【作者】 惠苗；

【导师】 潘晋孝；

【作者基本信息】 中北大学 ， 信号与信息处理， 2007， 硕士

【摘要】 X射线CT (Computed Tomography计算机断层摄影术)自1972年问世以来得到了越来越广泛的应用。CT的广泛应用又反过来推动了对它的研究,使它得到进一步的发展,在30年的发展过程中,它基本上经历了几次大的变革。CT的这些发展变化主要体现在两个方面,一是提高扫描速度,二是改善图像的质量。X射线CT图像是由计算机对物体的投影数据进行计算而获得的,因此CT的成像过程可以分为两大步,一是用X光系统进行投影数据的采集,获得充分的投影数据;二是图像重建,用计算机对投影数据进行计算来获得断层图像。扫描模式可以分为三种,平行束、扇形束和锥形束。平行束投影在工程上是不能直接实现的。和扇形束投影相比,锥形束投影一次性获得的信息量更大,因此锥形束投影结构有利于提高扫描速度和图像质量。但是锥形束投影数据和断层图像之间的关系很复杂,这会使计算的复杂度大大增加。近十年来,出现了很多针对锥形束CT的研究,但基本上都不是很成熟,到目前为止还没有出现真正意义上的商业化锥形束CT。针对CT目前存在的问题,本文主要研究的内容有以下几点:1.三维重建算法的可靠性和准确性的研究过程中,模型设计以及投影数据模拟是必不可少的一部分。本文以三维Shepp-Logan头部模型为例,详细介绍了其模型设计思路和仿真投影数据的计算方法,并利用经典FDK重建算法的重建结果验证了模型设计思路的准确性和投影数据计算的可行性。2.针对当前螺旋锥束CT存在算法实现复杂,重建相当耗时的问题,本论文提出了一种螺旋锥束近似重建算法,并在提高重建速度方面进行了研究。主要从算法结构、实现技巧及代码优化等方面研究了几种快速重建算法,计算机模拟实验证明了这些方法可有效提高图像重建的速度。3.在无约束最优化为基础的图像重建问题中,为了提高迭代效率及重建图像质量,首次提出将变度量法应用到图像重建中,并且介绍了最速下降法和共轭梯度法等算法。通过模拟实验,在迭代的次数和重建图像的质量方面比较了几种无约束最优化重建算法,得出变度量法在迭代效率和重建图像质量方面优于其它算法。本论文还对目前的一些常见的锥形束扫描重建算法进行了分析和比较,按照轨道类型、是否精确等进行了分类,并且讨论了它们各自的特点。介绍的锥束扫描重建算法有FDK、P-FDK、T-FDK、HT-FDK和S-FDK等。更多还原

【Abstract】 X-ray CT has been widely used in the world, since the birth of the first CT (Computed Tomography) in 1972。The broad using of CT also generates great impetus for CT research. Several big changes have been taken place during the past 30 years. These changes mainly involve in two aspects--speed and image quality.X-ray CT image is calculated from projection data by computer. So there are two steps to get image. Firstly, use X-ray to collect projection data. Secondly, calculate projection data to get image. There are three kinds of scan mode: parallel-beam, fan-beam and cone-beam. Parallel-beam projection data can’t be realized in the project directly. Compared with the fan-beam projection data, the cone-beam projection data get more information once. So it is in favor of improving scan speed and image quality. But the relationship between cone-beam projection data and the cross section image is very complex, and it increases the complexity of reconstruction algorithm and scan frame. In recent years, many research in the cone-beam scan technology appeared .But many of the algorithms are not very perfect, so the commercial cone-beam CT is not appeared at present. Three main questions have been researched in this thesis in order to solve the problem existed in CT.1. In the process of research in the accuracy of model computation and the feasibility of three-dimension reconstruction algorithm, the design of model and computer simulation of projection data is a necessary part. 3D Shepp-Logan head phantom is used as an example. The thesis introduces its design and the projection simulation method in detail. The projection data simulation is performed based on 3D Shepp-Logan head phantom. The results of image reconstruction using FDK algorithm indicate the accuracy of model design and the feasibility of computing projection data.2. Cone-beam helical CT is complex and time-consuming in reconstruction algorithm for the moment. The helical Cone-Beam approximate reconstruction algorithm is introduced in the thesis. And the thesis researches on reconstruction speed from the structure of algorithm、the technique of implementation and the optimization of code. Computer simulation experiment express that the methods can efficiently improve the speed of image reconstruction.3. In the image reconstruction basing on optimization without constraint,in order to improve iterative efficiency and reconstructed quality, the thesis firstly applies the variable metric method to reconstruct image, and describes variable metric method、steepest descent Method、conjugate gradient method respectively. The thesis compared three algorithms above at iterative efficiency and reconstruction quality respectively by simulating experiment. The result shows that variable metric method is better than other algorithms in the aspects of iterative efficiency and reconstruction quality.In this thesis, some familiar cone-beam scan reconstruction algorithms are also analyzed. These algorithms can be sorted by scan mode, reconstruction precision. The cone-beam scan reconstruction algorithms are introduced in this paper include FDK、P-FDK、T-FDK、HT-FDK and S-FDK, etc.更多还原