Multi-layer clustering-based residual sparsifying transform for low-dose CT image reconstruction

The recently proposed sparsifying transform (ST) 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 ST 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.

The proposed MCST model combines a multi-layer sparse representation structure with multiple clusters for the features in each layer that are modeled by a rich collection of transforms. We train the MCST model in an unsupervised manner via a block coordinate descent (BCD) algorithm. Since our method is patch-based, the training can be performed with a limited set of images. For CT image reconstruction, we devise a novel algorithm called PWLS-MCST by integrating the pre-learned MCST signal model with PWLS optimization.

We conducted LDCT reconstruction experiments on XCAT phantom data, Numerical Mayo Clinical CT dataset and "LDCT image and projection dataset" (Clinical LDCT dataset). We trained the MCST model with two (or three) layers and with five 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 and clinical results demonstrate that PWLS-MCST achieves better image reconstruction quality than the conventional filtered back-projection (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 (MARS) prior and PWLS with a union of learned transforms (ULTRA), especially for displaying clear edges and preserving subtle details.

In this work, a multi-layer sparse signal model with a nested network structure is proposed. We refer this novel model as the MCST model that exploits multi-layer residual maps to sparsify the underlying image and clusters the inputs in each layer for accurate sparsification. We presented a new PWLS framework with a learned MCST regularizer for LDCT reconstruction. Experimental results show that the proposed PWLS-MCST provides clearer reconstructions than several baseline methods. The code for PWLS-MCST is released at https://github.com/Xikai97/PWLS-MCST.