【作者】 张莹；

【导师】 王丹；

【作者基本信息】 北京工业大学 ， 计算机技术（专业学位）， 2015， 硕士

【摘要】 CT技术为现代生活的方方面面带来了无可估量的价值,无论是临床预诊断、工业无损检测还是生物传感领域都离不开CT技术的辅佐支持。CT技术的本质为透视成像,即通过对物体采集有效的投影数据,设计图像重建算法计算获知物体的内部横截面信息。CT图像重建算法从实现方式上可以划分成两大主线:解析图像重建算法和迭代图像重建算法。这两类算法各有千秋,解析重建算法在投影数据完全且均匀时重建速度快;而迭代重建算法可以在投影数据不足时得到较好质量的重建图像但运算时间的消耗却是巨大的。另一方面,投影设备扫描角度、照射剂量、采集效率等因素的严格限制并不能满足大型锥束CT重建系统的实际应用需求,这些就是近年来广受关注的不完全角度图像重建问题。压缩感知(Compressive Sensing,CS)理论为不完全角度重建提供了丰富的可能性。基于CS理论的图像重建算法打破了直接重建目标图像的常规,转而推导图像的稀疏化表示。其中各向同性TV最小化算法在保持重建图像真实度方面表现较为令人满意,重建图像质量比较突出。然而各向同性TV最小化算法毕竟是在迭代算法的框架下的进一步拓展延伸,在重建效率和收敛离散度上存在进一步的提升空间。因此,本论文主要从以下几个方面展开研究:1.在CS理论的思想指导下,研究图像的稀疏优化表示。考虑从两个方面对各向同性TV最小化算法进行完善:一是选择基于各向异性TV最小化的离散变换稀疏优化模型;二是在迭代过程,用线性近似的方法替换计算代价大的矩阵项,缩短子问题平均迭代周期,设计一种基于各向异性总变分最小化的CT图像重建算法。而后通过搭建仿真平台,进行仿真对照测试实验,客观的证明在极稀疏的角度数量下,本文提出的算法相对于各向同性TV最小化算法在收敛性和运行速度上的优异表现。2.采样条件的定量分析作为一种有效的数值分析手段有很高的实用价值。本文结合压缩感知的相关理论,研究系统矩阵性质与不完全角度重建所需投影角度数量的关系。而后本文给出了基于系统矩阵性质的精确重建必要条件,提出了一种基于系统矩阵分析的精确重建采集角度数量的下界估计方法,为不完全角度问题提供了实用的重建参考价值。更多还原

【Abstract】 CT technique is of great value in every aspect of modern life,because of its revolutionary influence on medical diagnosis, industrial nondestructive testing and biological sensing. The essence of CT technique is X-ray imaging, namely through the effective projection data, design reconstruction algorithm and calculate the internal cross section information about objects. From the implementation respect Classic traditional CT image reconstruction algorithm is divided into image reconstruction algorithm and iterative image reconstruction algorithm. These two kinds of algorithm each has his strong point. In practical application, limited to the acquisition time, irradiation dose, imaging system scanning geometry and other factors, projection data can only be obtained in the limited angle range. The above situation is the so called the incomplete angle image reconstruction problem.Compressed sensing(CS) theory provides new strategies and ideas for incomplete Angle reconstruction research.Basing on the CS theory Image reconstruction algorithm breaks the conventional which reconstructs image directly and turns to sparse image representation instead. Isotropic TV minimization algorithm is one of the most representative algorithms which has satisfactory fidelity and prominent reconstructed image quality. According to the piecewise continuity of the reconstruction object, basing on the regularization framework and using alternating direction method Isotropic TV minimization algorithm realizes good reconstruction details. However Isotropic TV minimization algorithm reveals the huge gap of the reconstruction efficiency and storage capacity comparing with the traditional analytic reconstruction algorithm.Above all, this thesis mainly involves the following several aspects:1. To start a research around issues of incomplete Angle reconstruction, the Anisotropic TV minimization CT image reconstruction algorithm is proposed which improves the original Isotropic TV minimization algorithm from two aspects: One is to choose the anisotropy of minimizing the TV image vector which optimizes sparse discrete transform optimization; the second is to apply solving strategy of nonmonotone line search in the process of iteration to speed up the sub-problem optimization solution.Then this paper builds the simulation platform, continuously tuning parameters of algorithm and completed the full simulation test. Through a large number of sample size control experiments, precision and efficiency of the algorithm is verified. By comparing with Isotropic TV minimization algorithm, we find that the conver-gence performance of the proposed algorithm is outstanding.2. Quantitative analysis of sampling as an effective means of numerical analysis is of high practical value in the incomplete perspective study. In this paper, based on the theory of compressive sensing, research rebuilds the relationship between system matrix properties and incomplete projection angle. Based on the exact reconstruction of the necessary conditions of system matrix, the paper presents an accurate system matrix reconstruction analysis method for collecting point of quantitative estimation of lower boundary which is of great value.更多还原