基于MARS系统的X射线能谱CT研究
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摘要
X射线是19世纪末物理学的三大发现（X射线1895年、放射性1896年、电子1897年）之一，这一发现标志着现代物理学的诞生。由于X射线是波长介于紫外线和γ射线之间的电磁辐射，因而它具有很高的穿透本领，能穿透许多对可见光不透明的物质，基于此，可用来帮助人们进行医学诊断和治疗，或者用于工业等领域的非破坏性材料的检查。X射线CT (X-ray Computed Tomography, X-CT)正是如此。X-CT是计算机层析成像或断层扫描成像技术的简称，它是通过对X射线的利用，采用一定的图像重建算法，重建出物体一个切面（断层）图像，能以图像的形式，直观、清晰展现物体内部结构状况及材质组成，已在生物医学、航空航天器械、地质考古、军工武器、桥梁堤坝建筑及放射性污染等领域得到了广泛的应用。
X射线是一种连续能谱，与可见光相似，因波长或频率的不同，可以分为不同的能谱。近年来，基于X射线能量分辨光子计数探测器（类似于白光三棱镜）技术，产生了一种新型X-CT技术——X射线能谱CT技术。它是利用不同能量的入射X射线与被检测物体作用后的透射X射线所携带的信息而进行计算机断层扫描成像的一种技术，不仅能够显示丰富的X射线衰减特性以呈现物体内部结构状况，而且还可以提供有利于判别物质特性的信息以鉴别材质的类别。因此，在X-CT技术发展历程中，X射线能谱CT技术的诞生具有里程碑意义，已成为目前X-CT领域追逐研究的前沿技术或竞相研究的一个热点。
本论文的研究工作成果，是作者在中国留学基金委“国家建设高水平大学公派研究生项目”（录取文号：2010605056，批件号：留金发[2010]3006）资助下，分别于美国弗吉尼亚理工大学（Virginia Polytechnic Institute and State University）生物医学成像实验室和新西兰坎特伯雷大学（University of Canterbury）空间与物理系历经四年多时间在国内外教授联合指导下完成的。研究工作立足于X射线能谱CT技术的典型代表——MARS（Medipix All Resolution System）CT系统，依托于美国国家卫生研究院(National Institutes of Health，NIH)有关科研项目（USNIH/NIBIB Grant EB011785）及国家自然科学基金项目（项目编号：60172074）、国家“深部探测计划”项目（项目编号：SinoProbe-03-01-4F）等科研课题而展开的。
论文的研究内容，主要包括：
①研究了MARS X射线能谱CT系统结构特点及成像系统几何校准方法。针对如何校准射线束水平中心平面位置问题，提出了一种基于正弦图中心线的射线束水平中心平面位置校准方法。较之于常规校准方法，该方法更为科学合理，易于实现，无需考虑系统旋转中心轴位置和参照物放置位置等问题，提高了系统校准精度，这为X射线能谱CT图像精确重建奠定了基础。
②研究了X射线能谱CT投影数据特点及图像重建算法。X射线能谱CT往往是在有限的X射线能量范围内探测X射线的，在有限的X射线能量范围内，多色（多能量）X射线光管产生的光子数目也是有限的，导致投影图像中存在较大的量子噪声。此外，目前X射线能谱CT探测系统（X射线能量分辨光子计数探测器）还存在一些不足，致使获取的投影数据存在较多的噪声和伪影。为了提高X射线能谱CT图像重建质量，在借助于预处理技术处理投影数据的同时，将基于图像全变差（Total Variation，TV）最小化的有序子集同时代数重建算法（Order-subsetSimultaneous Algebraic Reconstruction Technique，OS-SART）应用于X射线能谱CT图像重建中。该算法将基于TV的优化算法与OS-SART重建算法相结合，使得在加速迭代收敛性的同时，可以有效抑制重建图像中的噪声和伪影。
③研究了基于K-edge（K边缘）特性的物质识别方法。从物理学角度分析，不同物质有着不同的X射线吸收特性，尤其是，物质的K-edge特性不同，借以鉴别其材质。与传统或常规X-CT技术相比，X射线能谱CT技术能够显示不同能量X射线的衰减特性。为了分析物质的不同物理特性，本文基于MARS X射线能谱CT系统，试验研究了一些对比剂（造影剂）和金属材料的K-edge特性，进而评估了MARS X射线能谱CT鉴别材质的能力。
④研究了X射线能谱CT数据评估及彩色CT图像重建方法。为了展示X射线能谱CT能够提供判别物质特性的潜能，本文利用主成分分析（PrincipalComponents Analysis， PCA）方法对X射线能谱CT数据进行了分析评估，提取和量化了X射线能谱CT数据的主要特征，重新表征了X射线能谱CT数据。与此同时，将新的能谱CT数据矩阵中最大的三个特征值所对应的三个特征向量作为彩色图像RGB（Red/Green/Blue）分量，融合出彩色的CT图像，借以彩色CT图像，呈现了丰富的X射线衰减特性信息。
⑤系统、深入研究了K-edge（K边缘）成像技术。K-edge成像是X射线能谱CT重要的应用之一。在物质K-edge前后，X射线衰减系数差异很大，为了提高已知材料成像对比度，可以利用X射线能谱CT在衰减系数跳变前后两个X射线能量段分别进行成像。本文针对如何设置K-edge前后两个X射线能量段的宽度问题，提出了一种优化的K-edge成像理论模型。该理论模型将信号差异噪声比（SignalDifference to Noise Ratio， SDNR）作为最优化准则，在这个最优化准则的约束下，选取了最佳的X射线能量段的宽度进行K-edge成像。实验研究表明，该理论模型能够在保证重建的两个能谱CT图像感兴趣区域噪声最小化的同时，可以获得最大的对比度差异，从而达到提高已知材料成像对比度的目的。
本文主要研究工作处于学科研究前沿，属于交叉学科范畴，涉及了核技术领域的X射线原理与探测应用研究，光学工程领域的精密机械扫描系统校准研究，量子物理领域的物质K-edge特性分析研究，计算机领域的数字图像处理和CT图像重建研究，以及数学领域的最优化模型研究，等等。因此，研究成果综合了各学科研究工作的结晶，凸显了多学科交叉研究的优势。目前，X射线能谱CT技术尚处于研究与开发的初创阶段，但因其有着传统X-CT技术无法比拟的优势，因此，开展X射线能谱CT技术的研究，不仅具有重要而深远的理论意义，而且有助于拓展更为广阔的应用领域。
X-ray is one of three vital physics discoveries (X-ray discovered in1895,Radiation discovered' in1896and Electron discovered in1897) at the end of the19thcentury, and the three discoveries mean the naissance of modern physics. X-ray is a kindof electromagnetic radiation, whose wavelength range is between ultraviolet and gammarays, it has a high penetrating ability, and penetrate many substances which visible lightcould not penetrate. Thus x-ray could be used for medical diagnosis and treatment, ornon-destructive inspection of materials in industry or other fields. Especially, X-CT(X-ray Computed Tomography) makes use of x-ray, by means of reconstructionalgorithm, to reconstruct a slice image of three-dimensional object, X-CT technique hasbeen widely used in biomedicine, aerospace, geology&archaeology, weapons,bridge&dam, radioactive contamination fields.
X-ray is a continuous energy spectrum, similar to visible light, due to the differentwavelengths or frequencies, x-ray can be divided into different energy spectrums.Recently based on x-ray energy-discriminative photon-counting detector (similar tovisible light prism), a new type of X-CT technology--x-ray spectal CT technique wasdeveloped. It is a x-ray computed tomography technique using the information carriedby different energy x-ray interacted with the object, which could display richer x-rayattenuation characteristics to present the interior structure of the object, and providemore substances properties information to identify categories of material. X-ray spectralCT is a milestone for X-CT development, which is an advanced CT technique and aresearch hotspot in the current CT field.
