基于MRF先验的PET图像重建和动力学参数估计
|
摘要
正电子发射断层成像(Positron Emission Tomography,PET)是功能分子影像技术的杰出代表,PET借助扫描测量前注入活体内的放射性核素标记的示踪剂进行显像,够在分子水平上利用影像技术反映机体心脑代谢和功能,已经在肿瘤学,心血管疾病学和神经系统疾病学研究中,以及新医药学开发研究等领域中显示出它卓越的性能。PET成像的目的是通过放射性核素标记示踪剂分布得到感兴趣(region of interest,ROI)组织的生理参数,因而,如何在重建方法中建立生理参数与放射性示踪剂浓度动态分布之间的联系,从而在重建PET图像的同时,对相关生理参数进行估计,将是PET图像重建今后发展的方向。所以对于PET图像重建来说,有二个主要的研究方向:一方面是根据PET测量数据准确的重建示踪剂浓度分布图,即PET图像重建问题;另一方面是PET除了能定性提供组织器官的新陈代谢情况外,还可通过动态成像的方式定量分析具体的生理、生化过程,即PET参数估计问题。
由于受到低计数率和一些物理噪声的影响,PET图像的重建问题在理论上是一个病态的问题。传统的滤波反投影(Filtered Back-Projection,FBP)重建方法虽然具有成像速度快的优点,但其重建图像却含有大量噪声,图像质量较差。最大似然期望最大法(Maximum-Likelihood Expectation-Maximization,ML-EM)能够针对系统模型的物理效应和探测数据和噪声的统计泊松特性建立数学模型,其重建的图像质量要优于传统的FBP方法。然而,单纯的传统ML-EM方法收敛速度较慢,而且在迭代过程中会产生质量退化的图像而导致的棋盘效应,从而导致非收敛的迭代过程。
近年以来,基于马尔可夫随机场(Markov Random Fields,MRF)的贝叶斯(Bayesian)重建方法或者最大化后验估计(Maximum A Posteriori,MAP)的方法已经在包括PET图像重建在内的图像重建中得到广泛的应用。Bayesian方法通过正则化在迭代过程中引进放射性示踪剂浓度在空间上概率分布的先验信息,能够明显改善重建图像质量以及迭代过程的收敛性,该方法已被证明了其在理论上的正确性和实际上的有效性。虽然引入了图像先验信息的Bayesian方法能够在很大程度上改善迭代重建的效果,但是依赖于传统的局部空间邻域信息的Bayesian方法只能为重建提供有限的先验信息。而且在当前PET问题的研究中,通常将时间和空间分开来考虑。但在实际问题中,时间和空间是相辅相成、互相影响、互相作用的。
PET测量数据中已经隐含了很多生理信息,但往往未能直接表示出来。传统的间接参数估计方法如加权最小二乘参数估计方法(Weighted Least SquareMethod,WLS),需要首先从测量数据重建出PET动态放射性活度图像,然后在这些时间上连续的重建图像应用适当的动力学模型上估计感兴趣的生理参数,然而PET重建图像中往往含有极大的噪声,这些噪声将影响参数估计的准确性。
本文对于PET重建算法的研究工作同样也是基于PET研究中的两个主要研究方向,作者做了以下关于PET图像重建和动力学参数估计方面的工作:
1,提出一种新的综合了QM先验、QP先验和QTO先验的MRF二次混合多阶先验模型,新的混合先验可依据目标图像不同位置的特性自适应的决定QM先验、QP先验和QTO先验的作用效果,其重建结果比单独使用QM先验、QP先验的效果好。同时也优于与传统的TV先验和中值根先验的重建结果。
2,从引入更多先验知识指导PET图像重建角度进行研究,对采用不同邻域大小的常用先验和非局部先验进行大量对比实验。从实验结果中可以看到,简单的增大邻域大小是无法有效的结合空间大尺寸信息至Bayesian重建。另一方面非局部先验能够利用目标图像中大尺寸信息或全局信息,其对发射断层重建作用比传统的QM先验和Huber先验有效,而且鲁棒性好。
3,提出一种新的基于二房室模型和空间邻域信息的时空先验模型,新的时空先验综合考虑时间和空间因素,根据探测器得到的sinogram数据直接求解出动力学参数,同时重建PET动态图像。实验中给出了新方法与传统方法的定量比较。模拟实验证明基于该时空先验的动态PET重建图像和动力学参数图像均要优于传统方法重建结果。
试验中将以上三种方法应用于相应的PET断层发射成像和动力学参数估计中,相关试验分析表明:本文所提出的基于MRF和优化理论的新算法均能够分别在不同程度上提高PET图像重建和动力学参数估计的质量。
Positron emission computed tomography (PET) is the effective medical imaging technique that provides functional information of physiological activity by displaying the concentration distribution of radioisotope labeled tracer (chemical compounds or biological molecular) which pre-injected into the human body before imaging process. PET is able to represent heart and brain metabolism and functions on molecule level by imaging techniques, and has shown great performance in oncology, cardiopathy, neurology and new medicine studies. The purpose of PET reconstruction is to get physiological parameters about the region of interest (ROI) through tracer activity distribution. So, it is the direction of development that PET activity image reconstruction and parameters estimate simultaneously through the relationship between physiological parameters and tracer activity distribution. There are two main research directions in PET reconstruction study: 1, accurate reconstruction static activity images of the radioactive tracer spatial distribution; 2, dynamic PET activity image reconstruction and precise physiological parameters estimate.
But positron emission tomography is an ill-posed inverse problem because the observed projection data are contaminated by noise due to low count rate and physical effects. Though needing less computation cost, traditional filter back projection (FBP) method often reconstruct noisy images of low quality. Better expressing system models of physical effects and modeling the statistical poisson character of the data, the famous maximum-likelihood expectation-maximization (ML-EM) approach outperforms the FBP method with regard to image quality. However, pure traditional ML-EM approach suffers slow convergence and the reconstructed activity images always start deteriorating to produce "checkerboard effect" as the iteration proceeds.
In recently years, Bayesian methods or equivalently MAP (Maximum A Posteriori) methods has been widely used in image reconstruction. Bayesian methods incorporate MRF prior information of objective tracer concentration distribution data into the ML-EM algorithm through regularization or prior terms and have been proved theoretically correct and practically effective compared to other methods. Compared to traditional ML-EM algorithm, Bayesian reconstruction shows a better performance in both improving convergence behavior and producing more appealing images. Bayesian reconstruction can greatly improve reconstruction by incorporating image prior information. However we also find that, heavily relied on the information within a limited neighborhood, conventional Bayesian methods can only contribute limit spatial local prior information to reconstruction.
And at persent PET srudy, space and time are divided into two problems. In conventional indirected parameter estimate, such as Weighted Least Square Method (WLS), the changing activity of the injected radiotracer is conventionally measured through multiple consecutive PET image reconstructions. The image of the radioactivity distribution in each frame is reconstructed independently and the whole set of frames is then used to estimate the distribution of the physiological parameter of interest by the application of an appropriate pharmacokinetic model to the time radioactivity curve either of appropriately selected functional regions or of each image element. However, the noisy PET reconstruction image will influence the accuracy of parameters estimate.
Our work on PET reconstruction is based on the two mian research direction in PET study: how to further improve the quality for activity image reconstructions and how to further improve accuracy of parameters estimate. We have done following work:
1, proposing a noval Markov Quadratic Hybrid Multi-Order Priors which has the effects of QM prior, QP prior and QTO prior adaptively according to different properties of different positions in objective image effectively. The new MRF hybrid prior outperforms unitary QM prior and unitary QP prior.
2, studing how to incorporate more prior knowledge to guide PET image reconstruction, a great quantity of experiments were carried out with common prior with different size and and non-local a priori a priori. From the analyses and experiments presented in this paper, we can see that just enlarging the sizes of neighborhood can not effectively incorporate more large-scale knowledge into Bayesian reconstruction. On the other hand, the nonlocal prior, which is devised to exploit the large-scale or global connectivity and continuity knowledge in the image, demonstrates a more effective and robust regularization for emission reconstruction than the conventional local QM prior and Huber prior.
