基于最大后验概率的PET图像重建算法研究
发布时间：2018-09-04 17:17
【摘要】：正电子发射断层成像(Positron Emission Tomography,PET)是继计算机断层成像(Computed Tomography,CT)和磁共振成像(Magnetic Resonance Imaging,MRI)之后应用于临床的一种新型影像技术,现已广泛地使用于肿瘤细胞的探测、心脏病的诊断、神经和精神类疾病的诊断以及新药物的开发等领域。PET成像的目的是得到一个放射性物质在人体内部的分布图,因此,如何根据扫描数据来重建出高质量的图像,一直是PET领域的一个重要研究课题。总体来说,PET图像重建算法可以分为解析法和迭代法两类。解析法的代表是以中心切片定理和傅立叶变换为基础的滤波反投影算法,它具有计算简单,成像速度快等优点。但是当投影数据中含有大量噪声时,解析法很难重建出令人满意的图像,从而会影响临床诊断的效果。迭代法可以分为代数迭代法和统计迭代法两类。其中,代数迭代法的工作原理与解析法类似,由于其在重建图像的过程中较难引入各种物理成像条件及统计模型,因此很难重建出高质量的图像,故此方法在PET图像重建中使用较少。统计迭代法建立在观测数据的统计模型基础上,能够重建出高精度的重建图像,是目前PET图像重建中使用最广泛的一种方法。统计迭代法中经典的PET图像重建算法有很多,如最大似然期望最大算法(Maximum Likelihood Expectation Maximized,MLEM)、有序子集期望值最大算法(Ordered Subset Expectation Maximization,OSEM)和最大后验概率算法(Maximum A Posterior,MAP)等。本文的主要研究内容是MAP算法,又称为惩罚最大似然算法或Bayesian算法。本学位论文共五章,具体内容安排如下:在第一章中,我们首先介绍了PET成像技术的背景及意义,然后回顾了PET图像重建算法的历史与发展概况,最后简单地概述了本文的主要研究内容与结构安排。第二章是PET图像重建算法的基础理论知识部分,主要介绍了PET中的一些经典重建算法及它们的优缺点。剩下三章是本文的主要工作,所取得的研究成果如下所述。在第三章中,我们通过把各向异性中值扩散滤波器(Anisotropic Median-Diffusion,AMD)融合到中值根先验算法(Median Root Prior,MRP)中,提出了一种新的Bayesian图像重建算法。由于中值滤波器对高斯和Poisson两种噪声的抑制效果不明显,所以MRP算法很难取得令人满意的重建结果。新算法通过把AMD滤波器融合到MRP算法中,有效地抑制了重建图像中的所有噪声。模拟仿真实验结果表明,新算法在抑制噪声和保护边缘两方面取得了良好的折中,较大程度地提高了重建图像的质量。在第四章中,我们通过把AMD模型引入到PET图像重建算法中,提出了一种基于惩罚最大似然的PET图像重建算法。通过实验比较可知,新算法能取得较好的重建结果。此外,跟类似算法相比(如MLEM-PDE),新算法由于吸收了AMD模型的优点,参数设置简单,迭代过程中对梯度阈值和扩散次数的值不敏感,实用性较强。在第五章中,我们通过把一种修正的全变分模型(Total Variation,TV)和MLEM算法结合起来,提出了一种新的基于惩罚最大似然的PET图像重建算法。PET图像中的噪声主要是以Poisson噪声为主,一些传统的PET图像重建算法,如MLEM、MRP和MAP等,它们对一般的加性噪声有较好的抑制效果,但是对与信号相关的Poisson噪声的抑制效果却很不理想。新算法通过把PMTV模型(Poisson-modified Total Variation,PMTV)引入到MLEM算法中,有效地抑制了重建图像中的Poisson噪声,较大程度地提高了重建图像的质量。
[Abstract]:Positron Emission Tomography (PET) is a new imaging technique which has been used in clinic after Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). It has been widely used in tumor detection, heart disease diagnosis, neurological and psychiatric diseases. The purpose of PET imaging is to obtain a map of the distribution of radioactive substances in the human body. Therefore, how to reconstruct high-quality images from scanned data has always been an important research topic in the field of PET. There are two kinds of analytic methods. They are based on the central slice theorem and Fourier transform. They have the advantages of simple calculation and fast imaging speed. However, when there is a lot of noise in the projection data, it is difficult to reconstruct a satisfactory image by analytic method, which will affect the effect of clinical diagnosis. Algebraic iteration method and statistical iteration method are two kinds of methods. The principle of algebraic iteration method is similar to analytic method. Because it is difficult to introduce various physical imaging conditions and statistical models in the process of image reconstruction, it is difficult to reconstruct high-quality images, so this method is less used in PET image reconstruction. Based on the statistical model of measured data, it can reconstruct the reconstructed image with high precision, which is one of the most widely used methods in PET image reconstruction. Ordered Subset Expectation Maximization (OSEM) and Maximum A Posterior (MAP), etc. The main contents of this paper are MAP algorithm, also known as penalty maximum likelihood algorithm or Bayesian algorithm. In the second chapter, the basic theory of PET image reconstruction algorithm is introduced, and some classical reconstruction algorithms in PET and their advantages and disadvantages are introduced. The remaining three chapters are the following In the third chapter, we propose a new Bayesian image reconstruction algorithm by fusing anisotropic median diffusion filter (AMD) into Median Root Prior (MRP). The new algorithm can effectively suppress all the noises in the reconstructed image by fusing the AMD filter into the MRP algorithm. Simulation results show that the new algorithm achieves a good compromise between noise suppression and edge protection. In Chapter 4, we introduce AMD model into PET image reconstruction algorithm, and propose a PET image reconstruction algorithm based on penalty maximum likelihood. The experimental results