正电子发射断层的图像重建方法研究
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摘要
正电子发射断层(positron emission tomography:PET)是现代核科学的代表,它利用放射性核素标记物对组织功能进行显像,也是当今能够无创地以动态、定量的方式观测到活体生理和生化变化的医学成像工具之一。本文主要研究了关于正电子发射断层的若干新的重建方法,即基于可变索引集的SAGE(space alternating generalized expectation maximization)算法以及在高斯PET观测模型中的应用,尝试研究了基于小波变换的多尺度迭代MAP(maximum a posteriori)重建,探讨了序列化递推WLS(weighted least squares)重建和状态空间Kalman滤波重建法,最后研究了基于正交矩(moment)的有限角度投影数据解析重建算法。
统计迭代重建方法,尤其是具有快速收敛特征的迭代算法,是PET重建的研究重点之一。本文研究了其中一类基于近似高斯观测模型的ML(maximum likelihood)估计问题,提出了新的基于SAGE的优化估计算法。为了减少运算耗时,本文给出了基于可变索引集的SAGE算法。实验验证了算法的可行性和优越性。
针对ML估计的非稳定性,本文进一步研究了MAP估计方法。将小波变换的多分辨率特性与SAGE算法灵活选取的隐含数据空间相结合,本文首次提出了一种新的小波系数多尺度快速迭代MAP重建方法。在实验中,该方法与其它MAP方法进行了比较。结果表明了基于小波变换的重建方法在保留图像细节以及提高重建图像质量上具有一定的优势。
序列化WLS估计结合了观测数据的时变性,给出了核素动态跟踪的基本解决思路。实验表明该方法具备很快的收敛速度。另一方面,从所获得的均匀一致估计方差上说明了该估计方法具有一定的稳健性。基于状态空间模型的Kalman滤波重建方法是序列化WLS估计的推广,它统一了核素动态估计的模型,有着较好的应用前景。然而运算复杂度较高是该方法的一个主要缺陷。为了缓解该问题,本文试探性地设计了一种次优Kalman滤波。尽管该次优滤波方法比Kalman滤波性能略差,然而其在计算上有着明显的优势。
解析法是研究断层重建的根本出发点。本文借助经典的Radon变换,给出了投影正交矩与图像正交矩之间的一般描述,推导了投影与图像Legendre矩之间的解析关系。根据这一关系,本文首次提出了基于Legendre矩的有限角度投影数据重建方法。该方法利用已知投影数据的矩信息恢复出未知投影的矩,然后由估计的矩重构出未知投影,从而补偿缺少投影信息,提高重建质量。
Positron emission tomography (PET) acts as one of representative techniques of modern nuclear science playing an important role in clinical diagnosis. It provides tissue functional imaging with the aid of radioisotope, which currently makes it one of noninvasion medical imaging tools observing dynamically and quantitatively the physiological and biochemical changes in vivo.
The main purpose of this dissertation aims at the methodology of PET image reconstruction which serves as a critical preprocessing step that approaches the unknown image or distribution of radioactivity by using the observed photon counts generated during the progress of scanning. In this dissertation, several novel PET reconstruction methods are introduced: the new space alternating generalized expectation maximization (SAGE) algorithm using variable index set and its application to the nonstationary Gaussian observation model for PET imaging; the multiscale wavelet-based iterative MAP reconstruction algorithm; the reconstruction methods using the sequential WLS (weighted least squares) and the state-spaced based Kalman filtering technique; and finally, the orthogonal moment-based image reconstruction for the limited-angle tomography.
Statistical iterative reconstruction methods, particularly those with fast convergent rate, are increasingly important in PET image reconstruction. In this dissertation, the maximum likelihood (ML) estimate for one kind of nonstationary Gaussian observation model is first studied. The model optimization is conducted by the using of the SAGE algorithm. For the reduction of computational time cost, the variable index set technique is further suggested, which also makes full use of the a priori underlying physiological information of PET images. The feasibility and efficiency of the proposed method are verified experimentally in comparison with other commonly used ML estimate methods.