3, proposing a noval spatio-temporal prior based on two-tissue compartmental model and neighborhood information. Time and space factors are general take into account in the new spatio-temporal prior. Based on spatio-temporal prior, kinetic parameters and PET activity images could be estimated and reconstructed synchronous. And in the simulation experiment, activity reconstruction image and parameter estimation based on spatio-temporal prior has better quality than that with the conventional method.
由于受到低计数率和一些物理噪声的影响,PET图像的重建问题在理论上是一个病态的问题。传统的滤波反投影(Filtered Back-Projection,FBP)重建方法虽然具有成像速度快的优点,但其重建图像却含有大量噪声,图像质量较差。最大似然期望最大法(Maximum-Likelihood Expectation-Maximization,ML-EM)能够针对系统模型的物理效应和探测数据和噪声的统计泊松特性建立数学模型,其重建的图像质量要优于传统的FBP方法。然而,单纯的传统ML-EM方法收敛速度较慢,而且在迭代过程中会产生质量退化的图像而导致的棋盘效应,从而导致非收敛的迭代过程。
近年以来,基于马尔可夫随机场(Markov Random Fields,MRF)的贝叶斯(Bayesian)重建方法或者最大化后验估计(Maximum A Posteriori,MAP)的方法已经在包括PET图像重建在内的图像重建中得到广泛的应用。Bayesian方法通过正则化在迭代过程中引进放射性示踪剂浓度在空间上概率分布的先验信息,能够明显改善重建图像质量以及迭代过程的收敛性,该方法已被证明了其在理论上的正确性和实际上的有效性。虽然引入了图像先验信息的Bayesian方法能够在很大程度上改善迭代重建的效果,但是依赖于传统的局部空间邻域信息的Bayesian方法只能为重建提供有限的先验信息。而且在当前PET问题的研究中,通常将时间和空间分开来考虑。但在实际问题中,时间和空间是相辅相成、互相影响、互相作用的。
PET测量数据中已经隐含了很多生理信息,但往往未能直接表示出来。传统的间接参数估计方法如加权最小二乘参数估计方法(Weighted Least SquareMethod,WLS),需要首先从测量数据重建出PET动态放射性活度图像,然后在这些时间上连续的重建图像应用适当的动力学模型上估计感兴趣的生理参数,然而PET重建图像中往往含有极大的噪声,这些噪声将影响参数估计的准确性。
本文对于PET重建算法的研究工作同样也是基于PET研究中的两个主要研究方向,作者做了以下关于PET图像重建和动力学参数估计方面的工作:
1,提出一种新的综合了QM先验、QP先验和QTO先验的MRF二次混合多阶先验模型,新的混合先验可依据目标图像不同位置的特性自适应的决定QM先验、QP先验和QTO先验的作用效果,其重建结果比单独使用QM先验、QP先验的效果好。同时也优于与传统的TV先验和中值根先验的重建结果。
2,从引入更多先验知识指导PET图像重建角度进行研究,对采用不同邻域大小的常用先验和非局部先验进行大量对比实验。从实验结果中可以看到,简单的增大邻域大小是无法有效的结合空间大尺寸信息至Bayesian重建。另一方面非局部先验能够利用目标图像中大尺寸信息或全局信息,其对发射断层重建作用比传统的QM先验和Huber先验有效,而且鲁棒性好。
3,提出一种新的基于二房室模型和空间邻域信息的时空先验模型,新的时空先验综合考虑时间和空间因素,根据探测器得到的sinogram数据直接求解出动力学参数,同时重建PET动态图像。实验中给出了新方法与传统方法的定量比较。模拟实验证明基于该时空先验的动态PET重建图像和动力学参数图像均要优于传统方法重建结果。
试验中将以上三种方法应用于相应的PET断层发射成像和动力学参数估计中,相关试验分析表明:本文所提出的基于MRF和优化理论的新算法均能够分别在不同程度上提高PET图像重建和动力学参数估计的质量。
Positron emission computed tomography (PET) is the effective medical imaging technique that provides functional information of physiological activity by displaying the concentration distribution of radioisotope labeled tracer (chemical compounds or biological molecular) which pre-injected into the human body before imaging process. PET is able to represent heart and brain metabolism and functions on molecule level by imaging techniques, and has shown great performance in oncology, cardiopathy, neurology and new medicine studies. The purpose of PET reconstruction is to get physiological parameters about the region of interest (ROI) through tracer activity distribution. So, it is the direction of development that PET activity image reconstruction and parameters estimate simultaneously through the relationship between physiological parameters and tracer activity distribution. There are two main research directions in PET reconstruction study: 1, accurate reconstruction static activity images of the radioactive tracer spatial distribution; 2, dynamic PET activity image reconstruction and precise physiological parameters estimate.
But positron emission tomography is an ill-posed inverse problem because the observed projection data are contaminated by noise due to low count rate and physical effects. Though needing less computation cost, traditional filter back projection (FBP) method often reconstruct noisy images of low quality. Better expressing system models of physical effects and modeling the statistical poisson character of the data, the famous maximum-likelihood expectation-maximization (ML-EM) approach outperforms the FBP method with regard to image quality. However, pure traditional ML-EM approach suffers slow convergence and the reconstructed activity images always start deteriorating to produce "checkerboard effect" as the iteration proceeds.
In recently years, Bayesian methods or equivalently MAP (Maximum A Posteriori) methods has been widely used in image reconstruction. Bayesian methods incorporate MRF prior information of objective tracer concentration distribution data into the ML-EM algorithm through regularization or prior terms and have been proved theoretically correct and practically effective compared to other methods. Compared to traditional ML-EM algorithm, Bayesian reconstruction shows a better performance in both improving convergence behavior and producing more appealing images. Bayesian reconstruction can greatly improve reconstruction by incorporating image prior information. However we also find that, heavily relied on the information within a limited neighborhood, conventional Bayesian methods can only contribute limit spatial local prior information to reconstruction.
And at persent PET srudy, space and time are divided into two problems. In conventional indirected parameter estimate, such as Weighted Least Square Method (WLS), the changing activity of the injected radiotracer is conventionally measured through multiple consecutive PET image reconstructions. The image of the radioactivity distribution in each frame is reconstructed independently and the whole set of frames is then used to estimate the distribution of the physiological parameter of interest by the application of an appropriate pharmacokinetic model to the time radioactivity curve either of appropriately selected functional regions or of each image element. However, the noisy PET reconstruction image will influence the accuracy of parameters estimate.
Our work on PET reconstruction is based on the two mian research direction in PET study: how to further improve the quality for activity image reconstructions and how to further improve accuracy of parameters estimate. We have done following work:
1, proposing a noval Markov Quadratic Hybrid Multi-Order Priors which has the effects of QM prior, QP prior and QTO prior adaptively according to different properties of different positions in objective image effectively. The new MRF hybrid prior outperforms unitary QM prior and unitary QP prior.
2, studing how to incorporate more prior knowledge to guide PET image reconstruction, a great quantity of experiments were carried out with common prior with different size and and non-local a priori a priori. From the analyses and experiments presented in this paper, we can see that just enlarging the sizes of neighborhood can not effectively incorporate more large-scale knowledge into Bayesian reconstruction. On the other hand, the nonlocal prior, which is devised to exploit the large-scale or global connectivity and continuity knowledge in the image, demonstrates a more effective and robust regularization for emission reconstruction than the conventional local QM prior and Huber prior.
3, proposing a noval spatio-temporal prior based on two-tissue compartmental model and neighborhood information. Time and space factors are general take into account in the new spatio-temporal prior. Based on spatio-temporal prior, kinetic parameters and PET activity images could be estimated and reconstructed synchronous. And in the simulation experiment, activity reconstruction image and parameter estimation based on spatio-temporal prior has better quality than that with the conventional method.
引文
[1]潘中允主编.PET诊断学[M].北京:人民卫生出版社.2005.
[2]Phelps ME,Homan EJ and Mullani NA et al.Application of annihilation coincidence detection to transaxial reconstruction tomography[J].J.Nuc.Med,vol.16,no.3,pp.210-224,March 1975.
[3]TerPogossian MM,Phelps ME and Homan ME et al.A positronemission transaxial tomograph for nuclear imaging[J].Radiology,vol.114,pp.89-98,1975.
[4]Herman G.Image Reconstruction from Projections:The Fundamentals of Computerized Tomography[M].Academic Press,New York,1980.
