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Fourier Properties of Symmetric-Geometry Computed Tomography and Its Linogram Reconstruction with Neural Network.
IEEE Transactions on Medical Imaging ( IF 10.6 ) Pub Date : 2020-08-31 , DOI: 10.1109/tmi.2020.3020720
Tao Zhang , Li Zhang , Zhiqiang Chen , Yuxiang Xing , Hewei Gao

In this work, we investigate the Fourier properties of a symmetric-geometry computed tomography (SGCT) with linearly distributed source and detector in a stationary configuration. A linkage between the 1D Fourier Transform of a weighted projection from SGCT and the 2D Fourier Transform of a deformed object is established in a simple mathematical form (i.e., the Fourier slice theorem for SGCT). Based on its Fourier slice theorem and its unique data sampling in the Fourier space, a Linogram-based Fourier reconstruction method is derived for SGCT. We demonstrate that the entire Linogram reconstruction process can be embedded as known operators into an end-to-end neural network. As a learning-based approach, the proposed Linogram-Net has capability of improving CT image quality for non-ideal imaging scenarios, a limited-angle SGCT for instance, through combining weights learning in the projection domain and loss minimization in the image domain. Numerical simulations and physical experiments on an SGCT prototype platform showed that our proposed Linogram-based method can achieve accurate reconstruction from a dual-SGCT scan and can greatly reduce computational complexity when compared with the filtered backprojection type reconstruction. The Linogram-Net achieved accurate reconstruction when projection data are complete and significantly suppressed image artifacts from a limited-angle SGCT scan mimicked by using a clinical CT dataset, with the average CT number error in the selected regions of interest reduced from 67.7 Hounsfield Units (HU) to 28.7 HU, and the average normalized mean square error of overall images reduced from 4.21e-3 to 2.65e-3.

中文翻译:

对称几何计算机断层扫描的傅里叶性质及其神经网络的线性图重建。

在这项工作中,我们研究了线性分布的源和探测器在固定配置下的对称几何计算机体层摄影(SGCT)的傅里叶特性。以简单的数学形式(即SGCT的傅里叶切片定理)建立了SGCT加权投影的1D傅里叶变换与变形对象的2D傅里叶变换之间的联系。基于傅立叶切片定理和在傅立叶空间中的唯一数据采样,推导了基于线性图的傅立叶重构方法用于SGCT。我们证明了整个Linogram重建过程可以作为已知算子嵌入到端到端神经网络中。作为一种基于学习的方法,建议的Linogram-Net具有为非理想成像场景(例如,有限角度SGCT)改善CT图像质量的能力,通过组合投影域中的权重学习和图像域中的损失最小化。在SGCT原型平台上进行的数值模拟和物理实验表明,我们提出的基于Linogram的方法可以通过双SGCT扫描实现准确的重建,并且与滤波反投影类型重建相比,可以大大降低计算复杂度。当投影数据完成时,Linogram-Net实现了准确的重建,并且通过使用临床CT数据集模拟的有限角度SGCT扫描显着抑制了图像伪影,所选目标区域中的平均CT数误差从67.7 Hounsfield单位降低了( HU)降至28.7 HU,整体图像的平均归一化均方误差从4.21e-3降至2.65e-3。
更新日期:2020-08-31
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