Chen Ling, Yang Xikai, Huang Zhishen, Long Yong, Ravishankar Saiprasad
University of Michigan - Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai, China.
Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan, USA.
Med Phys. 2023 Oct;50(10):6096-6117. doi: 10.1002/mp.16645. Epub 2023 Aug 3.
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.
最近提出的稀疏变换（ST）模型计算成本低，已应用于医学成像。同时，具有嵌套网络结构的深度模型在学习不同层的特征方面显示出巨大潜力。在本研究中，我们提出了一种用于X射线计算机断层扫描（CT）的网络结构ST学习方法，我们将其称为基于多层聚类的残差稀疏变换（MCST）学习。所提出的MCST方案通过将每层的输入划分为几个类别，在每层中学习多个不同的酉变换。我们通过将学习到的MCST模型部署到惩罚加权最小二乘（PWLS）重建的正则化器中，将MCST模型应用于低剂量CT（LDCT）重建。
所提出的MCST模型将多层稀疏表示结构与多个聚类相结合，用于由丰富的变换集合建模的每层特征。我们通过块坐标下降（BCD）算法以无监督方式训练MCST模型。由于我们的方法是基于补丁的，因此可以使用有限的图像集进行训练。对于CT图像重建，我们通过将预先学习的MCST信号模型与PWLS优化相结合，设计了一种名为PWLS-MCST的新算法。
我们对XCAT体模数据、梅奥临床数值CT数据集和“LDCT图像与投影数据集”（临床LDCT数据集）进行了LDCT重建实验。我们训练了具有两层（或三层）且每层有五个聚类的MCST模型。同一层中学习到的变换显示出丰富的特征，同时从表示残差中提取了额外信息。我们的模拟结果和临床结果表明，PWLS-MCST比传统的滤波反投影（FBP）方法和具有边缘保持（EP）正则化器的PWLS实现了更好的图像重建质量。它也优于最近的先进方法，如具有学习到的多层残差稀疏变换（MARS）先验的PWLS和具有学习到的变换联合（ULTRA）的PWLS，特别是在显示清晰边缘和保留细微细节方面。
在这项工作中，提出了一种具有嵌套网络结构的多层稀疏信号模型。我们将这个新模型称为MCST模型，它利用多层残差图来稀疏化基础图像，并对每层的输入进行聚类以实现精确的稀疏化。我们提出了一个带有学习到的MCST正则化器的新PWLS框架用于LDCT重建。实验结果表明，所提出的PWLS-MCST比几种基线方法提供了更清晰的重建。PWLS-MCST的代码在https://github.com/Xikai97/PWLS-MCST上发布。
