正电子发射断层成像的统计迭代方法及加速方法研究
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摘要
正电子发射断层成像(Positron Emission Tomography，PET)是当代先进的无创伤且高品质的医学诊断技术，是最高水平核医学诊断的代表。本文讨论了正电子发射断层成像的原理和重建算法，主要研究了PET的统计迭代重建方法及加速方法。论文主要分成三大部分：PET成像原理和PET经典重建算法；基于各向异性扩散的PET重建算法；及基于改进的有序子集加速算法。
本文首先简单地描述了PET成像原理及其系统结构；接着，详细地论述了经典的PET重建算法，主要分为解析法和迭代法。解析法是研究断层成像的根本出发点，该方法具有算法简单，成像速度快等特点，但重建结果差；迭代算法可分为代数迭代算法和统计迭代算法。代数迭代算法是一类以线性方程组理论为基础的重建算法；而统计迭代算法是以一类以某种估计准则为基础的重建算法，如最小二乘算法、最大似然的期望最大化算法、贝叶斯算法等。由于迭代算法在迭代过程中考虑了系统的物理特性和观测数据的统计模型，重建结果要好于解析法。
针对P-M模型的缺陷，本文介绍了一种新的扩散模型，该模型在原来的基础上引入局部灰度方差。将该扩散模型与正则化MLEM算法结合起来形成了一种新的重建算法，并应用到PET重建中。在仿真实验中，新算法与其他重建算法进行了比较，结果表明本文的算法在提高重建图像的质量和保护细节上具有一定的优越性。
由于结合各向异性扩散的中值先验的PET重建算法(PDEMedian)采用了存有缺陷的P-M模型，从而造成重建算法保持边缘不够准确，且重建的图像含有阶梯伪影。本文将结合非局部均值方法和基于模糊理论的各向异性扩散模型应用到PET图像重建中。实验验证了新算法在PET重建中的优越性和可行性。
最后，研究了基于有序子集的统计迭代加速算法。我们将随着迭代次数增加而子集数逐渐减少的可变有序子集方法应用于统计迭代算法中，同时运用多分辨率(Multi- resolution, MR)概念对观测数据进行重组。实验证明该方法加快了算法的收敛速度，但并不以牺牲重建图像的质量为代价。
Positron emission tomography (PET) is one of advanced noninvasive diagnositic tech-nique of modern medical science, and it acts as one of representative techniques of modern nuclear medical diagnosis. The basic fundamentals and image reconstruction methodology of PET are discussed in the paper. And the later is the main purposes of this dissertation. Gener-ally three reconstruction algorithms are discussed in the paper: PML image reconstructionmodel based on nonlocal means, fuzzy theory and anisotropic diffusion; PML approach base the gray variance of neighborhood pixels and anitropic diffusion; Stactical iteration recon-struction based on modified order subsets.
The fundamentals and system structure of PET are introduced in the first part of the pa-per. Furthermore, PET image reconstruction approaches, which are classified into analytical and iterative method, are discussed detailly. The study of tomography reconstruction stems from the analytical method which is characteristic of simplicity and fastness. However, its re-constructed images are very noisy. Iterative algorithms can be separated into algebratic itera-tion method and statistical iteration method. The former one is based on linear equation theory, while the latter one is ground on some kinds of evaluation criterias which contains lots of methods such as least square algorithm, maximum likelihood expectation maximization algo-rithm, bayesian algorithm and so on. Due to introducing the physical properties of system and the stactistical model of projection data into the reconstruction, iterative algorithm can get better images than analytical method.
Against defects of P-M model, the gray variance of neighborhood pixels is brung into the diffusion model. And a new method, which combines the proposed diffusion model with re-gularized MLEM algorithm, is proposed in PET image reconstruction. The results show expe-rimentally that it has some performance of improving quality of reconstructed images and the protecting images edges in comparison with other common methods.
The method of PET image recontruction combined with anisotropic diffusion filter with median filter (PDEMedian) cannot protect the edges accurately as well as the step artifacts can be found obviously in the image reconstructed by PDEMedian due to the P-M diffusion model s poor properties. Such a novel diffusion model combined nonlocal means with fuzzy theory is introduced into PET image reconstruction. The feasibility and efficiency of the new method are verified experimentally in comparison with other traditional algorithms.
Finaly, the dissertation discuses the accelerated algorithm for statistical iteration based on modified ordered subset. And the modified ordered subset, whose number of subset de-creases with iteration, is introduced into iterative method. At the same, the projected data are rebuilted by the method of multi-resolution. The simulation results show the proposed method acceralate convergent rate of algorithm, but not at the expense of the reconstructed image squality.
