A content-adaptive unstructured grid based regularized CT reconstruction method with a SART-type preconditioned fixed-point proximity algorithm
A content-adaptive unstructured grid based regularized CT reconstruction method with a SART-type preconditioned fixed-point proximity algorithm
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DOI：
10.1088/1361-6420/ac490f
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发表时间：
2022-03-01
期刊：
影响因子：
2.1
通讯作者：
Xu，Yuesheng
中科院分区：
文献类型：
--
作者：
Chen，Yun;Lu，Yao;Xu，Yuesheng
本研究的目的是开发一种新的计算机断层扫描（CT）图像重建方法，旨在提高现有方法的重建图像的质量，同时降低计算成本。现有的CT重建是通过描述CT投影数据采集过程的积分方程的基于像素的分段常数近似来建模的。使用这些近似施加了一个瓶颈模型误差，并在一个大尺寸的离散系统的结果。我们建议开发一种基于内容自适应非结构化网格（CAUG）的正则化CT重建方法来解决这些问题。具体来说，我们设计了一个CAUG的图像域稀疏表示的底层图像，并引入了基于BLOG的分段线性近似的积分方程采用配置方法。我们进一步应用正则化定义的CAUG的不适定的线性系统，这可能会导致一个稀疏的线性表示的基础解决方案。将正则化CT重建问题转化为一个凸优化问题，其目标函数由基于加权最小二乘范数的保真度项、正则化项和约束项组成。在这里，相应的加权矩阵是从同时代数重建技术（SART）。然后，我们开发了一个SART型预处理定点邻近算法来解决优化问题。收敛性分析所得到的迭代算法。数值实验表明，所提出的方法优于现有的几种方法在抑制噪声和减少计算成本。这些方法包括无正则化和二次正则化的SART方法、传统的全变差正则化重建方法和像素网格上的全变差优化共轭梯度法。
The goal of this study is to develop a new computed tomography (CT) image reconstruction method, aiming at improving the quality of the reconstructed images of existing methods while reducing computational costs. Existing CT reconstruction is modeled by pixel-based piecewise constant approximations of the integral equation that describes the CT projection data acquisition process. Using these approximations imposes a bottleneck model error and results in a discrete system of a large size. We propose to develop a content-adaptive unstructured grid (CAUG) based regularized CT reconstruction method to address these issues. Specifically, we design a CAUG of the image domain to sparsely represent the underlying image, and introduce a CAUG-based piecewise linear approximation of the integral equation by employing a collocation method. We further apply a regularization defined on the CAUG for the resulting ill-posed linear system, which may lead to a sparse linear representation for the underlying solution. The regularized CT reconstruction is formulated as a convex optimization problem, whose objective function consists of a weighted least square norm based fidelity term, a regularization term and a constraint term. Here, the corresponding weighted matrix is derived from the simultaneous algebraic reconstruction technique (SART). We then develop a SART-type preconditioned fixed-point proximity algorithm to solve the optimization problem. Convergence analysis is provided for the resulting iterative algorithm. Numerical experiments demonstrate the superiority of the proposed method over several existing methods in terms of both suppressing noise and reducing computational costs. These methods include the SART without regularization and with the quadratic regularization, the traditional total variation (TV) regularized reconstruction method and the TV superiorized conjugate gradient method on the pixel grid.