Model-Based Normalization of a Fractional-Crystal Collimator for Small-Animal PET Imaging

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