As one of the state-of-the-art detectors, photon counting detector is used in spectral CT to classify the received photons
into several energy channels and generate multichannel projection simultaneously. However, the projection always
contains severe noise due to the low counts in each energy channel. How to reconstruct high-quality images from photon
counting detector based spectral CT is a challenging problem. It is widely accepted that there exists self-similarity over
the spatial domain in a CT image. Moreover, because a multichannel CT image is obtained from the same object at
different energy, images among channels are highly correlated. Motivated by these two characteristics of the spectral CT,
we employ tensor decomposition and nonlocal means methods for spectral CT iterative reconstruction. Our method
includes three basic steps. First, each channel image is updated by using the OS-SART. Second, small 3D volumetric
patches (tensor) are extracted from the multichannel image, and higher-order singular value decomposition (HOSVD) is
performed on each tensor, which can help to enhance the spatial sparsity and spectral correlation. Third, in order to
employ the self-similarity in CT images, similar patches are grouped to reduce noise using the nonlocal means method.
These three steps are repeated alternatively till the stopping criteria are met. The effectiveness of the developed
algorithm is validated on both numerically simulated and realistic preclinical datasets. Our results show that the proposed
method achieves promising performance in terms of noise reduction and fine structures preservation.