Current clinical dynamic PET has an effective temporal resolution of 5-10 seconds, which can be adequate for traditional compartmental modeling but is inadequate for exploiting the benefit of more advanced tracer kinetic modeling. There is a need to improve dynamic PET to allow 1-second temporal sampling. However, reconstruction of these short-time frames from tomographic data is extremely challenging as the count level of each frame is very low and high noise presents in both spatial and temporal domains. Previously the kernel framework has been demonstrated as a statistically efficient approach to utilizing image prior for low-count image reconstruction. Nevertheless, the existing kernel methods mainly explore spatial correlations in the data and only have a limited ability in suppressing temporal noise. In this paper, we propose a new kernel method which extends the previous spatial kernel method to the general spatiotemporal domain. The new kernelized model encodes the spatiotemporal correlations obtained from image prior information and is incorporated into the PET forward projection model to improve the maximum likelihood (ML) image reconstruction. Computer simulations show that the proposed approach can achieve effective noise reduction in both spatial and temporal domains and outperform the spatial kernel method and conventional ML reconstruction method for improving high temporal-resolution dynamic PET imaging.