PET has been widely used for imaging 2D or 3D tomography of radioisotope distribution within the patient. But due to the high level noise of the measurement, accurate estimation of isotope distribution is still a challenging issue. During the early development of PET, researches developed the filtered back-projection (FBP) model based on Radon transform for reconstructing PET images. On the other hand, assuming data is Poisson distributed, iterative statistical reconstruction algorithms are able to model the physical detection process, and thus have been the primary focus of many recent efforts. However, from the perspective of statistical inference, such high dimensional maximum likelihood estimators are inevitably ill-conditioning. In this talk, I will discuss the limitation of PET, and the possible solutions.