  The recently proposed sparsifying transform models incur low computational
cost and have been applied to medical imaging. Meanwhile, deep models with
nested network structure reveal great potential for learning features in
different layers. In this study, we propose a network-structured sparsifying
transform learning approach for X-ray computed tomography (CT), which we refer
to as multi-layer clustering-based residual sparsifying transform (MCST)
learning. The proposed MCST scheme learns multiple different unitary transforms
in each layer by dividing each layer's input into several classes. We apply the
MCST model to low-dose CT (LDCT) reconstruction by deploying the learned MCST
model into the regularizer in penalized weighted least squares (PWLS)
reconstruction. We conducted LDCT reconstruction experiments on XCAT phantom
data and Mayo Clinic data and trained the MCST model with 2 (or 3) layers and
with 5 clusters in each layer. The learned transforms in the same layer showed
rich features while additional information is extracted from representation
residuals. Our simulation results demonstrate that PWLS-MCST achieves better
image reconstruction quality than the conventional FBP method and PWLS with
edge-preserving (EP) regularizer. It also outperformed recent advanced methods
like PWLS with a learned multi-layer residual sparsifying transform prior
(MARS) and PWLS with a union of learned transforms (ULTRA), especially for
displaying clear edges and preserving subtle details.
