Spectral computed tomography has developed greatly in recent years because of its potential in material identification. It is difficult to obtain ideal reconstruction results only based on measured data. In order to obtain high quality reconstructed images, it always need to exploit prior knowledge as regularization terms in reconstruction model. However, when the prior changes, the overall framework of the algorithm changes accordingly. In this paper, we establish a reconstruction model that composed of a data fidelity term and a regularization term of tensor prior. The latter is simplified into a subproblem via the alternating direction method of multipliers, which can be flexibly replaced and solved under the plug-and-play framework.  Then, framelet tensor nuclear norm is acted on the tensors formed by similar block matching extraction and plugged as the regularization into the iterative scheme to update algorithm. The performance of the proposed method was verified by an industrial QRM phantom. Experimental results show that the proposed method has advantages in preserving structural details, even if projection views decrease.

spectral CT,plug-and-play,framelet,tensor nuclear norm,alternating direction method of multipliers