Author completed thesis study work with some domestic and overseas professors'supervision in the biomedical imaging laboratory, Virginia Tech.,USA and thedepartment of Physics and Astronomy, University of Canterbury, New Zealand, whoreceive a scholarship “Chinese Building for High-level University graduateprograms”granted by China Scholarship Council (Admission No.2010605056, File No.[2010]3006). The study work focuses on a typical x-ray spectral CT system--MARS(Medipix All Resolution System) CT, which was partially supported by U.S.NIH/NIBIB Grant EB011785, National Natural Science Foundation of China (No.60172074) and Chinese Deep Exploration Program Foundation (No.SinoProbe-03-01-4F).
Thesis study content mainly contains:
①Study for MARS spectral CT system structure and geometrical alignment. Weproposed a sinogram center line alignment method to determine the horizontal plane ofcone-beam. There is no need to take into account system axis and sample position, thismethod is more efficient to determine the horizontal plane of cone-beam, which isfoundation for exact reconstruction of the x-ray spectral CT image.
②Study for x-ray spectral CT projection data characteristics and the imagereconstruction algorithm. X-ray spectral CT often detect x-ray photon within the limitedenergy range, while the x-ray photon number is limited in the limited energy range,resulting in a mount of quantum noise in the projection image. In addition, there aresome deficiencies for x-ray spectral CT detective system (energy-discriminativephoton-counting detector), which could generate some noise and artifacts in theacquired projection data. In order to improve reconstruction image quality, we usedsome pre-processing method to deal with the projection data, moreover, we utilize basedon image total variation (TV) minimum ordered subset simultaneous algebraicreconstruction algorithm (OS-SART) to reconstruct x-ray spectral CT image. Thealgorithm is a combination of TV-based optimization algorithm and OS-SARTreconstruction algorithm, which could accelerate the iterative convergence and suppressnoise and artifacts of reconstructed images.
③Study for Substance identification method based on K-edge characteristics.Physically, different materials have different x-ray absorption characteristics, especiallythe K-edge characteristics could be used for identifying different materials. Unlikeconvertional X-CT, x-ray spectral CT is able to analyze the x-ray spectrumcharacteristics. In order to analyze the characteristics of the x-ray spectrum, we used theMARS x-ray spectral CT to identify the K-edge characteristics of some contrast agentsand metal materials, which could demonstrate energy-discriminative performance of thespectral CT.
④Study for x-ray spectral CT data evaluation and color CT image reconstruction.To demonstrate material-discriminative potential of the spectral CT, we used principalcomponent analysis (PCA) method to analyze and evaluate the spectral CT data, andextract and quantify these spectrum data, finally we considered the first threeeigenimages corresponding to the first three maximum eigenvalues as RGB(Red/Green/Blue) components of the color image, and reconstructed the true-color CTimage, which could display much richer x-ray attenuation information.
⑤Further research on K-edge imaging technique. K-edge imaging is a vitalapplication for x-ray spectral CT. Before and after K-edge, x-ray attenuation coefficientis very different, so imaging with two energy bins on both sides of a K-edge couldimprove the image contrast of the known materials. This paper proposed a K-edgeimaging optimization model to determine how to select two energy bins for optimalK-edge imaging. This model used the signal difference to noise ratio (SDNR) as acriterion to optimize the energy bin widths on both sides of the K-edge in the K-edgeimaging. The experiment results demonstrate that this model could improve the contrastof ROI of the two reconstructed imaging and minimize noise level.
