Positron emission tomography (PET) is a widely used, highly sensitive molecular imaging in clinical diagnosis. There is interest in reducing the radiation exposure from PET but also maintaining adequate image quality. Recent methods using convolutional neural networks (CNNs) to generate synthesized high-quality PET images from low-dose counterparts have been reported to be state-of-the-art for low-to-high image recovery methods. However, these methods are prone to exhibiting discrepancies in texture and structure between synthesized and real images. Furthermore, the distribution shift between low-dose PET and standard PET has not been fully investigated. To address these issues, we developed a self-supervised adaptive residual estimation generative adversarial network (SS-AEGAN). We introduce (1) An adaptive residual estimation mapping mechanism, AE-Net, designed to dynamically rectify the preliminary synthesized PET images by taking the residual map between the low-dose PET and synthesized output as the input, and (2) A self-supervised pre-training strategy to enhance the feature representation of the coarse generator. Our experiments with a public benchmark dataset of total-body PET images show that SS-AEGAN consistently outperformed the state-of-the-art synthesis methods with various dose reduction factors.