[5]Bertero M,DeMol C and Pike ER.Linear inverse problems with discrete data-Ⅰ:General formulation and singular system analysis[J].Inverse Prob,vol.1,no.4,pp.301-330,Nov.1985.
[6]Bertero M,Poggio T and Torre V.Ill posed problems in early vision[C].Proc.IEEE,vol.76,pp.869-889,Aug.1988.
[7]Budinger TF,Gullberg GT and Huesman RH.Emission computed tomography [M].Image Reconstruction from Projections:Implementation and applications,Herman GT,Ed.Berlin:Springer Verlag,1979,ch.5,pp.147-246.
[8]Shepp LA and Vardi Y.Maximum likelihood reconstruction for emission tomography[J].IEEE Transactions on Medical Imaging,vol.1,no.2,pp.113-122,October 1982.
[9]Snyder DL and Miller MI.The use of sieves to stabilized images produced with the EM algorithm for emission tomography[J].IEEE Trans.Nucl.Sci.,vol.NS-32,pp.3864-3872.Oct.1985.
[10]Levitan E and Herman GT.A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography[J].IEEE Trans.Med.Imag.,vol.MI-6,pp.185-192,Sept.1987.
[11]Green PJ.Bayesian reconstruction from emission tomography data using a modified EM algorithm[J].IEEE Trans.Med.Imag,vol.9,pp.84-93,Mar.1990.
[12]Lange K.Convergence of EM image reconstruction algorithms with Gibbs smoothing[J].IEEE Trans.Med.Imag,vol.9,pp.439-446,Dec.1990.
[13]Butler CS and Miller MI.Maximum A Posteriori estimation for SPECT using regularization techniques on massive parallel computers[J].IEEE Trans.Med.Imag.,vol 12,no.1,pp.84-89,March 1993.
[14]M.E.Kamasak,C.A.Bouman,E.D.Morris,and K.Sauer,"Direct reconstruction of kinetic parameter images from dynamic PET data," IEEE Trans.Med.Image,vol.24,no.5,pp.636-650,2005.
[15]G.B.Wang,L.Fu,and J.Qi,"Maximum a posteriori reconstruction of the patlak parametric image from sinograms in dynamic PET," Phys.Med.Biol.,vol.53,no.3,pp.593-604,2008.
[1]Dale L.Bailey,David W.Townsend,Peter E.Valk,Michael N.Maisey,Positron Emission Tomography:Basic Sciences,Springer,ISBN-10:1852337982,2005.
[2]Phelps ME,Homan EJ and Mullani NA et al.Application of annihilation coincidence detection to transaxial reconstruction tomography[J].J.Nuc.Med,vol.16,no.3,pp.210-224,March 1975.
[3]TerPogossian MM,Phelps ME and Homan ME et al.A positroncmission transaxial tomograph for nuclear imaging[J].Radiology,vol.114,pp.89-98,1975.
[4]Sorenson JA and Phelps ME.Physics in nuclear medicine[M].Saunders,Philadelphia,2 edition,1987.
[5]Alonso M and Finn E.Fundamental University Physics,volume Ⅲ Quantum and Statistical Physics[M].Addison-Wesley,Reading,Massachusetts,1983.
[6]Dahlbom M and Homan EJ.An evaluation of a two-dimensional array detector for high resolution PET[J].IEEE Transactions on Image Processing,vol.7,no.4,pp.264-272,December 1988.
[7]Michale E.Phelps.PET:Physics,instrumentation and scanners.2006,Springer New York
[8]王世真,林汉,周前,核医学与核生物学-基础及应用[M].科学出版社,1990
[9]Phelps ME,Hoffman EJ,Mullani NA,Ter-Pogossian MM.Application of annihilation coincidence detection to transaxial reconstruction tomography.J Nucl Med.1975;16:210-233.
[10]P.Sprawls,医学成像的物理原理,黄治悼等译,高等教育出版社,1993
[11]DL Bailey,JS Karp,S Surti,Physics and Instrumentation in PET,Positron Emission Tomography:Basic Science and Clinical,2003,Springer
[12]Hoffman EJ,Guerrero TM,Germano G,Digby WM,Dahlbom M.PET system calibration and corrections for quantitative and spatially accurate images.IEEE Trans Nucl Sci.1989;36:1108-1112
[13]Jaszczak R and Hoffman E.Scatter and attenuation.In H.Wagner,editor,Principles of Nuclear Medicine,chapter 19,section 3[M].W.B.Saunders Company,Philadelphia,2nd edition,1995.
[14]Bailey D.Transmission scanning in emission tomography[J].European Journal of Nuclear Medicine,25(7):774-787,July.1998.
[15]Meikle S,Dahlbom M,and Cherry S.Attenuation correction using count-limited transmission data in positron emission tomography[J].Journal of Nuclear Medicine,vol.34,pp.143-150,Jan.1993.
[16]Hoffman EJ,Huang S-C,Phelps ME,Kuhl DE,Quantitation in positron emission computed tomography:Ⅵ.Effect of accidental coincidences.J Comput assist Tomogr.1981;5;391-400.
[17]Williams CW,Crabtree MC,Brugiss SG.Design and performance characteristics of a positron emission computed axial tomography-ECAT-Ⅱ.IEEE Trans Nucl sci.1979;26:619-627.
[18]Eriksson L,Wienhard K,Dahlbom M,A simple data loss model for positron camera systems.IEEE Trans Nucl.Sci 1994;41:1566-1570.
[19]Kak A and Slaney M.Principles of Computerized Tomographic Imaging[M].IEEE Press,New York,1988.
[20]Bertero M,De Mol C,and Pike ER.Linear inverse problems with discrete data-Ⅰ:General formulation and singular system analysis[J].Inverse Prob,vol.1,no.4,pp.301-330,Nov.1985.
[21]Bertero M,Poggio T and Torre V.Ill posed problems in early vision[C].Proceedings of the IEEE,vol.76,pp.869-889,Aug.1988.
[22]Yu DF and Fessler JA.Mean and variance of coincidence photon counting with deadtime[J].Phys.Med.Biol,vol.15,pp.231-245,Aug.1999.
[23]Goitein M.Three-dimensional density reconstruction from a series of two dimensional projections[J].Nucl.Instr.Meth,vol.101,no.15,pp.509-518,June 1972.
[24]Rockmore AJ and Macovski A.A maximum likelihood approach to emission image reconstruction from projections[J].IEEE Tr.Nuc.Sci,vol.23,pp.1428-1432,1976.
[25]Shepp LA and Vardi Y.Maximum likelihood reconstruction for emission tomography[J].IEEE Transactions on Medical Imaging,vol.1,no.2,pp.113-122,October 1982.
[26]Houdson HM,and Larkin RS.Accelerated Image Reconstruction using Ordered Sunsets of Projection Data[J].IEEE Trans.on Medical Imagin.,vol.13,no.4,pp.601-609,December.1994.
[27]Byrne C,Soares E,and Pan TS.Accelerating the EM algorithm using rescaled block-iterative methods[C].Proc.IEEE Nuc.Sci.Symp.Med.Im.Conf.,volume 3,pp.1752-6,1996.
[28]Lange K.Convergence of EM image reconstruction algorithms with Gibbs smoothness[J].IEEE Transactions on Medical Imaging,vol.9,pp.439-446,Dec.1990.
[29]Fessler JA,Ficaro E,Clinthorne N,and K.Lange.Grouped-coordinate ascent algorithms for penalized likelihood transmission image reconstruction[J].IEEE Transactions on Medical Imaging,vol.16,Apr.1997.
[30]Lange K and Fessler JA.Globally convergent algorithms for maximum a posteriori transmission tomography[J].IEEE Transactions on Image Processing,4(10),pp.1430--1438,1995.
[31]R.M.Lewitt and S.Matej,Qverview of methods for image reconstruction from projections in emission computed tomography.Proceedings of the IEEE,91:1588-1611,2003.
[32]Fessler JA.Aspire 3.0 user's guide:A sparse reconstruction library[R].Communication & Signal Processing Laboratory Technical Report No.293,Department of Electrical and Computer Engineering,University of Michigan,Ann Arbor,1998.
[33]Lange K and Carson R.EM reconstruction algorithms for emission and transmission tomography[J].J.Comp.Assisted Tomo,vol.8,no.2,pp.306-316,April 1984.
