  Attenuation correction (AC) is essential for the generation of artifact-free
and quantitatively accurate positron emission tomography (PET) images. However,
AC of PET faces challenges including inter-scan motion and erroneous
transformation of structural voxel-intensities to PET attenuation-correction
factors. Nowadays, the problem of AC for quantitative PET have been solved to a
large extent after the commercial availability of devices combining PET with
computed tomography (CT). Meanwhile, considering the feasibility of a deep
learning approach for PET AC without anatomical imaging, this paper develops a
PET AC method, which uses deep learning to generate continuously valued CT
images from non-attenuation corrected PET images for AC on brain PET imaging.
Specifically, an invertible network combined with the variable augmentation
strategy that can achieve the bidirectional inference processes is proposed for
synthetic CT generation (IVNAC). To evaluate the performance of the proposed
algorithm, we conducted a comprehensive study on a total of 1440 data from 37
clinical patients using comparative algorithms (such as Cycle-GAN and Pix2pix).
Perceptual analysis and quantitative evaluations illustrate that the invertible
network for PET AC outperforms other existing AC models, which demonstrates the
potential of the proposed method and the feasibility of achieving brain PET AC
without CT.
