  Spectral computed tomography (CT) has a great potential in material
identification and decomposition. To achieve high-quality material composition
images and further suppress the x-ray beam hardening artifacts, we first
propose a one-step material reconstruction model based on Taylor first-order
expansion. Then, we develop a basic material reconstruction method named
material simultaneous algebraic reconstruction technique (MSART). Considering
the local similarity of each material image, we incorporate a powerful block
matching frame (BMF) into the material reconstruction (MR) model and generate a
BMF based MR (BMFMR) method. Because the BMFMR model contains the L0-norm
problem, we adopt a split-Bregman method for optimization. The numerical
simulation and physical phantom experiment results validate the correctness of
the material reconstruction algorithms and demonstrate that the BMF
regularization outperforms the total variation and no-local mean
regularizations.
