  In positron emission tomography (PET) imaging, statistical iterative
reconstruction (IR) techniques appear particularly promising since they can
provide accurate system model. The system model matrix which describes the
relationship between image space and projection space is important to the image
quality. It contains some factors such as geometrical component and blurring
component. The blurring component is usually described by point spread function
(PSF). A PSF matrix derived from the single photon incidence response function
is studied. And then an IR method based on the system matrix containing the PSF
is developed. More specifically, the gamma photon incidence on 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 is 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 PSF is finally established. Using this
system matrix, the image is reconstructed by ordered subset expectation
maximization (OSEM) algorithm. The experimental results show that the proposed
system matrix can obviously improve the image radial resolution, contrast and
noise property. Furthermore, the simulated single gamma-ray incidence response
function only depends on the crystal configuration, so the method could be
extended to any PET scanners with the same detector crystal configuration.
