基于自适应迭代的有限投影CT图像重建

发布时间：2018-06-01 16:54

本文选题：计算机断层成像 + 有限投影　；参考：《天津大学》2016年硕士论文

【摘要】：X射线计算机断层成像是一种医学成像技术,该技术被广泛应用于疾病的诊断与治疗等领域中。研究表明X射线的辐射可能诱发癌症。为了降低CT扫描的患癌风险,有必要减少射线的辐射剂量。在有限投影数据条件下,迭代算法展现了其重建出高质量图像的潜力。本文对有限投影数据重建算法展开研究,主要研究内容如下:(1)本文提出了两种自适应调整步长的CT图像重建算法。两种算法均将重建问题视为有约束的总变分最小化问题,采用两步式交替求解策略:凸集投影运算实现数据一致性约束和非负约束,最速下降法实现总变分最小化。本文所提算法根据凸集投影运算前后图像域或投影域的预测数据的变化值调整总变分最小化的下降步长,根据投影数据的噪声水平确定凸集投影的更新步长。本文设置了一个误差阈值,当投影误差小于阈值时,不进行凸集投影更新以减小算法的计算量。仿真数据和真实物体数据证明了本文两种算法的可行性。(2)考虑到光子数检测过程的统计特性,本文将CT图像重建问题视为带惩罚项的加权最小二乘优化问题,并将此问题转化为一个有约束的总变分最小化问题。通过交替进行总变分最小化和数据一致性约束求解该问题。采用一阶原始对偶算法实现总变分最小化,而采用凸集投影实现数据一致性约束和非负约束。本文提出的这种一阶原始对偶-凸集投影算法,包括一个隐式的平衡控制机制,用于控制凸集投影和一阶原始对偶算法运算过程的平衡。该算法开始时,凸集投影具有较大作用,一阶原始对偶算法实现的总变分最小化具有较小的作用,促使中间结果迅速满足数据一致性约束。再通过省略部分凸集投影,增强TV最小对结果的作用。本文算法与经典的ASD-POCS算法进行了实验对比,比较了算法重建图像的图像质量。所提算法还与一个保证收敛的一阶原始对偶算法Sidky-A7算法进行实验对比,研究了算法的收敛性。实验结果表明,本文算法可以以简单的参数调整完成重建过程,且重建的图像质量较好,算法的收敛速度较快。
[Abstract]:X-ray computed tomography (CT) is a medical imaging technology, which is widely used in the diagnosis and treatment of diseases. Studies have shown that X-ray radiation may cause cancer. In order to reduce the cancer risk of CT scan, it is necessary to reduce the radiation dose. Under the condition of finite projection data, the iterative algorithm shows its potential to reconstruct high quality images. In this paper, the finite projection data reconstruction algorithm is studied. The main research contents are as follows: 1) in this paper, two kinds of CT image reconstruction algorithms with adaptive step adjustment are proposed. In both algorithms, the reconstruction problem is regarded as a constrained total variational minimization problem, and a two-step alternating solution strategy is adopted: convex set projection to realize data consistency constraints and non-negative constraints, and the steepest descent method to minimize total variation. The algorithm proposed in this paper adjusts the descent step size of total variation minimization according to the change of prediction data in image domain or projection domain before and after projection operation of convex set, and determines the update step size of convex set projection according to the noise level of projection data. In this paper, an error threshold is set. When the projection error is less than the threshold, the projection update of the convex set is not carried out to reduce the computational complexity of the algorithm. Simulation data and real object data prove the feasibility of the two algorithms. Considering the statistical characteristics of photon number detection process, this paper regards CT image reconstruction as a weighted least square optimization problem with penalty term. The problem is transformed into a constrained total variational minimization problem. The problem is solved by alternating total variational minimization and data consistency constraints. The first order primal duality algorithm is used to minimize the total variation, while the convex set projection is used to realize the data consistency constraint and non-negative constraint. The first order primal dual convex set projection algorithm proposed in this paper includes an implicit balance control mechanism which is used to control the balance between the convex set projection and the first order primitive dual algorithm. At the beginning of the algorithm, the projection of convex sets plays an important role, and the minimization of the total variation realized by the first order primitive dual algorithm has a small effect, which makes the intermediate results satisfy the data consistency constraints quickly. Then, by omitting the projection of partial convex sets, the effect of TV minimum on the result is enhanced. The algorithm is compared with the classical ASD-POCS algorithm, and the image quality of the reconstructed image is compared. The proposed algorithm is also compared with a first-order primal dual algorithm (Sidky-A7), which guarantees convergence, and the convergence of the algorithm is studied. The experimental results show that the algorithm can complete the reconstruction process with simple parameter adjustment, and the reconstruction image quality is better, and the convergence speed of the algorithm is faster.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP391.41

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