Due to the stabilization of the ML estimate, the MAP estimate is introduced accordingly. Conventional MAP algorithm controls the noise behavior by introducing the so-called image a priori information. Such priori plays the role as a smoothness constraint that penalizes the roughness of image estimate and then removes the noisy degradations. Instead of seeking a MAP estimate in image domain, this dissertation considers an efficient alternative within the domain of wavelet. The presented method utilizes a two-step algorithm as follows: 1) the determination of image wavelet coefficients from the observed projection data, and 2) image reconstruction via the wavelet inversion. Moreover, a novel SAGE based optimization
统计迭代重建方法,尤其是具有快速收敛特征的迭代算法,是PET重建的研究重点之一。本文研究了其中一类基于近似高斯观测模型的ML(maximum likelihood)估计问题,提出了新的基于SAGE的优化估计算法。为了减少运算耗时,本文给出了基于可变索引集的SAGE算法。实验验证了算法的可行性和优越性。
针对ML估计的非稳定性,本文进一步研究了MAP估计方法。将小波变换的多分辨率特性与SAGE算法灵活选取的隐含数据空间相结合,本文首次提出了一种新的小波系数多尺度快速迭代MAP重建方法。在实验中,该方法与其它MAP方法进行了比较。结果表明了基于小波变换的重建方法在保留图像细节以及提高重建图像质量上具有一定的优势。
序列化WLS估计结合了观测数据的时变性,给出了核素动态跟踪的基本解决思路。实验表明该方法具备很快的收敛速度。另一方面,从所获得的均匀一致估计方差上说明了该估计方法具有一定的稳健性。基于状态空间模型的Kalman滤波重建方法是序列化WLS估计的推广,它统一了核素动态估计的模型,有着较好的应用前景。然而运算复杂度较高是该方法的一个主要缺陷。为了缓解该问题,本文试探性地设计了一种次优Kalman滤波。尽管该次优滤波方法比Kalman滤波性能略差,然而其在计算上有着明显的优势。
解析法是研究断层重建的根本出发点。本文借助经典的Radon变换,给出了投影正交矩与图像正交矩之间的一般描述,推导了投影与图像Legendre矩之间的解析关系。根据这一关系,本文首次提出了基于Legendre矩的有限角度投影数据重建方法。该方法利用已知投影数据的矩信息恢复出未知投影的矩,然后由估计的矩重构出未知投影,从而补偿缺少投影信息,提高重建质量。
Positron emission tomography (PET) acts as one of representative techniques of modern nuclear science playing an important role in clinical diagnosis. It provides tissue functional imaging with the aid of radioisotope, which currently makes it one of noninvasion medical imaging tools observing dynamically and quantitatively the physiological and biochemical changes in vivo.
The main purpose of this dissertation aims at the methodology of PET image reconstruction which serves as a critical preprocessing step that approaches the unknown image or distribution of radioactivity by using the observed photon counts generated during the progress of scanning. In this dissertation, several novel PET reconstruction methods are introduced: the new space alternating generalized expectation maximization (SAGE) algorithm using variable index set and its application to the nonstationary Gaussian observation model for PET imaging; the multiscale wavelet-based iterative MAP reconstruction algorithm; the reconstruction methods using the sequential WLS (weighted least squares) and the state-spaced based Kalman filtering technique; and finally, the orthogonal moment-based image reconstruction for the limited-angle tomography.
Statistical iterative reconstruction methods, particularly those with fast convergent rate, are increasingly important in PET image reconstruction. In this dissertation, the maximum likelihood (ML) estimate for one kind of nonstationary Gaussian observation model is first studied. The model optimization is conducted by the using of the SAGE algorithm. For the reduction of computational time cost, the variable index set technique is further suggested, which also makes full use of the a priori underlying physiological information of PET images. The feasibility and efficiency of the proposed method are verified experimentally in comparison with other commonly used ML estimate methods.
Due to the stabilization of the ML estimate, the MAP estimate is introduced accordingly. Conventional MAP algorithm controls the noise behavior by introducing the so-called image a priori information. Such priori plays the role as a smoothness constraint that penalizes the roughness of image estimate and then removes the noisy degradations. Instead of seeking a MAP estimate in image domain, this dissertation considers an efficient alternative within the domain of wavelet. The presented method utilizes a two-step algorithm as follows: 1) the determination of image wavelet coefficients from the observed projection data, and 2) image reconstruction via the wavelet inversion. Moreover, a novel SAGE based optimization
引文
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