【作者】 张敏；

【导师】 陈明；

【作者基本信息】 山东科技大学 ， 数学， 2023， 硕士

【摘要】 计算机断层成像技术是一种无损、先进的检测技术,简称为CT(Computed Tomography)技术。根据放射源的摆放位置,断层成像可分为发射型断层成像和透射型断层成像。发射型断层成像将放射性粒子植入肿瘤病灶后,放射源发射γ射线,射线会在病灶内部进行衰减,破坏其组织细胞和组织功能,从而达到杀死肿瘤细胞的目的;透射型断层成像的放射源置于物体外部,一般采用X射线源,射线经过检测对象时发生衰减,根据探测器采集到的衰减后的数据获取检测对象内容的结构信息。射线衰减信息的获取和重建是断层成像的核心,针对典型CT成像中射线衰减信息重构的问题,本文研究了SPECT成像中植入碘粒子的γ射线放射性计数问题,以及X射线能谱CT成像中射线衰减的图像重构问题,主要内容如下:(1)在植入碘粒子的介入治疗中,SPECT系统可检测γ射线,其放射性计数值反映了γ射线在组织内的衰减情况,从而根据肿瘤性质来精准计算植入的放射性粒子信息和它们的放射剂量。本文模拟了多个碘125粒子在体内的放射性计数分布情况,设计了一个多参数可控的泊松分布模型,基于最小二乘逼近思想,用L-M方法进行模型中相关参数的求解。在数值实验中,使用C++对不同活性、数量和位置的放射性粒子的计数值进行编程设计以及计算分析,并通过MATLAB将数值可视化。研究结果表明,利用设计的放射性粒子的分布和数量计算结果,可以为介入治疗中粒子植入信息提供有效的模拟测试。(2)在使用X-CT扫描物体时,物质对不同能量的X射线会产生不同的衰减特性,通过这种能谱特性能够更好地获得物质所反映的信息。本文研究了三能谱CT成像中射线衰减规律,提出了一种迭代型三能谱CT重建算法,以获得被测物体的三个基材料分解图像,能够更直观地观察物体的内部组成。该算法利用泰勒展开对多个能谱的投影数据进行处理,通过算法推导获得加权残差投影,再利用FBP算法直接重建加权残差投影获得加权残差图像,迭代过程累加残差图像更新基图像,从而获得分离的基材料图像。实验表明,该算法可以在3-4步迭代后便能收敛到效果满意的基材料分离图像。更多还原

【Abstract】 Computed Tomography is a lossless and advanced testing technology,called CT for short.According to the location of the radioactive source,tomography can be divided into emission tomography and transmission tomography.After radioactive particles are implanted into the tumor lesion,the radioactive source emitsγ-rays,which attenuate inside the lesion and destroy its tissue cells and tissue function,thus killing the tumor cells.The radioactive source of transmission tomography is placed outside the object,and X-ray source is generally used.The ray attenuates when passing through the detected object,and the structure information of the detected object is obtained according to the attenuated data collected by the detector.The acquisition and reconstruction of ray attenuation information is the core of tomography.In view of the reconstruction of ray attenuation information in typical CT imaging,this thesis studies theγ-ray radioactive counting problem implanted iodine particles in SPECT imaging,and the reconstruction problem of ray attenuation image in X-ray energy spectrum CT imaging.The main contents are as follows:(1)In interventional therapy with implanted iodine particles,the SPECT system can detectγ-rays,and its radiometer value reflects the attenuation ofγ-rays within the tissue,thereby accurately calculating the information of implanted radioactive particles and their radiation dose based on the nature of the tumor.This thesis simulates the distribution of radioactive counts of multiple iodine 125 particles in vivo,and designs a multi parameter controllable Poisson distribution model.Based on the least squares approximation idea,the L-M method is used to solve the relevant parameters in the model.In the numerical experiment,C++was used for programming design and calculation analysis of counting values of radioactive particles with different activities,quantities and positions,and the numerical visualization was carried out by MATLAB.The results show that the distribution and quantity of designed radioactive particles can provide an effective simulation test for particle implantation information in interventional therapy.(2)When using X-CT to scan objects,substances exhibit different attenuation characteristics for X-rays of different energies,which can better obtain the information reflected by the substance through this spectral characteristic.This thesis studies the attenuation law of rays in three energy spectrum CT imaging and proposes an iterative three energy spectrum CT reconstruction algorithm to obtain decomposed images of the three base materials of the tested object,which can more intuitively observe the internal composition of the object.The algorithm uses Taylor expansion to process the projection data of multiple energy spectra,obtains the weighted residual projection through the algorithm derivation,then reconstructs the weighted residual projection directly by FBP algorithm to obtain the weighted residual image,and updates the base image by adding residual images in the iterative process,so as to obtain the separated base material image.The experiment shows that the algorithm can converge to a satisfactory separation image of the base material after 3-4 iterations.更多还原