The quantitative accuracy of positron emission tomography (PET) is affected by several factors, including the intrinsic resolution of the imaging system and inherently noisy data, which result in a low signal-to-noise ratio (SNR) of PET image. To address this problem, in this paper, we proposed a novel deep learning denoising framework aiming to enhance the quantitative accuracy of dynamic PET images via introduction of deep image prior (DIP) combined with Regularization by Denoising (RED), as such the method is labeled as DeepRED denoising. The network structure is based on encoder-decoder architecture and uses skip connections to combine hierarchical features to generate the estimated image. The network input can be random noise or other prior images (such as the patient's own static PET image), avoiding the need of high quality noiseless images, which is limited in PET clinical practice due to high radiation dose. Based on simulated data and real patient data, the quantitative performance of the proposed method was compared with conventional Gaussian filtering (GF), non-local mean (NLM), block-matching and 3D filtering (BM3D), DIP and stochastic gradient Langevin dynamics (SGLD) method. Overall, the proposed method can outperform other conventional methods in substantial visual as well as quantitative accuracy improvements (in terms of noise versus bias performance) with and without prior images.INDEX TERMS Positron emission tomography, deep neural networks, deep image prior, regularization by denoising.