Model-based normalization of a fractional-crystal collimator prototype for small-animal PET imaging

Previously, we proposed to use a coincidence collimator to determine four lines of response (LORs) within a crystal pair and achieve fractional-crystal resolution in PET imaging. We have designed and fabricated a collimator prototype for a small-animal PET, A-PET scanner. To compensate for imperfections in the fabricated collimator prototype, collimator as well as scanner normalization is required to reconstruct quantitative and artifact-free images. In this study, we developed a normalization method for the collimator prototype based on the A-PET normalization using a uniform cylinder phantom with diameter of 10 cm (and length of 15 cm). We performed data acquisition without the collimator for scanner normalization first, and then with the collimator from 8 different rotation views for collimator normalization. After a reconstruction without correction, we extracted the cylinder parameters from which we generated expected emission sinograms with attenuation correction. Single scatter simulation was used to generate the scattered sinograms. The least-squares method was used to generate the normalization coefficient for each LOR based on measured, expected and scattered sinograms. The scanner and collimator normalization coefficients were factorized by performing two normalizations separately. We developed a model-base collimator normalization that can significantly reduce variance and produce collimator normalization with adequate statistical quality within feasible scan time. The normalization methods were verified using experimental data.