Thesis studies lie in a frontier field, but also in a typical interdisciplinary, involvingx-ray detection and application in the nuclear field, precision mechanical scanningsystem calibration in the optical engineering field, material K-edge characteristics in thequantum physics field, digital image processing and CT image reconstruction in thecomputer field, optimization model analysis in the mathematics field, etc. Therefore, thestudy results integrated interdisciplinary research essence, and highlighted theadvantage of interdisciplinary research. At present, x-ray spectral CT technique is still atthe research and development stage, but it has more advantages than the conventionalX-CT technique, thus, carrying out the study on x-ray spectral CT has vital andprofound theoretical significance, which has a great application potential.
X射线是一种连续能谱，与可见光相似，因波长或频率的不同，可以分为不同的能谱。近年来，基于X射线能量分辨光子计数探测器（类似于白光三棱镜）技术，产生了一种新型X-CT技术——X射线能谱CT技术。它是利用不同能量的入射X射线与被检测物体作用后的透射X射线所携带的信息而进行计算机断层扫描成像的一种技术，不仅能够显示丰富的X射线衰减特性以呈现物体内部结构状况，而且还可以提供有利于判别物质特性的信息以鉴别材质的类别。因此，在X-CT技术发展历程中，X射线能谱CT技术的诞生具有里程碑意义，已成为目前X-CT领域追逐研究的前沿技术或竞相研究的一个热点。
本论文的研究工作成果，是作者在中国留学基金委“国家建设高水平大学公派研究生项目”（录取文号：2010605056，批件号：留金发[2010]3006）资助下，分别于美国弗吉尼亚理工大学（Virginia Polytechnic Institute and State University）生物医学成像实验室和新西兰坎特伯雷大学（University of Canterbury）空间与物理系历经四年多时间在国内外教授联合指导下完成的。研究工作立足于X射线能谱CT技术的典型代表——MARS（Medipix All Resolution System）CT系统，依托于美国国家卫生研究院(National Institutes of Health，NIH)有关科研项目（USNIH/NIBIB Grant EB011785）及国家自然科学基金项目（项目编号：60172074）、国家“深部探测计划”项目（项目编号：SinoProbe-03-01-4F）等科研课题而展开的。
论文的研究内容，主要包括：
①研究了MARS X射线能谱CT系统结构特点及成像系统几何校准方法。针对如何校准射线束水平中心平面位置问题，提出了一种基于正弦图中心线的射线束水平中心平面位置校准方法。较之于常规校准方法，该方法更为科学合理，易于实现，无需考虑系统旋转中心轴位置和参照物放置位置等问题，提高了系统校准精度，这为X射线能谱CT图像精确重建奠定了基础。
②研究了X射线能谱CT投影数据特点及图像重建算法。X射线能谱CT往往是在有限的X射线能量范围内探测X射线的，在有限的X射线能量范围内，多色（多能量）X射线光管产生的光子数目也是有限的，导致投影图像中存在较大的量子噪声。此外，目前X射线能谱CT探测系统（X射线能量分辨光子计数探测器）还存在一些不足，致使获取的投影数据存在较多的噪声和伪影。为了提高X射线能谱CT图像重建质量，在借助于预处理技术处理投影数据的同时，将基于图像全变差（Total Variation，TV）最小化的有序子集同时代数重建算法（Order-subsetSimultaneous Algebraic Reconstruction Technique，OS-SART）应用于X射线能谱CT图像重建中。该算法将基于TV的优化算法与OS-SART重建算法相结合，使得在加速迭代收敛性的同时，可以有效抑制重建图像中的噪声和伪影。
③研究了基于K-edge（K边缘）特性的物质识别方法。从物理学角度分析，不同物质有着不同的X射线吸收特性，尤其是，物质的K-edge特性不同，借以鉴别其材质。与传统或常规X-CT技术相比，X射线能谱CT技术能够显示不同能量X射线的衰减特性。为了分析物质的不同物理特性，本文基于MARS X射线能谱CT系统，试验研究了一些对比剂（造影剂）和金属材料的K-edge特性，进而评估了MARS X射线能谱CT鉴别材质的能力。
④研究了X射线能谱CT数据评估及彩色CT图像重建方法。为了展示X射线能谱CT能够提供判别物质特性的潜能，本文利用主成分分析（PrincipalComponents Analysis， PCA）方法对X射线能谱CT数据进行了分析评估，提取和量化了X射线能谱CT数据的主要特征，重新表征了X射线能谱CT数据。与此同时，将新的能谱CT数据矩阵中最大的三个特征值所对应的三个特征向量作为彩色图像RGB（Red/Green/Blue）分量，融合出彩色的CT图像，借以彩色CT图像，呈现了丰富的X射线衰减特性信息。
⑤系统、深入研究了K-edge（K边缘）成像技术。K-edge成像是X射线能谱CT重要的应用之一。在物质K-edge前后，X射线衰减系数差异很大，为了提高已知材料成像对比度，可以利用X射线能谱CT在衰减系数跳变前后两个X射线能量段分别进行成像。本文针对如何设置K-edge前后两个X射线能量段的宽度问题，提出了一种优化的K-edge成像理论模型。该理论模型将信号差异噪声比（SignalDifference to Noise Ratio， SDNR）作为最优化准则，在这个最优化准则的约束下，选取了最佳的X射线能量段的宽度进行K-edge成像。实验研究表明，该理论模型能够在保证重建的两个能谱CT图像感兴趣区域噪声最小化的同时，可以获得最大的对比度差异，从而达到提高已知材料成像对比度的目的。
本文主要研究工作处于学科研究前沿，属于交叉学科范畴，涉及了核技术领域的X射线原理与探测应用研究，光学工程领域的精密机械扫描系统校准研究，量子物理领域的物质K-edge特性分析研究，计算机领域的数字图像处理和CT图像重建研究，以及数学领域的最优化模型研究，等等。因此，研究成果综合了各学科研究工作的结晶，凸显了多学科交叉研究的优势。目前，X射线能谱CT技术尚处于研究与开发的初创阶段，但因其有着传统X-CT技术无法比拟的优势，因此，开展X射线能谱CT技术的研究，不仅具有重要而深远的理论意义，而且有助于拓展更为广阔的应用领域。
X-ray is one of three vital physics discoveries (X-ray discovered in1895,Radiation discovered' in1896and Electron discovered in1897) at the end of the19thcentury, and the three discoveries mean the naissance of modern physics. X-ray is a kindof electromagnetic radiation, whose wavelength range is between ultraviolet and gammarays, it has a high penetrating ability, and penetrate many substances which visible lightcould not penetrate. Thus x-ray could be used for medical diagnosis and treatment, ornon-destructive inspection of materials in industry or other fields. Especially, X-CT(X-ray Computed Tomography) makes use of x-ray, by means of reconstructionalgorithm, to reconstruct a slice image of three-dimensional object, X-CT technique hasbeen widely used in biomedicine, aerospace, geology&archaeology, weapons,bridge&dam, radioactive contamination fields.