本文首先简单地描述了PET成像原理及其系统结构；接着，详细地论述了经典的PET重建算法，主要分为解析法和迭代法。解析法是研究断层成像的根本出发点，该方法具有算法简单，成像速度快等特点，但重建结果差；迭代算法可分为代数迭代算法和统计迭代算法。代数迭代算法是一类以线性方程组理论为基础的重建算法；而统计迭代算法是以一类以某种估计准则为基础的重建算法，如最小二乘算法、最大似然的期望最大化算法、贝叶斯算法等。由于迭代算法在迭代过程中考虑了系统的物理特性和观测数据的统计模型，重建结果要好于解析法。
针对P-M模型的缺陷，本文介绍了一种新的扩散模型，该模型在原来的基础上引入局部灰度方差。将该扩散模型与正则化MLEM算法结合起来形成了一种新的重建算法，并应用到PET重建中。在仿真实验中，新算法与其他重建算法进行了比较，结果表明本文的算法在提高重建图像的质量和保护细节上具有一定的优越性。
由于结合各向异性扩散的中值先验的PET重建算法(PDEMedian)采用了存有缺陷的P-M模型，从而造成重建算法保持边缘不够准确，且重建的图像含有阶梯伪影。本文将结合非局部均值方法和基于模糊理论的各向异性扩散模型应用到PET图像重建中。实验验证了新算法在PET重建中的优越性和可行性。
最后，研究了基于有序子集的统计迭代加速算法。我们将随着迭代次数增加而子集数逐渐减少的可变有序子集方法应用于统计迭代算法中，同时运用多分辨率(Multi- resolution, MR)概念对观测数据进行重组。实验证明该方法加快了算法的收敛速度，但并不以牺牲重建图像的质量为代价。
Positron emission tomography (PET) is one of advanced noninvasive diagnositic tech-nique of modern medical science, and it acts as one of representative techniques of modern nuclear medical diagnosis. The basic fundamentals and image reconstruction methodology of PET are discussed in the paper. And the later is the main purposes of this dissertation. Gener-ally three reconstruction algorithms are discussed in the paper: PML image reconstructionmodel based on nonlocal means, fuzzy theory and anisotropic diffusion; PML approach base the gray variance of neighborhood pixels and anitropic diffusion; Stactical iteration recon-struction based on modified order subsets.
The fundamentals and system structure of PET are introduced in the first part of the pa-per. Furthermore, PET image reconstruction approaches, which are classified into analytical and iterative method, are discussed detailly. The study of tomography reconstruction stems from the analytical method which is characteristic of simplicity and fastness. However, its re-constructed images are very noisy. Iterative algorithms can be separated into algebratic itera-tion method and statistical iteration method. The former one is based on linear equation theory, while the latter one is ground on some kinds of evaluation criterias which contains lots of methods such as least square algorithm, maximum likelihood expectation maximization algo-rithm, bayesian algorithm and so on. Due to introducing the physical properties of system and the stactistical model of projection data into the reconstruction, iterative algorithm can get better images than analytical method.
Against defects of P-M model, the gray variance of neighborhood pixels is brung into the diffusion model. And a new method, which combines the proposed diffusion model with re-gularized MLEM algorithm, is proposed in PET image reconstruction. The results show expe-rimentally that it has some performance of improving quality of reconstructed images and the protecting images edges in comparison with other common methods.
The method of PET image recontruction combined with anisotropic diffusion filter with median filter (PDEMedian) cannot protect the edges accurately as well as the step artifacts can be found obviously in the image reconstructed by PDEMedian due to the P-M diffusion model s poor properties. Such a novel diffusion model combined nonlocal means with fuzzy theory is introduced into PET image reconstruction. The feasibility and efficiency of the new method are verified experimentally in comparison with other traditional algorithms.
Finaly, the dissertation discuses the accelerated algorithm for statistical iteration based on modified ordered subset. And the modified ordered subset, whose number of subset de-creases with iteration, is introduced into iterative method. At the same, the projected data are rebuilted by the method of multi-resolution. The simulation results show the proposed method acceralate convergent rate of algorithm, but not at the expense of the reconstructed image squality.
引文
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[5] G T Smith, K F Hubner, T McDonald. Cost analysis of FDG PET for managing patientswith ovarian cancer [J]. Clin Positron Imaging, 1999, 2(2): 63-70.
[6] D S Tyler, M Onaitis, A Kherani. Positron emission tomography scanning in malignantmelanoma [J]. Cancer, 2000, 89(5): 1019-1025.
[7] R Bar-Shalom, A Y Valdivia, M D Blaufox. PET imaging in oncology [J]. Seminars.Nuclear. Medical. 2000, 30(3): 150-185.
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