) in accuracy over conventional FORE+FBP at matched noise levels.