X-ray is a continuous energy spectrum, similar to visible light, due to the differentwavelengths or frequencies, x-ray can be divided into different energy spectrums.Recently based on x-ray energy-discriminative photon-counting detector (similar tovisible light prism), a new type of X-CT technology--x-ray spectal CT technique wasdeveloped. It is a x-ray computed tomography technique using the information carriedby different energy x-ray interacted with the object, which could display richer x-rayattenuation characteristics to present the interior structure of the object, and providemore substances properties information to identify categories of material. X-ray spectralCT is a milestone for X-CT development, which is an advanced CT technique and aresearch hotspot in the current CT field.
Author completed thesis study work with some domestic and overseas professors'supervision in the biomedical imaging laboratory, Virginia Tech.,USA and thedepartment of Physics and Astronomy, University of Canterbury, New Zealand, whoreceive a scholarship “Chinese Building for High-level University graduateprograms”granted by China Scholarship Council (Admission No.2010605056, File No.[2010]3006). The study work focuses on a typical x-ray spectral CT system--MARS(Medipix All Resolution System) CT, which was partially supported by U.S.NIH/NIBIB Grant EB011785, National Natural Science Foundation of China (No.60172074) and Chinese Deep Exploration Program Foundation (No.SinoProbe-03-01-4F).
Thesis study content mainly contains:
①Study for MARS spectral CT system structure and geometrical alignment. Weproposed a sinogram center line alignment method to determine the horizontal plane ofcone-beam. There is no need to take into account system axis and sample position, thismethod is more efficient to determine the horizontal plane of cone-beam, which isfoundation for exact reconstruction of the x-ray spectral CT image.
②Study for x-ray spectral CT projection data characteristics and the imagereconstruction algorithm. X-ray spectral CT often detect x-ray photon within the limitedenergy range, while the x-ray photon number is limited in the limited energy range,resulting in a mount of quantum noise in the projection image. In addition, there aresome deficiencies for x-ray spectral CT detective system (energy-discriminativephoton-counting detector), which could generate some noise and artifacts in theacquired projection data. In order to improve reconstruction image quality, we usedsome pre-processing method to deal with the projection data, moreover, we utilize basedon image total variation (TV) minimum ordered subset simultaneous algebraicreconstruction algorithm (OS-SART) to reconstruct x-ray spectral CT image. Thealgorithm is a combination of TV-based optimization algorithm and OS-SARTreconstruction algorithm, which could accelerate the iterative convergence and suppressnoise and artifacts of reconstructed images.
③Study for Substance identification method based on K-edge characteristics.Physically, different materials have different x-ray absorption characteristics, especiallythe K-edge characteristics could be used for identifying different materials. Unlikeconvertional X-CT, x-ray spectral CT is able to analyze the x-ray spectrumcharacteristics. In order to analyze the characteristics of the x-ray spectrum, we used theMARS x-ray spectral CT to identify the K-edge characteristics of some contrast agentsand metal materials, which could demonstrate energy-discriminative performance of thespectral CT.
④Study for x-ray spectral CT data evaluation and color CT image reconstruction.To demonstrate material-discriminative potential of the spectral CT, we used principalcomponent analysis (PCA) method to analyze and evaluate the spectral CT data, andextract and quantify these spectrum data, finally we considered the first threeeigenimages corresponding to the first three maximum eigenvalues as RGB(Red/Green/Blue) components of the color image, and reconstructed the true-color CTimage, which could display much richer x-ray attenuation information.
⑤Further research on K-edge imaging technique. K-edge imaging is a vitalapplication for x-ray spectral CT. Before and after K-edge, x-ray attenuation coefficientis very different, so imaging with two energy bins on both sides of a K-edge couldimprove the image contrast of the known materials. This paper proposed a K-edgeimaging optimization model to determine how to select two energy bins for optimalK-edge imaging. This model used the signal difference to noise ratio (SDNR) as acriterion to optimize the energy bin widths on both sides of the K-edge in the K-edgeimaging. The experiment results demonstrate that this model could improve the contrastof ROI of the two reconstructed imaging and minimize noise level.
