Space variant PSF parameterization in image space using printed point source arrays on the HiRez PET/CT

A new practical and computationally efficient method for deriving and applying the space-variant blurring component of the system matrix is proposed and applied to the HiRez PET/CT scanner. The point spread function (PSF) was sampled at 14400 locations within the field-of-view (FOV) using an array of 120 18-F printed point sources. An HP printer was modified to print the sources on a sheet of A4 paper. To provide enough annihilating material for the positrons and move the array accurately within the FOV a Perspex phantom was designed. The reconstructed PSFs were parameterized in image space and modeled with a pair of multidimensional (3-D) Gaussian distributions. Through the fitting of appropriate functions, model parameters were interpolated and extrapolated for the remaining positions in the FOV. Image reconstruction with resolution modeling was implemented using the expectation maximization algorithm (OP-OSEM) and space variant image based convolution operations. Initial analysis shows significant improvements in the resolution using space variant kernels (reduction of FWHM from 5.5 mm down to 2 mm at 20 cm radially). The improvements are more pronounced at the edge of the FOV when compared to the space invariant method where the discrepancy between the measured space variant blurring kernel and the invariant kernel are larger. Using the printer for producing radioactive point sources, the PSF was sampled at 14400 positions in less than 24 h. Parameterizing the kernels in image space also provides a computation efficient alternative to projection space PSF parameterization with similar resolution improvements (a uniform resolution of 2 mm throughout the FOV) and minimal increase in the reconstruction time.