  Positron emission tomography (PET) is widely used for clinical diagnosis. As
PET suffers from low resolution and high noise, numerous efforts try to
incorporate anatomical priors into PET image reconstruction, especially with
the development of hybrid PET/CT and PET/MRI systems. In this work, we proposed
a novel 3D structural convolutional sparse coding (CSC) concept for
penalized-likelihood PET image reconstruction, named 3D PET-CSC. The proposed
3D PET-CSC takes advantage of the convolutional operation and manages to
incorporate anatomical priors without the need of registration or supervised
training. As 3D PET-CSC codes the whole 3D PET image, instead of patches, it
alleviates the staircase artifacts commonly presented in traditional
patch-based sparse coding methods. Moreover, we developed the residual-image
and order-subset mechanisms to further reduce the computational cost and
accelerate the convergence for the proposed 3D PET-CSC method. Experiments
based on computer simulations and clinical datasets demonstrate the superiority
of 3D PET-CSC compared with other reference methods.