Thesis studies lie in a frontier field, but also in a typical interdisciplinary, involvingx-ray detection and application in the nuclear field, precision mechanical scanningsystem calibration in the optical engineering field, material K-edge characteristics in thequantum physics field, digital image processing and CT image reconstruction in thecomputer field, optimization model analysis in the mathematics field, etc. Therefore, thestudy results integrated interdisciplinary research essence, and highlighted theadvantage of interdisciplinary research. At present, x-ray spectral CT technique is still atthe research and development stage, but it has more advantages than the conventionalX-CT technique, thus, carrying out the study on x-ray spectral CT has vital andprofound theoretical significance, which has a great application potential.
引文
[1]庄天戈. CT原理和算法[M].第一版.上海：上海交通大学出版社,1992.
[2] G.T. Herman著,王洪范等译.由投影重建图像[M].北京:科学出版社,1985.
[3] H.H.巴雷特, W.斯温德尔著,庄天戈,周松凯译.放射成像——图像形成、检测和处理理论[M].第二卷.北京:科学出版社,1988.
[4]吴世法.中国工程物理研究院科技丛书——近代成像技术与图像处理[M].北京:国防工业出版社,1997.
[5] Hsieh Jiang. Computed Tomography：Principle, Design, Artifacts and Recent Advances[M].第一版.北京:科学出版社,2006.
[6] G. Dichiro and R. A. Brooks.1979Nobel-Prize in Physiology or Medicine[J]. Science,1979,206(4422):1060-1062.
[7] R. E. Alvarez and A. Macovski. Energy-selective reconstructions in x-ray computerizedtomography[J]. Physics in Medicine and Biology,1976,21(5):733-744.
[8] J. L. Ducote, Y. Alivov and S. Molloi. Imaging of nanoparticles with dual-energy computedtomography[J]. Physics in Medicine and Biology,2011,56(7):2031-2044.
[9] A. Graser, T. R. Johnson, H. Chandarana, et al. Dual energy CT: preliminary observations andpotential clinical applications in the abdomen[J]. European Radiology,2009,19(1):13–23.
[10] C. Baumer, G. Martens, B. Menser, et al. Testing an energy-dispersive counting-mode detectorwith hard x-rays from a synchrotron source[J]. IEEE Transactions on Nuclear Science,2008,55(3):1785-1790.
[11] J. H. Kinney and M. C. Nichols. X-ray tomographic microscopy (XTM) using synchrotronradiation[J]. Annual Review of Materials Science,1992,22:121-152.
[12] E. Schultke, S. Fiedler, C. Nemoz, et al. Synchrotron-based intra-venous K-edge digitalsubtraction angiography in a pig model: A feasibility study[J]. European Journal ofRadiology,2010,73(3):677-681.
[13] M. Campbell, E. H. M Heijne, G. Meddeler, et al. A readout chip for a64×64pixel matrixwith15-bit single Photon Counting[J]. IEEE Transactions on Nuclear Science,1998,45(3):751-753.
[14] C. Ponchut and F. Zontone. Evaluation of medipix-1in X-ray scattering and X-ray diffractionapplications[J]. Nuclear Instruments and Methods in Physics Research A,2003,510(1-2):29-34.
[15] A. Manuilskiy, B. Norlin, H. E. Nilsson, et al. Spectroscopy applications for the Medipixphoton counting X-ray system[J]. Nuclear Instruments and Methods in Physics Research A,2004,531(1-2):251-257.
[16] X. Llopart, M. Campbell, D. S. Segundo, et al. Medipix2: a64-k pixel readout chip with55-μm square elements working in single photon counting mode[J]. IEEE Transactions onNuclear Science,2002,49(5):2279-2283.
[17] M. Fiederle, D. Greiffenberg, J. Idarraga, et al. Energy calibration measurements ofMedipix2[J]. Nuclear Instruments and Methods in Physics Research A,2008,591(1):75-79.
[18] R. Ballabriga, M. Campbell, E. Heijne, et al. Medipix3: A64k pixel detector readout chipworking in single photon counting mode with improved spectrometric performance[J].Nuclear Instruments and Methods in Physics Research A,2011,633(1):15-18.
[19] R. Ballabriga, G. Blaj, M. Campbell, et al. Characterization of the Medipix3pixel readoutchip[J]. Journal of Instrumentation,2011,6(1):1052-1058.
[20] R. Ballabriga, M. Campbell, E. Heijne, et al. The Medipix3Prototype, a Pixel Readout ChipWorking in Single Photon Counting Mode With Improved Spectrometric Performance[J].IEEE Transaction on Nuclear Science,2007,54(5):1824-1829.
[21] A. S. Wang and N. J. Pelc. Sufficient Statistics as a Generalization of Binning in SpectralX-ray Imaging[J]. IEEE Transaction on Medical Imaging,2011,30(1):84-93.
[22] K. Taguchi, E. C. Frey and X. Wang. An analytical model of the effects of pulse pileup on theenergy spectrum recorded by energy resolved photon counting x-ray detectors[J]. MedicalPhysics,2010,37(8):3957-3969.
[23] X. Wang, D. Meier, S. Mikkelsen, et al. MicroCT with energy-resolved photon-countingDetectors[J]. Physics in Medicine and Biology,2011,56(9):2791-2816.
[24] J. Giersch, M. Firsching, D. Niederlohner, et al. Material reconstruction with spectroscopicpixel X-ray detectors[J]. Nuclear Instruments and Methods in Physics Research Section A,2005,546(1-2):125-130.
