Accelerated Cross-Reference Maximum Likelihood Estimates for Positron Emission Tomography

The state of art of positron emission tomography (PET) takes into account the accidental coincidence events and attenuation. The maximum likelihood estimator can handle this kind of random variation in the reconstruction of a PET image. However, the reconstruction is ill-posed and needs regularization. The boundary information, either from an expert or from the other medical modality of the same object, like the X-ray CT scan, MRI, and so forth, can be used to regularize the reconstruction. We have investigated new, efficient and robust approaches to extract the related but incomplete boundary information. Fast algorithms adapted from the expectation/conditional maximization (ECM) and space alternating generalized expectation maximization (SAGE) algorithms are proposed to accelerate the computation. The method of generalized approximate cross validation (GACV) is adjusted to select the penalty parameter from observed data quickly. The Monte Carlo studies demonstrate the improvement.