Image reconstruction algorithm for a special geometry of the PET-insert system

We are developing a PET-insert system with a half-ring insert that can not only image breast at a high resolution as other dedicated mammography systems but also image the chest and ancillary wall at a better resolution than the existing PET systems. Three different types of coincidences are acquired; coincidences between insert and insert (Type II), coincidences between insert and scanner (Type IS), and coincidences between scanner and scanner (Type SS). The type II and IS data acquired in the proposed system does not sample the imaging FOV completely, hence an 2D iterative algorithm based on expectation maximization is developed that can estimate the activity in the FOV using all the three data sets. A novel approach to compute the 2D system matrix for the detector pairs acquiring coincidencs of type IS is developed that can account for gamma rays hitting the lateral surface of the detectors in the insert. This requires developing a new model for computing the system matrix in which the probabilities are computed using the lateral surfaces as well as the front surface of the detectors in the insert. Normalization factors are computed using a direct method to compensate for the non-uniformity in the intrinsic detection efficiency that depends on the material and length of the crystal. The proposed system is built in GATE and the data is generated with no attenuation and scatter from the phantom. It is demonstrated qualitatively using the simulation data that images with no visible artifacts can be reconstructed using the developed model for the system matrix and the normalization factors incorporated with the system matrix. A singular value decomposition and point source study is also performed to demonstrate the improvement in the proposed model compared to a conventional model for the system matrix.