[25] M. Firsching, P. T. Talla, T. Michel, et al. Material resolving X-ray imaging using spectrumreconstruction with Medipix2[J]. Nuclear Instruments and Methods in Physics Research A,2008,591(1):19-23.
[26] M. Firsching, A. P. Butler, N. Scott, et al. Contrast agent recognition in small animal CT usingthe Medipix2detector[J]. Nuclear Instruments and Methods in Physics Research Section A,2009,607(1):179-192.
[27] Q. Xu, H. Yu, J. Bennett, et al. Image reconstruction for hybrid true-color micro-CT[J]. IEEETransactions on Biomedical Engineering,2012,59,1711-1719.
[28] P. M. Frallicciardi, J. Jakubek, D. Vavrik, et al. Comparison of single-photon counting andcharge-integrating detectors for X-ray high-resolution imaging of small biological objects[J].Nuclear Instruments and Methods in Physics Research A: Accelerators SpectrometersDetectors and Associated Equipment,2009,607(1):221-222.
[29] J. Dammer, P. M. Frallicciardi, J. Jakubek, et al. Real-time in-vivo mu-imaging withMedipix2[J]. Nuclear Instruments and Methods in Physics Research A: AcceleratorsSpectrometers Detectors and Associated Equipment,2009,607(1):205-207.
[30] N. G. Anderson, A. Butler, N. Scott, et al. Spectroscopic (multi-energy) CT distinguishesiodine and barium contrast material in MICE[J]. European Radiology,20(9)(2010):2126-2134.
[31]郝佳,张丽,陈志强,等.多能谱X射线成像技术及其在CT中的应用[J]. CT理论与应用研究,2011,20(1):141-150.
[32] L. Tlustos, M. Campbell, E. Heijne, et al. Signal variations in high-granularity Si pixeldetectors[J]. IEEE Transaction on Nuclear Science,2004,51(6):3006-3012.
[33] G. Mettivier, M. C. Montesi and P. Russo. First images of a digital autoradiography systembased on a Medipix2hybrid silicon pixel detector[J]. Physics in Medicine and Biology,2003,48(12):173-181.
[34] L. Tlustos, R. Ballabriga, M. Campbell, et al. Imaging properties of the Medipix2systemexploiting single and dual energy thresholds[J]. IEEE Transaction on Nuclear Science,2005,53(1):367-372.
[35] P. Fischer, J.Hausmann, A. Helmich, et al. Counting pixel chip and sensor system for X-rayimaging[J]. IEEE Transactions on Nuclear Science,1999,46(4):1070-1074.
[36] T. Kubicki, K. Lubelsmeyer, J. Ortmanns, et al. Calculation of the electric field in GaAsparticle detectors[J]. Nuclear Instruments and Methods in Physics Research A,1994,345(3):468-473.
[37] J. W. Chen, T. Frommichen, J. Ludwig, et al. Evaluation of active layer properties and chargecollection efficiency of GaAs particle detectors[J]. Nuclear Instruments and Methods inPhysics Research A,1995,365(2-3):273-284.
[38] A. Cola, F. Quaranta, M. A. Ciocci, et al. Fantacci. A study of the electrical andcharge-collection properties of semi-insulating GaAs detectors[J]. Nuclear Instruments andMethods in Physics Research A: Accelerators, Spectrometers, Detectors and AssociatedEquipment,1996,380(1-2):66-69.
[39] R. Irsigler, J. Andersson, J. Alverbro, et al. X-ray imaging using a320×240hybrid gaas pixeldetector[J]. IEEE Transactions on Nuclear Science,1999,46(2-3):507-512.
[40] P. Fischer, J. Hausmann, M. Overdick, et al. A counting pixel readout chip for imagingapplications[J]. Nuclear Instruments and Methods in Physics Research A: Accelerators,Spectrometers, Detectors and Associated Equipment,1998,405(1):53-59.
[41] C. Schwarz, M. Campbell, R. Goeppert, et al. Measurements with Si and GaAs pixeldetectors bonded to photon counting readout chips[J]. Nuclear Instruments and Methods inPhysics Research A,2001,466:87-94.
[42] M. Lindner, P. Fischer, S. Florin, et al. Comparison of hybrid pixel detectors with Si andGaAs sensors[J]. Nuclear Instruments and Methods in Physics Research A,2001,466:63-73.
[43] H. Tajima, T. Kamae, G. Madejski, et al. Application of CdTe for the NeXT mission[J].Nuclear Instruments and Methods in Physics Research A,2005,541:332-341.
[44] G. Sato, A. Parsons, D. Hullinger, et al. Development of a spectral model based on chargetransport for the swift/BAT32K CdZnTe detector array[J]. Nuclear Instruments and Methodsin Physics Research A,2005,541:372-384.
[45] V. B. Cajipe, R. F. Calderwood, M. Clajus, et al. Multi-energy x-ray imaging with linear CZTpixel arrays and integrated electronics[J]. IEEE Nuclear Science Symposium ConferenceRecord,2004,7:4548-4551.
[46] P. M. Shikhaliev. Computed tomography with energy resolved detection: a feasibility study[J].Physics in Medicine and Biology,2008,53(5):1475-1495.
[47] P. M. Shikhaliev. Energy resolved computed tomography: first experimental results[J].Physics in Medicine and Biology,2008,53(20):5595-5613.
[48] P. M. Shikhaliev. Projection x-ray imaging with photon energy weighting: experimentalevaluation with a prototype detector[J]. Physics in Medicine and Biology,2008,54(16):4971-4992.
