As the segment of diseased tissue in PET images is time-consuming, laborious and low accuracy, this work proposes an automated framework for PET image screening, denoising and diseased tissue segmentation. First, taking into account the characteristics of PET images, the framework uses a differential activation filter to select whole-body images containing lesion tissue. Second, a new neural network containing residual connections which has powerful generalization performance compared with normal FCN network is proposed for PET image reconstruction and denoising. Finally, in the segmentation of lesion tissues, a custom clustering algorithm based on the density is used to distinguishe the lesion tissue part from the normal tissue. Tests on real medical PET images show that the whole automated framework has good performance and time cost in PET lesion image screening, image denoising and lesion tissue segmentation compared with other algorithms. The framework shows promising scientific study and application prospects.