PET image reconstruction with a system matrix containing point spread function derived from single photon incidence response

A point spread function (PSF) for the blurring component in positron emission tomography (PET) is studied. The PSF matrix is derived from the single photon incidence response function. A statistical iterative reconstruction (IR) method based on the system matrix containing the PSF is developed. More specifically, the gamma photon incidence upon a crystal array is simulated by Monte Carlo (MC) simulation, and then the single photon incidence response functions are calculated. Subsequently, the single photon incidence response functions are used to compute the coincidence blurring factor according to the physical process of PET coincidence detection. Through weighting the ordinary system matrix response by the coincidence blurring factors, the IR system matrix containing the PSF is finally established. By using this system matrix, the image is reconstructed by an ordered subset expectation maximization (OSEM) algorithm. The experimental results show that the proposed system matrix can substantially improve the image radial resolution, contrast, and noise property. Furthermore, the simulated single gamma-ray incidence response function depends only on the crystal configuration, so the method could be extended to any PET scanner with the same detector crystal configuration.