[49] J. P. Schlomka, E. Roessl, R. Dorscheid, et al. Experimental feasibility of multi-energyphoton-counting K-edge imaging in pre-clinical computed tomography[J]. Physics inMedicine and Biology,2008,53(15):4031–4047
[50] P. M. Shikhaliev and S. G. Fritz. Photon counting spectral CT versus conventional CT:comparative evaluation for breast imaging application[J]. Physics in Medicine and Biology,2011,56(7):1905-1930.
[51] M. Hurrell, A. Butler, N. Cook, et al. Spectral Hounsfield units: a new radiological concept[J].European Radiology,2012,22(5):1008-1013.
[52] R. Carmi, A. Livne, A. Gringauz, et al. Experimental Evaluation of Image-Based SpectralAnalysis Method for Multi Energy Window Photon Counting X-Ray CT[J]. IEEE NuclearScience Symposium and Medical Imaging Conference,2009,1-9:3178-3180.
[53] S. Gleason, H. Sari-Sarraf, M. Paulus, et al. Reconstruction of multi-energy x-ray computedtomography images of laboratory mice[J]. IEEE Transactions on Nuclear Science,1999,46(4):1081-1086.
[54] E. Roessl and R. Proksa. K-edge imaging in x-ray computed tomography using multi-binphoton counting detectors[J]. Physics in Medicine and Biology,2007,52(15):4679-4696.
[55] P. He, H. Yu, P. Thayer, X. Jin, Q. Xu, J. Bennett, R. Tappenden, B. Wei, A. Goldstein, P.Renaud, A. Butler, P. Butler and G. Wang. Preliminary Experimental Results from a MARSMicro-CT System[J]. Journal of X-ray Science and Technology,2012,20,199-211.
[56] R. Gordon, R. Bender and G.T. Herman. Algebraic reconstruction techniques (ART) forthree-dimensional electron microscopy and x-ray photography[J]. Journal of TheoreticalBiology,1970,29(3):471-482.
[57] A.H. Andersen and A. C. Kak. Simultaneous Algebraic Reconstruction Technique (SART): asuperior implementation of the ART algorithm[J]. Ultrasonic Imaging,1984,6(1):81-94.
[58] G. Wang and M. Jiang. Ordered-Subset Simultaneous Algebraic Reconstruction Techniques(OS-SART)[J]. Journal of X-ray Science and Technology,2004,12(3):169-177.
[59] M. Jiang and G. Wang. Convergence studies on iterative algorithms for imagereconstruction[J]. IEEE Transaction on Medical Imaging,2003,22(5):569-579.
[60] D. L. Donoho. Compressed sensing[J]. IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[61] E. J. Candes, J. Romberg and T. Tao. Robust uncertainty principles: exact signalreconstruction from highly incomplete frequency information[J]. IEEE Transactions onInformation Theory,2006,52(2):489-509.
[62] G. Wang, H. Yu and B. DeMan. An outlook on x-ray CT research and development[J].Medical Physics,2008,35(3):1051-1064.
[63] G. H. Chen, J. Tang and S. Leng. Prior image constrained compressed sensing (PICCS): Amethod to accurately reconstruct dynamic CT images from highly undersampled projectiondatasets[J]. Medical Physics,2008,35(2):660-663.
[64] H. Yu and G. Wang. Compressed sensing based interior tomography[J]. Physics in Medicineand Biology,2009,54(9):2791-2805.
[65] E. Y. Sidky, C. M. Kao and X. Pan. Accurate image reconstruction from few-views andlimited-angle data in divergent-beam CT[J]. Journal of X-ray Science and Technology,2006,14:119-139.
[66] Y. Ye, H. Yu, Y. Wei, et al. A general local reconstruction approach based on a truncatedHilbert transform[J]. International journal of biomedical imaging,2007:1-8.
[67] H. Kudo, M. Courdurier, F. Noo, et al. Tiny a priori knowledge solves the interior problem incomputed tomography[J]. Physics in Medicine and Biology,2008,53:2207-2231.
[68] M. Courdurier, F. Noo, M. Defrise, et al. Solving the interior problem of computedtomography using a priori knowledge[J]. Inverse Problems,2008,24,065001.
[69] H. Yu and G. Wang, A soft-threshold filtering approach for reconstruction from a limitednumber of projections[J]. Physics in Medicine and Biology,2010,55(13):3905-3916.
[70] J.S. Yang, H. Yu, M. Jiang, et al, High-order total variation minimization for interiortomography[J]. Inverse Problems,2010,26,035013.
[71] Q. Xu, X. Mou, G. Wang, et al. Statistical Interior Tomography[J]. IEEE Transactions onMedical Imaging,2011,30(5):1116-1128.
[72] E. C. Frey, X. Wang, Y. Du, et al. Investigation of the use of Photon Counting X-RayDetectors with Energy Discrimination Capability for Material Decomposition inMicro-Computed Tomography[J]. Physics of Medical Imaging,2007,6510:93-103.
[73] S. J. Nik，J. Meyer and R. Watts. Optimal material discrimination using spectral x-rayimaging[J]. Physics in Medicine and Biology,2011,56(18):5969-5983.
[74] B. Norlin, A. Manuilskiy, H. Nilsson, et al. Material recognition with the Medipix photoncounting colour X-ray system[J]. Nuclear Instruments and Methods in Physics Research A,2004,531(1-2):265-269.
[75] H. Le and S. Molloi. Least squares parameter estimation methods for material decompositionwith energy discriminating detectors[J]. Medical Physics,2010,38:245-55.
[76] M. Firsching, D. Niederlohner, T. Michel, et al. Quantitative material reconstruction in CTwith spectroscopic x-ray pixel detectors—a simulation study[J]. IEEE Nuclear ScienceSymposium Conference Record,2006,4:2257-2259.