[34]Herman G and Odhner D.Performance evaluation of an iterative image reconstruction algorithm for positron emission tomography[J].IEEE Transactions on Medical Imaging,10(3):336-346,Sept.1991.
[35]Fox PT,Mintun MA,Reiman EM,and Raichle ME.Enhanced detection of focal brain responses using intersubject averaging and change-distribution analysis of subtracted PET images[J].Journal of Cerebral Blood Flow and Metabolism,8(5):642-653,1988.
[36]M.Dwass.Probability and Statistics[M].W.A.Benjamin,Inc.,NewYork,1970.
[37]Fessler JA.Aspire 3.0 user's guide:A sparse reconstruction library JR].Communication & Signal Processing Laboratory Technical Report No.293,Department of Electrical and Computer Engineering,University of Michigan,Ann Arbor,1998.
[38]Lalush DS and Tsui BMW.A fast and stable maximum a posteriod conjugate gradient reconstruction algorithm[J].Med.Phys.,vol.22,no.8,pp.1273-84,Aug.1995.
[39]Fessler JA and Booth SD.Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction[J].IEEE Tr.Ira.Proc.,vol.8,no.5,pp.688-99,May 1999.
[40]Booth SD and Fessler JA.Combined diagonal/Fourier preconditioning methods for image reconstruction in emission tomography[C].Proc.IEEE Intl.Conf.on Image Processing,vol.2,pp.441-4,1995.
[41]Sauer K and Bouman C.A local update strategy for iterative reconstruction from projections[J].IEEE Tr.Sig.Proc.,vol.41,no.2,pp.534-548,February 1993.
[42]Bouman CA and Sauer K.A unified approach to statistical tomography using coordinate descent optimization[J].IEEE Tr.Im.Proc.,vol.5,no.3,pp.480-92,March 1996.
[43]Fessler JA and Hero AO.Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms[J].IEEE Tr.Im.Proc.,vol.4,no.10,pp.1417-29,October 1995.
[44]Fessler JA and Erdo(?)an H.A paraboloidal surrogates algorithm for convergent penalized-likelihood emission reconstruction[J].Proc.IEEE Nuc.Sci.Symp.Med.Im.Conf,volume 2,pp.1132-5,1998.
[45]Fessler JA and Erdo(?)an H.Accelerated monotonic algorithms for transmission tomography[C].Proc.IEEE Intl.Conf.on Image Processing,volume 2,pp.680-4,1998.
[46]Fessler JA and Erdo(?)an H.Monotonic algorithms for transmission tomography [J].IEEE Trans.Image Processing,vol.18,no.9,pp.801-14,September.1999.
[47]Geman S and Geman D.Stochastic relaxation,Gibbs distribution,and the Bayesian restoration of images[J].IEEE Trans,Pattern,Anal.Machine Intell,vol.PAMI-6,pp.721-741,Nov.1984.
[48]Li SZ.Markov Random Field Modeling in image Analysis[M].Springer-Verlag,Tokyo,2001.
[49]Levitan E and Herman GT.A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography[J].IEEE Trans.Image Processing,vol.MI-6,pp.185-192,Sept.1987.
[50]Green PJ.Bayesian reconstruction from emission tomography data using a modified EM algorithm[J].IEEE Trans.Image Processing,vol.9,pp.84-93,Mar.1990.
[51]Butler CS and Miller MI.Maximum A Postedori estimation for SPECT using regularization techniques on massive parallel computers[J].IEEE Trans.Med.Imag.,vol 12,no.1,pp.84-89,March 1993.
[52]Johnson V,Wong WH,Hu X,and Chen CT.Image restoration using Gibbs prior:Boundary modeling,treatment of blurring,and selection of hyperparameter [J].IEEE Trans.Pattern Anal Machine Intell.,vol.13,pp.413-425,May 1991.
[53]Chatziioannou A and Dahlbom M.Detailed investigation of transmission and emission data smoothing protocols and their effects on emission images[J].IEEE Transactions on Nuclear Science,vol.43,pp.290-294,Feb.1996.
[54]Jacquez JA.Compartmental analysis in biology and medicine.Amsterdam,Holland:Elsevier/North;1972.
[55]Wagner JG.Fundamentals of clinical pharmacokinetics.Hamilton,Ill.:Drug Intelligence Publications;1975.
[56]Anderson D.Compartmental modeling and tracer kinetics.Berlin:Springer-Verlag;1983.
[57]Robertson J,editor.Compartmental distribution of radiotracers.Boca Raton,FL:CRC Press;1983.
[58]C.-M.Kao,J.T.Yap,J.Mukherjee,and M.Wernick,Image reconstruction for dynamic PET based on low-order approximation and restoration of the sinogram,IEEE Trans.on Medical Imaging,vol.16,no.6,pp.738-749,1997.
[59]T.E.Nichols,J.Qi,E.Asma,and R.M.Leahy,Spatioternporal reconstruction of list-mode PET data,IEEE Trans.on Medical Imaging,vol.21,no.4,pp.396-404,2002.
[60]R.E.Carson and K.Lange,The EM parametric image reconstruction algorithm,Journal of the American Statistical Association,vol.80,no.389,pp.20-22,1985.
[61]M.E.Kamasak,C.A.Bouman,E.D.Morris,and K.Sauer,Direct reconstruction of kinetic parameter images from dynamic PET data,IEEE Trans.Med.Image, vol.24,no.5,pp.636-650,2005.
[62]C Tsoumpas,FE Turkheimer,K Thielemans,A survey of approaches for direct parametric image reconstruction in emission tomography,Med.Phys.Volume 35,Issue 9,pp.3963-3971,2008.
[63]Bard Y.Nonlinear parameter estimation:Academic Press,New York;1974.
[64]Beck JV,Arnold KJ.Parameter estimation in engineering and science.New York:John Wiley & Sons;1977.
[65]Carson RE.Parameter estimation in positron emission tomography.In:Phelps ME,Mazziotta JC,Schelbert HR,editors.Positron emission tomography and autoradiography.New York:Raven Press;1986.p.347-90.
[66]Press W,Flannery B,Teukolsy S,Vetterling W.Numerical Recipes:The art of scientific computing.Cambridge:Cambridge University Press;1986.
[67]Eastman R,Carson R,Gordon M,Berg G,Lillioja S,Larson S,etal.Brain glucose metabolism in non-insulin-dependent diabetes mellitus:A study in Pima Indians using positron emission tomography during hyperinsulinemia with euglycemic glucose clamp.J Clin Endocrinol Metab 1990;71:1602-10.
[1]K.Lange,"Convergence of EM image reconstruction algorithms with Gibbs smoothness," IEEE Trans.Med.Imag.,vol.9,pp.439-446,Dec.1990.
[2]C.A Bouman and K.Sauer,"A generalized Gaussian image model for edge-preserving MAP estimation," IEEE Trans.Image Processing,vol.2 pp.296-310,July.1993.
[3]V.Johnson,W.H.Wong,X.Hu,and C.T.Chen,"Image restoration using Gibbs prior:Boundary modeling,treatment of blurring,and selection of hyperparameter," IEEE Trans.Pattern Anal Machine Intell.,vol.13,pp.413-425,May 1991.
[4]V.Johnson,"A framework for incorporating structural prior information into the estimation of medical image," in Information processing in Medical Imaging,H.H.Barrett and A.F.Gmitro,Eds.Berlin,Germany:Springer-Verlag,1993,pp.307-321.
[5]J.E.Bowsher,V.E.Johnson,T.G.Turkington,R.J.Jaszczak,C.E Floyd,and R.E.Coleman,"Bayesian reconstruction and use of anatomical a priori information for emission tomography," IEEE Tran.Med.Imag.,vol 15,pp.673-686,Oct,1996.
[6]Daniel F.Yu and Jeffrey A.Fessler,"Edge-Preserving Tomographic Reconstruction with Nonlocal Regularization," IEEE Trans.Med.Imag.,vol.21,no.2 pp.159-173,Feb.2002.
[7]S.J.Lee,A.Rangarajan,and G Gindi,"Bayesian Image Reconstruction in SPECT Using Higher Order Mechanical Models as Priors," IEEE Trans.on Medical Imaging,MI-14(4),pp.669-680,Dec.1995.
