A Deep Kernel Method for PET Image Reconstruction

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 procedure, which may lead to suboptimal performance. In this paper, we describe the equivalence between the kernel representation and a trainable neural network model. A deep kernel method is proposed with the training process utilizing available image prior to seek the best way to form a set of robust kernels optimally rather than empirically. The results from computer simulations and a real patient dataset demonstrate that the proposed deep kernel method can outperform existing kernel method and neural network method for dynamic PET image reconstruction.