Abstract
Statistical image reconstruction methods can improve the quality of PET image results by using accurate probability model of photon detection. However, these statistical methods usually require repetitive forward and backward projections, which are computationally intensive. Implementation variations of the projection operations can greatly affect the reconstruction efficiency. The traditional on-the-fly method directly computes probability of the forward and backward projections during image iterations. As the probability model of photon detection become more complex, this approach will become less applicable due to the heavier computational load. In order to effectively compute projection operations, we suggest a matrix-based approach that each element of the matrix represents the probability of detecting a coincidence event from a voxel to a detector pair based on scanner’s geometry. Consequently, a forward or backward projection can be transformed into a simple matrix multiplication without repeated computation of probability during image reconstruction. In addition, probability matrix can incorporate non-uniform sampling distance, so that the PET data needs not to be pre-processed for geometric arc correction additionally. Because most PET scanners adopt cylindrical structure, there exist several geometric symmetries that can be used to reduce the numerical computation as well as the matrix storage by a factor of eight as suggested by Kaufman. Moreover, by integration of the symmetry and the sparseness of the probability matrix, the storage space can be further downsized to 0.18% of its original magnitude. In this work, we also examine two types of probabilistic model for coincidence detection: area-based and interpolative. From the experimental results, the area-based model shows better quality of the reconstructive image compared to interpolative one. In this thesis, we have shown that statistical image reconstructions with probability matrix and area-based detection model can generate more effective and accurate results for PET imaging.