[8]Stan Z.Li,Markov Random Field Modeling in image Analysis,Tokyo:Springer-Verlag,2001,ch,1,pp 1-40.
[9]J.A.Fessler and H.Erdo(?)an,"A paraboloidal surrogates algorithm for convergent penalized-likelihood emission reconstruction," in Proc.IEEE Nuc.Sci.Symp.Med.Im.Conf.,volume 2,pp.1132-5,1998.
[10]H.Erdo(?)an and J.A.Fessler,"Monotonic algorithms for transmission tomography," IEEE Tr.Med.Im.,vol.18,no.9,pp.801-14,September 1999.
[1]M.Bertero,C.De Mol,and E.R.Pike,Linear inverse problems with discrete data-Ⅰ:General formulation and singular system analysis,Inverse Prob,Vol.1,no.4,pp.301-330,Nov.1985.
[2]S.Geman and D.Geman,Stochastic relaxation,Gibbs distribution,and the Bayesian restoration of image,IEEE Trans.Pattern,Anal.Machine Intell,voI.PAMI-6,pp.721-741,Nov.1984.
[3]Stan Z.Li,Markov Random Field Modeling in image Analysis,Springer-Verlag,Tokyo,2001.
[4]K.Lange.Convergence of EM image reconstruction algorithms with Gibbs smoothness.IEEE Trans.Med.Imag.,vol.9,439-446,1990
[5]G.Gindi,A.Rangarajan,M.Lee,P.J.Hong,and G.Zubal.Bayesian Reconstruction for Emission Tomography via Deterministic Annealing.In H.Barrett and A.Gmitro,editors.Information Processing in Medical Imaging,Springer-Verlag,322-338,1993
[6]Daniel F.Yu and Jeffrey A.Fessler.Edge-preserving tomographic reconstruction with nonlocal regularization,IEEE Trans.Med.Imag.,vol.21,no.2,pp.159-173,Feb,2002
[7]Charbonnier.P,Blanc-F'eraud.L,Aubert.G and Barlaud.M.Deterministic edge preserving regularization in computer imaging.IEEE Trans.Image Processing,vol.6,no.2,298-311,1997.
[8]A.Buades,B.Coll,and J.M.Morel.A nonlocal algorithm for image denoising.Proc.IEEE Int.Conf.Computer Vision Pattern Recognition,vol.2,60-65,2005
[9]Yang Chen,Qianjin Feng,et al.Nonlocal Prior Bayesian Tomographic Reconstruction,Journal of Mathematical Imaging and Vision[J],2,133-146,2008
[10]J.Fessler,"Hybrid Poisson/polynomial objective functions for tomographic image reconstruction from transmission scans," IEEE Transactions on Image Processing.,vol.4,pp.1439C1450,Oct 1995.
[11]A.Chatziioannou and M.Dahlbom,"Detailed investigation of transmission and emission data smoothing protocols and their effects on emission images," IEEE Transactions on Nuclear Science.,vol.43,pp.290C294,Feb 1996.
[12]L.A.Shepp and Y.Vardi.Maximum likehood reconstruction for emission tomography.IEEE Trans.Med.Imag.,vol.1,pp.113-121,1982.
[13]Wufan Chen,Ming Chen,and Jie Zhou.Adaptively regularized constrained total least-squares Image Restoration ,”IEEE Trans.Image Processing,vol.9,588-596,2000
[14]J.A.Fessler and H.Erdogan.A paraboloidal surrogates algorithm for convergent pena ized-likelihood emission reconstruction.Proc.IEEE Nuc.Sci.Symp.Med.Im.Conf,volume 2,1132-5,1998
[15]H.Erdogan and J.A.Fessler.Monotonic algorithms for transmission tomography.IEEE Tr.Med.Im,vol.18,801-14,1999
[16]D.S.Lalush and B.M.W.Tsui..A fast and stable maximum a posteriori conjugate gradient reconstruction algorithm,Med.Phys.,vol.22,1273-84,1998
[17]J.A.Fessler and S.D.Booth,1999.Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction.IEEE Tr.Im.Proc,vol.8,688-99,1999
[1]M.N.Wernick,J.N.Aarsvold(Eds.),Emission Tomography:The Fundamentals of PET and SPECT,Elsevier,2004.
[2]A.A.Lammertsma and S.P.Hume,Simplified reference tissue model for PET receptor studies,Neuroimage,vol.4,pp.153-158,1996.
[3]J.Tseng,L.K.Dunnwald,E.K.Schubert,J.M.Link,S.Minoshima,M.Muzi,and D.A.Mankoff,F(18)-FDG kinetics in locally advanced breast cancer:correlation with tumor blood flow and changes in response to neoadjuvant chemotherapy,Journal of Nuclear Medicine,vol.45,pp.1829-1837,2004.
[4]C.-M.Kao,J.T.Yap,J.Mukherjee,and M.Wernick,Image reconstruction for dynamic PET based on low-order approximation and restoration of the sinogram,IEEE Trans.on Medical Imaging,vol.16,no.6,pp.738-749,1997.
[5]T.E.Nichols,J.Qi,E.Asma,and R.M.Leahy,Spatiotemporal reconstruction of list-mode PET data,IEEE Trans.on Medical Imaging,vol.21,no.4,pp.396-404,2002.
[6]R.E.Carson and K.Lange,The EM parametric image reconstruction algorithm,Journal of the American Statistical Association,vol.80,no.389,pp.20-22,1985.
[7]M.E.Kamasak,C.A.Bouman,E.D.Morris,and K.Sauer,Direct reconstruction of kinetic parameter images from dynamic PET data,IEEE Trans.Med.Image,vol.24,no.5,pp.636-650,2005.
[8]C Tsoumpas,FE Turkheimer,K Thielemans,A survey of approaches for direct parametric image reconstruction in emission tomography,Med.Phys.Volume 35,Issue 9,pp.3963-3971,2008.
[9]Lange K.Convergence of EM image reconstruction algorithms with Gibbs smoothing[J].IEEE Trans.Med.lmag,vol.9,pp.439-446,Dec.1990.
[10]Wufan Chen,Ming Chen,and Jie Zhou.Adaptively regularized constrained total least-squares Image Restoration,IEEE Trans.Image Processing,vol.9,588-596,2000
[11]Levitan E and Herman GT.A maximum a posteriod probability expectation maximization algorithm for image reconstruction in emission tomography[J].IEEE Trans.Med.Imag.,vol.MI-6,pp.185-192,Sept.1987.
[12]Green PJ.Bayesian reconstruction from emission tomography data using a modified EM algorithm[J].IEEE Trans.Image Processing,vol.9,pp.84-93,Mar.1990.
[13]DJ Kadrmas,GT Gullberg,4D maximum a posteriod reconstruction in dynamic SPECT using a compartmental model-based prior,Phys.Med.Biol.46(2001)1553-1574.
[14]A.A.Lammertsma and S.P.Hume,Simplified reference tissue model for PET receptor studies,NeuroImage,vol.4,p.153158,1996.
[15]R.N.Gunn,A.A.Lammertsma,S.P.Hume,and V.J.Cunningham,Parametric imaging of ligand-receptor binding in PET using a simplified reference region model,NeuroImage,vol.6,no.4,p.279287,1997.
[16]Lange K.Convergence of EM image reconstruction algorithms with Gibbs smoothing[J].IEEE Trans.Med.Imag,vol.9,pp.439-446,Dec.1990.
[17]Stan Z.Li,2001.Markov Random Field Modeling in image Analysis,first ed.Springer- Verlag,Tokyo,1-40
[18]Li,X.,Feng,D.,Lin,K.,Huang,S.:Estimation of myocardial glucose utilization with PET using the left ventricular time-activity curve as a noninvasive input function.Medical and Biological Engineering and Computing 36,112-117,1998.
[19]Wong,K.,Feng,D.,Meikle,S.,Fulham,M.,Simultaneous estimation of physiological parameters and the input function - in vivo PET data.IEEE Transactions on Information Technology In:Biomedcine.5,67-76,2001.
[2]Phelps ME,Homan EJ and Mullani NA et al.Application of annihilation coincidence detection to transaxial reconstruction tomography[J].J.Nuc.Med,vol.16,no.3,pp.210-224,March 1975.
[3]TerPogossian MM,Phelps ME and Homan ME et al.A positronemission transaxial tomograph for nuclear imaging[J].Radiology,vol.114,pp.89-98,1975.
