  Spectral computed tomography (CT) reconstructs material-dependent attenuation
images with the projections of multiple narrow energy windows, it is meaningful
for material identification and decomposition. Unfortunately, the multi-energy
projection dataset always contains strong complicated noise and result in the
projections has a lower signal-noise-ratio (SNR). Very recently, the
spatial-spectral cube matching frame (SSCMF) was proposed to explore the
non-local spatial-spectrum similarities for spectral CT. The method constructs
such a group by clustering up a series of non-local spatial-spectrum cubes. The
small size of spatial patch for such a group make SSCMF fails to encode the
sparsity and low-rank properties. In addition, the hard-thresholding and
collaboration filtering operation in the SSCMF are also rough to recover the
image features and spatial edges. While for all steps are operated on 4-D
group, we may not afford such huge computational and memory load in practical.
To avoid the above limitation and further improve image quality, we first
formulate a non-local cube-based tensor instead of the group to encode the
sparsity and low-rank properties. Then, as a new regularizer,
Kronecker-Basis-Representation (KBR) tensor factorization is employed into a
basic spectral CT reconstruction model to enhance the ability of extracting
image features and protecting spatial edges, generating the non-local low-rank
cube-based tensor factorization (NLCTF) method. Finally, the split-Bregman
strategy is adopted to solve the NLCTF model. Both numerical simulations and
realistic preclinical mouse studies are performed to validate and assess the
NLCTF algorithm. The results show that the NLCTF method outperforms the other
competitors.