show that the new algorithm can achieve better reconstruction results. In addition, compared with similar algorithms (such as MLEM-PDE), the new algorithm is more efficient. In Chapter 5, we propose a new PET image based on penalty maximum likelihood by combining a modified Total Variation (TV) with MLEM algorithm. The noise in PET image is mainly Poisson noise. Some traditional PET image reconstruction algorithms, such as MLEM, MRP and MAP, have good suppression effect on general additive noise, but the suppression effect on signal-related Poisson noise is not ideal. AlVariation (PMTV) is introduced into MLEM algorithm to suppress Poisson noise in reconstructed images and improve the quality of reconstructed images.
【学位授予单位】：湖南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.41
[Abstract]:Positron Emission Tomography (PET) is a new imaging technique which has been used in clinic after Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). It has been widely used in tumor detection, heart disease diagnosis, neurological and psychiatric diseases. The purpose of PET imaging is to obtain a map of the distribution of radioactive substances in the human body. Therefore, how to reconstruct high-quality images from scanned data has always been an important research topic in the field of PET. There are two kinds of analytic methods. They are based on the central slice theorem and Fourier transform. They have the advantages of simple calculation and fast imaging speed. However, when there is a lot of noise in the projection data, it is difficult to reconstruct a satisfactory image by analytic method, which will affect the effect of clinical diagnosis. Algebraic iteration method and statistical iteration method are two kinds of methods. The principle of algebraic iteration method is similar to analytic method. Because it is difficult to introduce various physical imaging conditions and statistical models in the process of image reconstruction, it is difficult to reconstruct high-quality images, so this method is less used in PET image reconstruction. Based on the statistical model of measured data, it can reconstruct the reconstructed image with high precision, which is one of the most widely used methods in PET image reconstruction. Ordered Subset Expectation Maximization (OSEM) and Maximum A Posterior (MAP), etc. The main contents of this paper are MAP algorithm, also known as penalty maximum likelihood algorithm or Bayesian algorithm. In the second chapter, the basic theory of PET image reconstruction algorithm is introduced, and some classical reconstruction algorithms in PET and their advantages and disadvantages are introduced. The remaining three chapters are the following In the third chapter, we propose a new Bayesian image reconstruction algorithm by fusing anisotropic median diffusion filter (AMD) into Median Root Prior (MRP). The new algorithm can effectively suppress all the noises in the reconstructed image by fusing the AMD filter into the MRP algorithm. Simulation results show that the new algorithm achieves a good compromise between noise suppression and edge protection. In Chapter 4, we introduce AMD model into PET image reconstruction algorithm, and propose a PET image reconstruction algorithm based on penalty maximum likelihood. The experimental results show that the new algorithm can achieve better reconstruction results. In addition, compared with similar algorithms (such as MLEM-PDE), the new algorithm is more efficient. In Chapter 5, we propose a new PET image based on penalty maximum likelihood by combining a modified Total Variation (TV) with MLEM algorithm. The noise in PET image is mainly Poisson noise. Some traditional PET image reconstruction algorithms, such as MLEM, MRP and MAP, have good suppression effect on general additive noise, but the suppression effect on signal-related Poisson noise is not ideal. AlVariation (PMTV) is introduced into MLEM algorithm to suppress Poisson noise in reconstructed images and improve the quality of reconstructed images.
【学位授予单位】：湖南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.41
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