[4]Herman G.Image Reconstruction from Projections:The Fundamentals of Computerized Tomography[M].Academic Press,New York,1980.
[5]Bertero M,DeMol C and Pike ER.Linear inverse problems with discrete data-Ⅰ:General formulation and singular system analysis[J].Inverse Prob,vol.1,no.4,pp.301-330,Nov.1985.
[6]Bertero M,Poggio T and Torre V.Ill posed problems in early vision[C].Proc.IEEE,vol.76,pp.869-889,Aug.1988.
[7]Budinger TF,Gullberg GT and Huesman RH.Emission computed tomography [M].Image Reconstruction from Projections:Implementation and applications,Herman GT,Ed.Berlin:Springer Verlag,1979,ch.5,pp.147-246.
[8]Shepp LA and Vardi Y.Maximum likelihood reconstruction for emission tomography[J].IEEE Transactions on Medical Imaging,vol.1,no.2,pp.113-122,October 1982.
[9]Snyder DL and Miller MI.The use of sieves to stabilized images produced with the EM algorithm for emission tomography[J].IEEE Trans.Nucl.Sci.,vol.NS-32,pp.3864-3872.Oct.1985.
[10]Levitan E and Herman GT.A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography[J].IEEE Trans.Med.Imag.,vol.MI-6,pp.185-192,Sept.1987.
[11]Green PJ.Bayesian reconstruction from emission tomography data using a modified EM algorithm[J].IEEE Trans.Med.Imag,vol.9,pp.84-93,Mar.1990.
[12]Lange K.Convergence of EM image reconstruction algorithms with Gibbs smoothing[J].IEEE Trans.Med.Imag,vol.9,pp.439-446,Dec.1990.
[13]Butler CS and Miller MI.Maximum A Posteriori estimation for SPECT using regularization techniques on massive parallel computers[J].IEEE Trans.Med.Imag.,vol 12,no.1,pp.84-89,March 1993.
[14]M.E.Kamasak,C.A.Bouman,E.D.Morris,and K.Sauer,"Direct reconstruction of kinetic parameter images from dynamic PET data," IEEE Trans.Med.Image,vol.24,no.5,pp.636-650,2005.
[15]G.B.Wang,L.Fu,and J.Qi,"Maximum a posteriori reconstruction of the patlak parametric image from sinograms in dynamic PET," Phys.Med.Biol.,vol.53,no.3,pp.593-604,2008.
[1]Dale L.Bailey,David W.Townsend,Peter E.Valk,Michael N.Maisey,Positron Emission Tomography:Basic Sciences,Springer,ISBN-10:1852337982,2005.
[2]Phelps ME,Homan EJ and Mullani NA et al.Application of annihilation coincidence detection to transaxial reconstruction tomography[J].J.Nuc.Med,vol.16,no.3,pp.210-224,March 1975.
[3]TerPogossian MM,Phelps ME and Homan ME et al.A positroncmission transaxial tomograph for nuclear imaging[J].Radiology,vol.114,pp.89-98,1975.
[4]Sorenson JA and Phelps ME.Physics in nuclear medicine[M].Saunders,Philadelphia,2 edition,1987.
[5]Alonso M and Finn E.Fundamental University Physics,volume Ⅲ Quantum and Statistical Physics[M].Addison-Wesley,Reading,Massachusetts,1983.
[6]Dahlbom M and Homan EJ.An evaluation of a two-dimensional array detector for high resolution PET[J].IEEE Transactions on Image Processing,vol.7,no.4,pp.264-272,December 1988.
[7]Michale E.Phelps.PET:Physics,instrumentation and scanners.2006,Springer New York
[8]王世真,林汉,周前,核医学与核生物学-基础及应用[M].科学出版社,1990
[9]Phelps ME,Hoffman EJ,Mullani NA,Ter-Pogossian MM.Application of annihilation coincidence detection to transaxial reconstruction tomography.J Nucl Med.1975;16:210-233.
[10]P.Sprawls,医学成像的物理原理,黄治悼等译,高等教育出版社,1993
[11]DL Bailey,JS Karp,S Surti,Physics and Instrumentation in PET,Positron Emission Tomography:Basic Science and Clinical,2003,Springer
[12]Hoffman EJ,Guerrero TM,Germano G,Digby WM,Dahlbom M.PET system calibration and corrections for quantitative and spatially accurate images.IEEE Trans Nucl Sci.1989;36:1108-1112
[13]Jaszczak R and Hoffman E.Scatter and attenuation.In H.Wagner,editor,Principles of Nuclear Medicine,chapter 19,section 3[M].W.B.Saunders Company,Philadelphia,2nd edition,1995.
[14]Bailey D.Transmission scanning in emission tomography[J].European Journal of Nuclear Medicine,25(7):774-787,July.1998.
[15]Meikle S,Dahlbom M,and Cherry S.Attenuation correction using count-limited transmission data in positron emission tomography[J].Journal of Nuclear Medicine,vol.34,pp.143-150,Jan.1993.
[16]Hoffman EJ,Huang S-C,Phelps ME,Kuhl DE,Quantitation in positron emission computed tomography:Ⅵ.Effect of accidental coincidences.J Comput assist Tomogr.1981;5;391-400.
[17]Williams CW,Crabtree MC,Brugiss SG.Design and performance characteristics of a positron emission computed axial tomography-ECAT-Ⅱ.IEEE Trans Nucl sci.1979;26:619-627.
[18]Eriksson L,Wienhard K,Dahlbom M,A simple data loss model for positron camera systems.IEEE Trans Nucl.Sci 1994;41:1566-1570.
[19]Kak A and Slaney M.Principles of Computerized Tomographic Imaging[M].IEEE Press,New York,1988.
[20]Bertero M,De Mol C,and Pike ER.Linear inverse problems with discrete data-Ⅰ:General formulation and singular system analysis[J].Inverse Prob,vol.1,no.4,pp.301-330,Nov.1985.
[21]Bertero M,Poggio T and Torre V.Ill posed problems in early vision[C].Proceedings of the IEEE,vol.76,pp.869-889,Aug.1988.
[22]Yu DF and Fessler JA.Mean and variance of coincidence photon counting with deadtime[J].Phys.Med.Biol,vol.15,pp.231-245,Aug.1999.
[23]Goitein M.Three-dimensional density reconstruction from a series of two dimensional projections[J].Nucl.Instr.Meth,vol.101,no.15,pp.509-518,June 1972.
[24]Rockmore AJ and Macovski A.A maximum likelihood approach to emission image reconstruction from projections[J].IEEE Tr.Nuc.Sci,vol.23,pp.1428-1432,1976.
[25]Shepp LA and Vardi Y.Maximum likelihood reconstruction for emission tomography[J].IEEE Transactions on Medical Imaging,vol.1,no.2,pp.113-122,October 1982.
[26]Houdson HM,and Larkin RS.Accelerated Image Reconstruction using Ordered Sunsets of Projection Data[J].IEEE Trans.on Medical Imagin.,vol.13,no.4,pp.601-609,December.1994.
[27]Byrne C,Soares E,and Pan TS.Accelerating the EM algorithm using rescaled block-iterative methods[C].Proc.IEEE Nuc.Sci.Symp.Med.Im.Conf.,volume 3,pp.1752-6,1996.
[28]Lange K.Convergence of EM image reconstruction algorithms with Gibbs smoothness[J].IEEE Transactions on Medical Imaging,vol.9,pp.439-446,Dec.1990.
[29]Fessler JA,Ficaro E,Clinthorne N,and K.Lange.Grouped-coordinate ascent algorithms for penalized likelihood transmission image reconstruction[J].IEEE Transactions on Medical Imaging,vol.16,Apr.1997.
[30]Lange K and Fessler JA.Globally convergent algorithms for maximum a posteriori transmission tomography[J].IEEE Transactions on Image Processing,4(10),pp.1430--1438,1995.
[31]R.M.Lewitt and S.Matej,Qverview of methods for image reconstruction from projections in emission computed tomography.Proceedings of the IEEE,91:1588-1611,2003.
[32]Fessler JA.Aspire 3.0 user's guide:A sparse reconstruction library[R].Communication & Signal Processing Laboratory Technical Report No.293,Department of Electrical and Computer Engineering,University of Michigan,Ann Arbor,1998.
