  PET image reconstruction is challenging due to the ill-poseness of the
inverse problem and limited number of detected photons. Recently deep neural
networks have been widely and successfully used in computer vision tasks and
attracted growing interests in medical imaging. In this work, we trained a deep
residual convolutional neural network to improve PET image quality by using the
existing inter-patient information. An innovative feature of the proposed
method is that we embed the neural network in the iterative reconstruction
framework for image representation, rather than using it as a post-processing
tool. We formulate the objective function as a constraint optimization problem
and solve it using the alternating direction method of multipliers (ADMM)
algorithm. Both simulation data and hybrid real data are used to evaluate the
proposed method. Quantification results show that our proposed iterative neural
network method can outperform the neural network denoising and conventional
penalized maximum likelihood methods.
