  Deep image prior (DIP) has recently attracted attention owing to its
unsupervised positron emission tomography (PET) image reconstruction, which
does not require any prior training dataset. In this paper, we present the
first attempt to implement an end-to-end DIP-based fully 3D PET image
reconstruction method that incorporates a forward-projection model into a loss
function. To implement a practical fully 3D PET image reconstruction, which
could not be performed due to a graphics processing unit memory limitation, we
modify the DIP optimization to block-iteration and sequentially learn an
ordered sequence of block sinograms. Furthermore, the relative difference
penalty (RDP) term was added to the loss function to enhance the quantitative
PET image accuracy. We evaluated our proposed method using Monte Carlo
simulation with [$^{18}$F]FDG PET data of a human brain and a preclinical study
on monkey brain [$^{18}$F]FDG PET data. The proposed method was compared with
the maximum-likelihood expectation maximization (EM), maximum-a-posterior EM
with RDP, and hybrid DIP-based PET reconstruction methods. The simulation
results showed that the proposed method improved the PET image quality by
reducing statistical noise and preserved a contrast of brain structures and
inserted tumor compared with other algorithms. In the preclinical experiment,
finer structures and better contrast recovery were obtained by the proposed
method. This indicated that the proposed method can produce high-quality images
without a prior training dataset. Thus, the proposed method is a key enabling
technology for the straightforward and practical implementation of end-to-end
DIP-based fully 3D PET image reconstruction.