[33]Lange K and Carson R.EM reconstruction algorithms for emission and transmission tomography[J].J.Comp.Assisted Tomo,vol.8,no.2,pp.306-316,April 1984.
[34]Herman G and Odhner D.Performance evaluation of an iterative image reconstruction algorithm for positron emission tomography[J].IEEE Transactions on Medical Imaging,10(3):336-346,Sept.1991.
[35]Fox PT,Mintun MA,Reiman EM,and Raichle ME.Enhanced detection of focal brain responses using intersubject averaging and change-distribution analysis of subtracted PET images[J].Journal of Cerebral Blood Flow and Metabolism,8(5):642-653,1988.
[36]M.Dwass.Probability and Statistics[M].W.A.Benjamin,Inc.,NewYork,1970.
[37]Fessler JA.Aspire 3.0 user's guide:A sparse reconstruction library JR].Communication & Signal Processing Laboratory Technical Report No.293,Department of Electrical and Computer Engineering,University of Michigan,Ann Arbor,1998.
[38]Lalush DS and Tsui BMW.A fast and stable maximum a posteriod conjugate gradient reconstruction algorithm[J].Med.Phys.,vol.22,no.8,pp.1273-84,Aug.1995.
[39]Fessler JA and Booth SD.Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction[J].IEEE Tr.Ira.Proc.,vol.8,no.5,pp.688-99,May 1999.
[40]Booth SD and Fessler JA.Combined diagonal/Fourier preconditioning methods for image reconstruction in emission tomography[C].Proc.IEEE Intl.Conf.on Image Processing,vol.2,pp.441-4,1995.
[41]Sauer K and Bouman C.A local update strategy for iterative reconstruction from projections[J].IEEE Tr.Sig.Proc.,vol.41,no.2,pp.534-548,February 1993.
[42]Bouman CA and Sauer K.A unified approach to statistical tomography using coordinate descent optimization[J].IEEE Tr.Im.Proc.,vol.5,no.3,pp.480-92,March 1996.
[43]Fessler JA and Hero AO.Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms[J].IEEE Tr.Im.Proc.,vol.4,no.10,pp.1417-29,October 1995.
[44]Fessler JA and Erdo(?)an H.A paraboloidal surrogates algorithm for convergent penalized-likelihood emission reconstruction[J].Proc.IEEE Nuc.Sci.Symp.Med.Im.Conf,volume 2,pp.1132-5,1998.
[45]Fessler JA and Erdo(?)an H.Accelerated monotonic algorithms for transmission tomography[C].Proc.IEEE Intl.Conf.on Image Processing,volume 2,pp.680-4,1998.
[46]Fessler JA and Erdo(?)an H.Monotonic algorithms for transmission tomography [J].IEEE Trans.Image Processing,vol.18,no.9,pp.801-14,September.1999.
[47]Geman S and Geman D.Stochastic relaxation,Gibbs distribution,and the Bayesian restoration of images[J].IEEE Trans,Pattern,Anal.Machine Intell,vol.PAMI-6,pp.721-741,Nov.1984.
[48]Li SZ.Markov Random Field Modeling in image Analysis[M].Springer-Verlag,Tokyo,2001.
[49]Levitan E and Herman GT.A maximum a posteriori probability expectation maximization algorithm for image reconstruction in emission tomography[J].IEEE Trans.Image Processing,vol.MI-6,pp.185-192,Sept.1987.
[50]Green PJ.Bayesian reconstruction from emission tomography data using a modified EM algorithm[J].IEEE Trans.Image Processing,vol.9,pp.84-93,Mar.1990.
[51]Butler CS and Miller MI.Maximum A Postedori estimation for SPECT using regularization techniques on massive parallel computers[J].IEEE Trans.Med.Imag.,vol 12,no.1,pp.84-89,March 1993.
[52]Johnson V,Wong WH,Hu X,and Chen CT.Image restoration using Gibbs prior:Boundary modeling,treatment of blurring,and selection of hyperparameter [J].IEEE Trans.Pattern Anal Machine Intell.,vol.13,pp.413-425,May 1991.
[53]Chatziioannou A and Dahlbom M.Detailed investigation of transmission and emission data smoothing protocols and their effects on emission images[J].IEEE Transactions on Nuclear Science,vol.43,pp.290-294,Feb.1996.
[54]Jacquez JA.Compartmental analysis in biology and medicine.Amsterdam,Holland:Elsevier/North;1972.
[55]Wagner JG.Fundamentals of clinical pharmacokinetics.Hamilton,Ill.:Drug Intelligence Publications;1975.
[56]Anderson D.Compartmental modeling and tracer kinetics.Berlin:Springer-Verlag;1983.
[57]Robertson J,editor.Compartmental distribution of radiotracers.Boca Raton,FL:CRC Press;1983.
[58]C.-M.Kao,J.T.Yap,J.Mukherjee,and M.Wernick,Image reconstruction for dynamic PET based on low-order approximation and restoration of the sinogram,IEEE Trans.on Medical Imaging,vol.16,no.6,pp.738-749,1997.
[59]T.E.Nichols,J.Qi,E.Asma,and R.M.Leahy,Spatioternporal reconstruction of list-mode PET data,IEEE Trans.on Medical Imaging,vol.21,no.4,pp.396-404,2002.
[60]R.E.Carson and K.Lange,The EM parametric image reconstruction algorithm,Journal of the American Statistical Association,vol.80,no.389,pp.20-22,1985.
[61]M.E.Kamasak,C.A.Bouman,E.D.Morris,and K.Sauer,Direct reconstruction of kinetic parameter images from dynamic PET data,IEEE Trans.Med.Image, vol.24,no.5,pp.636-650,2005.
[62]C Tsoumpas,FE Turkheimer,K Thielemans,A survey of approaches for direct parametric image reconstruction in emission tomography,Med.Phys.Volume 35,Issue 9,pp.3963-3971,2008.
[63]Bard Y.Nonlinear parameter estimation:Academic Press,New York;1974.
[64]Beck JV,Arnold KJ.Parameter estimation in engineering and science.New York:John Wiley & Sons;1977.
[65]Carson RE.Parameter estimation in positron emission tomography.In:Phelps ME,Mazziotta JC,Schelbert HR,editors.Positron emission tomography and autoradiography.New York:Raven Press;1986.p.347-90.
[66]Press W,Flannery B,Teukolsy S,Vetterling W.Numerical Recipes:The art of scientific computing.Cambridge:Cambridge University Press;1986.
[67]Eastman R,Carson R,Gordon M,Berg G,Lillioja S,Larson S,etal.Brain glucose metabolism in non-insulin-dependent diabetes mellitus:A study in Pima Indians using positron emission tomography during hyperinsulinemia with euglycemic glucose clamp.J Clin Endocrinol Metab 1990;71:1602-10.
[1]K.Lange,"Convergence of EM image reconstruction algorithms with Gibbs smoothness," IEEE Trans.Med.Imag.,vol.9,pp.439-446,Dec.1990.
[2]C.A Bouman and K.Sauer,"A generalized Gaussian image model for edge-preserving MAP estimation," IEEE Trans.Image Processing,vol.2 pp.296-310,July.1993.
[3]V.Johnson,W.H.Wong,X.Hu,and C.T.Chen,"Image restoration using Gibbs prior:Boundary modeling,treatment of blurring,and selection of hyperparameter," IEEE Trans.Pattern Anal Machine Intell.,vol.13,pp.413-425,May 1991.
[4]V.Johnson,"A framework for incorporating structural prior information into the estimation of medical image," in Information processing in Medical Imaging,H.H.Barrett and A.F.Gmitro,Eds.Berlin,Germany:Springer-Verlag,1993,pp.307-321.
[5]J.E.Bowsher,V.E.Johnson,T.G.Turkington,R.J.Jaszczak,C.E Floyd,and R.E.Coleman,"Bayesian reconstruction and use of anatomical a priori information for emission tomography," IEEE Tran.Med.Imag.,vol 15,pp.673-686,Oct,1996.
[6]Daniel F.Yu and Jeffrey A.Fessler,"Edge-Preserving Tomographic Reconstruction with Nonlocal Regularization," IEEE Trans.Med.Imag.,vol.21,no.2 pp.159-173,Feb.2002.
