CT迭代法重建中系统矩阵的构建方法及其在TV算法中的比较

发布时间：2018-02-11 06:07

本文关键词： 像素驱动射线驱动距离驱动 ASD-POCS算法不匹配算法　出处：《中北大学》2017年硕士论文　论文类型：学位论文

【摘要】：在医学CT中,过大的扫描剂量对被扫描病人是有害的。低剂量扫描的一种有效方法是仅仅扫描稀疏视角下的投影。然而,基于稀疏数据的解析法重建会产生严重的条状伪影,影响诊断。2006年,CS理论被提出,基于此理论设计的优化算法可以从稀疏投影重建出高精度图像。TV算法是一种有效的CS算法,该算法已经被从理论到实践深入研究,取得了一系列进展。TV算法本质上是迭代法,其成像问题被建模为一个线性方程组。线性方程组的系数矩阵就是系统矩阵,表示如何求取投影。系统矩阵的构建方法就是投影方法。投影方法的选取对TV算法的性能有一定影响。鉴于该问题尚未被深入研究,本文拟聚焦该问题,以期在系统比较各种投影方法的基础上,揭示投影方法的选取对TV重建的影响。本文主要做了如下研究:(1)设计并实现了4种系统矩阵建模方法:像素驱动,距离驱动,改进的距离驱动以及射线驱动(2)比较了它们的建模速度、建模精度(3)比较了在ASD-POCS算法中,4种建模方法对收敛速度的影响。(4)比较了它们在有噪声的情况下对噪声的敏感程度。(5)将不匹配理论与ASD-POCS算法相结合,实验验证在ASD-POCS算法中不同的不匹配对的表现性能。研究表明:距离驱动的建模速度最快;改进的距离驱动的建模精度最高;射线驱动在ASD-POCS算法中的收敛速度最快;匹配的投影、反投影对总是可以达到收敛但一些不匹配的对可能会导致发散,特别是在处理含噪的投影数据的时候,不匹配对更易发散。在所有不匹配对中,DD-RD具有良好的收敛性能可以成为不匹配对的推荐组合。这些研究,系统揭示了投影算法的选取对基于TV算法的图像重建的影响,对于实际的医学图像重建提供了模型选择依据。
[Abstract]:In medical CT, too much scanning dose is harmful to the scanned patients. One effective method of low dose scanning is to scan only the projection in sparse view. However, reconstruction based on sparse data can produce serious strip artifacts. In 2006, the CS theory was proposed. The optimized algorithm based on this theory can reconstruct high precision image from sparse projection. The algorithm is an effective CS algorithm, which has been studied from theory to practice. A series of progress has been made. The TV algorithm is essentially an iterative method, and its imaging problem is modeled as a linear equation system. The coefficient matrix of the linear equation system is the system matrix. The method of constructing system matrix is projection method. The selection of projection method has certain influence on the performance of TV algorithm. Since this problem has not been deeply studied, this paper intends to focus on the problem. In order to reveal the influence of the selection of projection methods on TV reconstruction on the basis of comparing various projection methods, this paper mainly studies the design and implementation of four system matrix modeling methods: pixel driving, distance driving, and so on. The improved distance drive and the ray drive compare their modeling speeds, In this paper, we compare the influence of four modeling methods on convergence rate in ASD-POCS algorithm. We compare their sensitivity to noise in the presence of noise. We combine the mismatch theory with ASD-POCS algorithm. The experimental results show that the performance of different mismatch pairs in ASD-POCS algorithm is the fastest, the improved distance driven modeling accuracy is the highest, the convergence speed of ray drive in ASD-POCS algorithm is the fastest, the projection of matching is the fastest. Backprojection pairs can always converge, but some mismatch pairs can lead to divergence, especially when processing noisy projection data. Mismatch pair is more prone to divergence. In all mismatch pairs, DD-RD has good convergence performance and can be used as a recommended combination of mismatch pairs. These studies reveal the influence of the selection of projection algorithm on image reconstruction based on TV algorithm. The model selection is provided for the actual medical image reconstruction.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

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