PET/SPECT/TAT成像重建算法研究及数值系统开发

【作者】 安聪沛；

【导师】 向淑晃；

【作者基本信息】 中南大学 ， 计算数学， 2008， 硕士

【摘要】 PET和SPECT是两个具有广阔医疗应用的现代成像技术。TAT是目前医疗成像仪器研究的热点,具有良好的发展前景。本文旨在研究PET、SPECT和TAT成像的数学模型、投影变换和重建公式,最终实现图像重建的数值实验。第一章介绍了PET、SPECT和TAT成像的数学原理及其中蕴含的数学问题,对于图像重建公式和算法作了初步的介绍后,将这些医疗成像仪器的成像数学原理总结为Radon-type变换及其逆Radon-type变换。第二章研究了KL变换在PET成像中的应用。将KL变换作用于经Radon变换后的图像数据,再提取各级主成分,最后对于各级主成分进行逆Radon变换实现了图像的重建。第三章数值实现了SPECT投影变换——衰减Radon变换并且对衰减Radon变换公式——Novikov公式进行了简单介绍。第四章首先考察TAT成像数学原理并且阐述了其投影变换——球平均Radon变换,其次对于3维图像重建公式进行了介绍;接着在对2维重建公式进行介绍的基础上,通过傅立叶变换和特殊函数积分将L.A.Kuyansky提出的含有振荡积分的2维重建公式化为简洁的含有Hilbert变换形式;并且利用Matlab开发出的TAT图像重建实验系统成功进行了2维情况下D.Finch的4个重建公式和本文推导得的重建公式的图像重建数值实验,做出了比较。第五章指出了全文中有待完善和进一步研究的工作。更多还原

【Abstract】 PET and SPECT are two modern imaging techniques of broad medical application.In nowadays,TAT is a research central point in the medical imaging equipment,with good prospects for development.This paper aims to study the imaging mathematical model of PET,SPECT TAT and projective transforms and the formulae of reconstruction,then eventually realizes the image reconstruction.In the first chapter,we introduce the imaging mathematical principles and the mathematical problems of the PET,SPECT and TAT. Give a preliminary introduction of the formulae and algorithms of the image reconstruction.Then we summarize the imaging mathematical principle of these medical imaging equipments into Radon-type transform and inverse Radon-type transform.In Chapter two,we study the application of the KL transform in the PET imaging.The KL transform operates on the image data of Radon transform,and then we gain all levels of the principle components.At last the inverse Radon transform operates on the principal components of all levels to achieve the image reconstruction.In Chapter three,we achieve some numerical experiments SPECT projective transformation - attenuation Radon transform and give a brief introduction about the inverse attenuation Radon transform formula-Novikov formula.In Chapter four,firstly we survey the imaging mathematical principle and state its projective transform - the Spherical Mean Radon transform of TAT.Secondly we introduce the imaging reconstruction formula of three-dimensional;Thirdly we apply the Fourier Transform and the special function integral to transform the two-dimensional reconstruction formula deduced by L.A.Kuyansky,including oscillatory integrals into a simple formula,which including Hilbert transform.Then we use Matlab to develop a simulation system of the TAT imaging reconstruction of the two-dimensional formulae,based on the D.Finch’s four reconstruction formulae and the formula which is derived in this chapter.The numerical experiments are successful.Therefore we gain a comparison.Last but not the least,we point out the text of the yet to be perfected and further research in chapter five.更多还原