Derivation of the system matrix for an animal SPECT scanner with rotational collimator and stationary ring detector

The aim of this work is to develop a cost-effective technology for performing SPECT imaging on an existing animal PET scanner. Two replaceable collimators attached to the PET ring detector to provide single-photon imaging capability are investigated: 1) a slit-slat collimator for large axial field of view and 2) a multi-pinhole collimator for high spatial resolution. The slit component of the slit-slat collimator and the pinhole collimator are rotated to acquire tomographic data sets. Every rotational step of the collimator forms a new detector system configuration, which requires a new system matrix and thus the overall system matrix increases linearly with the rotation steps. In this work, an efficient approach is first proposed for storing the system matrix. It reduces the matrix size by 98.5% in comparison to the original size if stored in direct form. To achieve a balance of accuracy and computational time, we investigate two ways to derive the system matrix: from Monte Carlo simulation which takes much longer time but is more accurate and from analytical calculation which is hundreds times faster but has reduced accuracy. The point spread functions calculated using both methods are compared and show general resemblance. The system matrices derived in both ways are used in reconstructing simulated and experimental data and have produced images with the expected resolution. The distinctive characteristics of the two methods make them useful at different stages of the system development.