  To obtain high-quality positron emission tomography (PET) images while
minimizing radiation exposure, various methods have been proposed for
reconstructing standard-dose PET (SPET) images from low-dose PET (LPET)
sinograms directly. However, current methods often neglect boundaries during
sinogram-to-image reconstruction, resulting in high-frequency distortion in the
frequency domain and diminished or fuzzy edges in the reconstructed images.
Furthermore, the convolutional architectures, which are commonly used, lack the
ability to model long-range non-local interactions, potentially leading to
inaccurate representations of global structures. To alleviate these problems,
we propose a transformer-based model that unites triple domains of sinogram,
image, and frequency for direct PET reconstruction, namely TriDo-Former.
Specifically, the TriDo-Former consists of two cascaded networks, i.e., a
sinogram enhancement transformer (SE-Former) for denoising the input LPET
sinograms and a spatial-spectral reconstruction transformer (SSR-Former) for
reconstructing SPET images from the denoised sinograms. Different from the
vanilla transformer that splits an image into 2D patches, based specifically on
the PET imaging mechanism, our SE-Former divides the sinogram into 1D
projection view angles to maintain its inner-structure while denoising,
preventing the noise in the sinogram from prorogating into the image domain.
Moreover, to mitigate high-frequency distortion and improve reconstruction
details, we integrate global frequency parsers (GFPs) into SSR-Former. The GFP
serves as a learnable frequency filter that globally adjusts the frequency
components in the frequency domain, enforcing the network to restore
high-frequency details resembling real SPET images. Validations on a clinical
dataset demonstrate that our TriDo-Former outperforms the state-of-the-art
methods qualitatively and quantitatively.
