  Image reconstruction for positron emission tomography (PET) is challenging
because of the ill-conditioned tomographic problem and low counting statistics.
Kernel methods address this challenge by using kernel representation to
incorporate image prior information in the forward model of iterative PET image
reconstruction. Existing kernel methods construct the kernels commonly using an
empirical process, which may lead to unsatisfactory performance. In this paper,
we describe the equivalence between the kernel representation and a trainable
neural network model. A deep kernel method is then proposed by exploiting a
deep neural network to enable automated learning of an improved kernel model
and is directly applicable to single subjects in dynamic PET. The training
process utilizes available image prior data to form a set of robust kernels in
an optimized way rather than empirically. The results from computer simulations
and a real patient dataset demonstrate that the proposed deep kernel method can
outperform the existing kernel method and neural network method for dynamic PET
image reconstruction.