[7]S.J.Lee,A.Rangarajan,and G Gindi,"Bayesian Image Reconstruction in SPECT Using Higher Order Mechanical Models as Priors," IEEE Trans.on Medical Imaging,MI-14(4),pp.669-680,Dec.1995.
[8]Stan Z.Li,Markov Random Field Modeling in image Analysis,Tokyo:Springer-Verlag,2001,ch,1,pp 1-40.
[9]J.A.Fessler and H.Erdo(?)an,"A paraboloidal surrogates algorithm for convergent penalized-likelihood emission reconstruction," in Proc.IEEE Nuc.Sci.Symp.Med.Im.Conf.,volume 2,pp.1132-5,1998.
[10]H.Erdo(?)an and J.A.Fessler,"Monotonic algorithms for transmission tomography," IEEE Tr.Med.Im.,vol.18,no.9,pp.801-14,September 1999.
[1]M.Bertero,C.De Mol,and E.R.Pike,Linear inverse problems with discrete data-Ⅰ:General formulation and singular system analysis,Inverse Prob,Vol.1,no.4,pp.301-330,Nov.1985.
[2]S.Geman and D.Geman,Stochastic relaxation,Gibbs distribution,and the Bayesian restoration of image,IEEE Trans.Pattern,Anal.Machine Intell,voI.PAMI-6,pp.721-741,Nov.1984.
[3]Stan Z.Li,Markov Random Field Modeling in image Analysis,Springer-Verlag,Tokyo,2001.
[4]K.Lange.Convergence of EM image reconstruction algorithms with Gibbs smoothness.IEEE Trans.Med.Imag.,vol.9,439-446,1990
[5]G.Gindi,A.Rangarajan,M.Lee,P.J.Hong,and G.Zubal.Bayesian Reconstruction for Emission Tomography via Deterministic Annealing.In H.Barrett and A.Gmitro,editors.Information Processing in Medical Imaging,Springer-Verlag,322-338,1993
[6]Daniel F.Yu and Jeffrey A.Fessler.Edge-preserving tomographic reconstruction with nonlocal regularization,IEEE Trans.Med.Imag.,vol.21,no.2,pp.159-173,Feb,2002
[7]Charbonnier.P,Blanc-F'eraud.L,Aubert.G and Barlaud.M.Deterministic edge preserving regularization in computer imaging.IEEE Trans.Image Processing,vol.6,no.2,298-311,1997.
[8]A.Buades,B.Coll,and J.M.Morel.A nonlocal algorithm for image denoising.Proc.IEEE Int.Conf.Computer Vision Pattern Recognition,vol.2,60-65,2005
[9]Yang Chen,Qianjin Feng,et al.Nonlocal Prior Bayesian Tomographic Reconstruction,Journal of Mathematical Imaging and Vision[J],2,133-146,2008
[10]J.Fessler,"Hybrid Poisson/polynomial objective functions for tomographic image reconstruction from transmission scans," IEEE Transactions on Image Processing.,vol.4,pp.1439C1450,Oct 1995.
[11]A.Chatziioannou and M.Dahlbom,"Detailed investigation of transmission and emission data smoothing protocols and their effects on emission images," IEEE Transactions on Nuclear Science.,vol.43,pp.290C294,Feb 1996.
[12]L.A.Shepp and Y.Vardi.Maximum likehood reconstruction for emission tomography.IEEE Trans.Med.Imag.,vol.1,pp.113-121,1982.
[13]Wufan Chen,Ming Chen,and Jie Zhou.Adaptively regularized constrained total least-squares Image Restoration ,”IEEE Trans.Image Processing,vol.9,588-596,2000
[14]J.A.Fessler and H.Erdogan.A paraboloidal surrogates algorithm for convergent pena ized-likelihood emission reconstruction.Proc.IEEE Nuc.Sci.Symp.Med.Im.Conf,volume 2,1132-5,1998
[15]H.Erdogan and J.A.Fessler.Monotonic algorithms for transmission tomography.IEEE Tr.Med.Im,vol.18,801-14,1999
[16]D.S.Lalush and B.M.W.Tsui..A fast and stable maximum a posteriori conjugate gradient reconstruction algorithm,Med.Phys.,vol.22,1273-84,1998
[17]J.A.Fessler and S.D.Booth,1999.Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction.IEEE Tr.Im.Proc,vol.8,688-99,1999
[1]M.N.Wernick,J.N.Aarsvold(Eds.),Emission Tomography:The Fundamentals of PET and SPECT,Elsevier,2004.
[2]A.A.Lammertsma and S.P.Hume,Simplified reference tissue model for PET receptor studies,Neuroimage,vol.4,pp.153-158,1996.
[3]J.Tseng,L.K.Dunnwald,E.K.Schubert,J.M.Link,S.Minoshima,M.Muzi,and D.A.Mankoff,F(18)-FDG kinetics in locally advanced breast cancer:correlation with tumor blood flow and changes in response to neoadjuvant chemotherapy,Journal of Nuclear Medicine,vol.45,pp.1829-1837,2004.
[4]C.-M.Kao,J.T.Yap,J.Mukherjee,and M.Wernick,Image reconstruction for dynamic PET based on low-order approximation and restoration of the sinogram,IEEE Trans.on Medical Imaging,vol.16,no.6,pp.738-749,1997.
[5]T.E.Nichols,J.Qi,E.Asma,and R.M.Leahy,Spatiotemporal reconstruction of list-mode PET data,IEEE Trans.on Medical Imaging,vol.21,no.4,pp.396-404,2002.
[6]R.E.Carson and K.Lange,The EM parametric image reconstruction algorithm,Journal of the American Statistical Association,vol.80,no.389,pp.20-22,1985.
[7]M.E.Kamasak,C.A.Bouman,E.D.Morris,and K.Sauer,Direct reconstruction of kinetic parameter images from dynamic PET data,IEEE Trans.Med.Image,vol.24,no.5,pp.636-650,2005.
[8]C Tsoumpas,FE Turkheimer,K Thielemans,A survey of approaches for direct parametric image reconstruction in emission tomography,Med.Phys.Volume 35,Issue 9,pp.3963-3971,2008.
[9]Lange K.Convergence of EM image reconstruction algorithms with Gibbs smoothing[J].IEEE Trans.Med.lmag,vol.9,pp.439-446,Dec.1990.
[10]Wufan Chen,Ming Chen,and Jie Zhou.Adaptively regularized constrained total least-squares Image Restoration,IEEE Trans.Image Processing,vol.9,588-596,2000
[11]Levitan E and Herman GT.A maximum a posteriod probability expectation maximization algorithm for image reconstruction in emission tomography[J].IEEE Trans.Med.Imag.,vol.MI-6,pp.185-192,Sept.1987.
[12]Green PJ.Bayesian reconstruction from emission tomography data using a modified EM algorithm[J].IEEE Trans.Image Processing,vol.9,pp.84-93,Mar.1990.
[13]DJ Kadrmas,GT Gullberg,4D maximum a posteriod reconstruction in dynamic SPECT using a compartmental model-based prior,Phys.Med.Biol.46(2001)1553-1574.
[14]A.A.Lammertsma and S.P.Hume,Simplified reference tissue model for PET receptor studies,NeuroImage,vol.4,p.153158,1996.
[15]R.N.Gunn,A.A.Lammertsma,S.P.Hume,and V.J.Cunningham,Parametric imaging of ligand-receptor binding in PET using a simplified reference region model,NeuroImage,vol.6,no.4,p.279287,1997.
[16]Lange K.Convergence of EM image reconstruction algorithms with Gibbs smoothing[J].IEEE Trans.Med.Imag,vol.9,pp.439-446,Dec.1990.
[17]Stan Z.Li,2001.Markov Random Field Modeling in image Analysis,first ed.Springer- Verlag,Tokyo,1-40
[18]Li,X.,Feng,D.,Lin,K.,Huang,S.:Estimation of myocardial glucose utilization with PET using the left ventricular time-activity curve as a noninvasive input function.Medical and Biological Engineering and Computing 36,112-117,1998.
[19]Wong,K.,Feng,D.,Meikle,S.,Fulham,M.,Simultaneous estimation of physiological parameters and the input function - in vivo PET data.IEEE Transactions on Information Technology In:Biomedcine.5,67-76,2001.