[77] L. A. Lehmann, R. E. Alvarez, A. Macovski, et al. Generalized image combinations in dualKVP digital radiography[J]. Medical Physics,1981,8(5):659-667.
[78] W. H. Marshall, R. E. Alvarez and A. Macovski. Initial results with prereconstructiondual-energy computed tomography (PREDECT)[J]. Radiology,1981,140(2):421-430.
[79] J. P. Stonestrom, R. E. Alvarez and A. Macovski. A framework for spectral artifact correctionsin x-ray CT[J]. IEEE Transactions on Biomedical Engineering,1981,28(2):128-41.
[80] R. A. Brooks. A quantitative theory of the Hounsfield unit and its application to dual energyscanning[J]. Journal of Computer Assisted Tomography,1977,1(4):487-93.
[81] H. J. Vinegar and S. L. Wellington. Method of Imaging the Atomic Number of a Sample.1986,US Patent4571491.
[82] G. Christ. Exact treatment of the dual-energy method in CT using polyenergetic X-rayspectra[J]. Physics in Medicine and Biology,1984,29(12):1501-1510.
[83] D. J. Drost and A. Fenster. Experimental dual xenon detectors for quantitative CT and spectralartifact correction[J]. Medical Physics,1980,7(2):101-107.
[84] M. van Straten, M. Schaap, M. L. Dijkshoorn, et al. Automated bone removal in CTangiography: Comparison of methods based on single energy and dual energy scans[J].Medical Physics,2011,38(11):6128-6137.
[85] B. M. Yeh, J. A. Shepherd, Z. J. Wang, et al. Dual-energy and low-kVp CT in the abdomen[J].American Journal of Roentgenology,2009,193(1):47-54.
[86] D. N. Tran, M. Straka, J. E. Roos, et al. Dual-energy CT discrimination of iodine and calcium:Experimental results and implications for lower extremity CT angiography[J]. AcademicRadiology,2009,16(2):160-171.
[87] I. T. Jolliffe. Principal Components Analysis[M]. New York: Springer-Verlag,1986.
[88] H. Hotelling. Analysis of a complex of statistical variables into principal components[J].Journal of Educational Psychology,1933,24:417-441and498-520.
[89] L. Sirovich and M. Kirby. Low-dimensional procedure for the characterization of humanfaces[J]. Journal of the Optical Society of America A,1987,4(3):519-524.
[90] A. R. Kalukin, M.Van Geet and R. Swennen, Principal components analysis of multienergyx-ray computed tomography of mineral samples[J]. IEEE Transaction on Nuclear Science,2000,47(5):1729-1736.
[91] A. P. Butler, J. Butzer, N. Schleich, et al, Processing of spectral X-ray data with principalcomponents analysis[J]. Nuclear Instruments and Methods in Physics Research A,2011,633(1):140-142.
[92] J.S. Butzer, A. P. Butler, P. H. Butler, et al. Medipix imaging—evaluation of datasets withPCA[J]. Proceedings of the23rd International Conference on Image and Vision ComputingNew Zealand,2008:1-6.
[93] S. Feuerlein, E. Roessl, R. Proksa, et al. Multienergy Photon-counting K-edge Imaging:Potential for Improved Luminal Depiction in Vascular Imaging[J]. Radiology,2008,249(3):1010-1016.
[94] P. He, B. Wei, W.X. Cong and G. Wang, Optimization of K-edge Imaging with Spectral CT[J].Medical Physics,2012,39(11):6572-6579.
[95] E. Roessl, B. Brendel, K. J. Engel, et al. Sensitivity of Photon-Counting Based K-edgeImaging in X-ray Computed Tomography[J]. IEEE Transactions on Medical Imaging,2011,30(9):1678-1690.
[96] A. Abudurexiti, M. Kameda, E. Sato, et al. Demonstration of iodine K-edge imaging by use ofan energy-discrimination X-ray computed tomography system with a cadmium telluridedetector[J]. Radiological physics and technology,2010,3(2):127-135.
[97]何鹏,魏彪,冯鹏,等. Color-CT技术研究简述[J].2012年全国射线数字成像与CT新技术研讨会论文集,2012,07.
[98]郝佳,张丽,陈志强,等.彩色X射线成像技术新进展[J].中国体视学与图像分析,2011,16(2):203-208
[99]陈克敏,林晓珠. CT能谱成像临床应用与研究价值及展望[J].现代实用医学,2011,23(8):841-844.
[100]李小虎,刘斌,余永强,等.能谱CT的基本原理与临床应用[J].中国医疗器械信息,2011,10:1-5.
[101]孙丛,柳澄,王锡明,等.双能CT成像在显示膝关节韧带中的价值[J].中国医学影像技术,2008,24(9):1323-1325.
[102]邓凯,张成琪,李伟,等.宝石能谱CT的特点及临床应用价值[J].中国医药导报,2011,25(8):16-17.
[103]汤昕烨,张丽,陈志强,等.双能DR物质识别算法在CT成像系统中的应用[J].中国体视学与图像分析,2007,12(2):88-92.
[104]郝佳,张丽,邢宇翔,等.双能量CT技术在电子密度测量中的应用[J].核电子学与探测技术,2011，31(10):1082-1085.
[105]张岚,李元景,郑晓翠,等.线阵计数型多能CZT成像系统的性能研究[J].第十五届全国核电子学与核探测技术学术年会论文集，2010,08.
[106]李霞,褚君浩,李陇遐,等.室温核辐射CdZnTe像素阵列探测器的研制[J].光电子激光,2008,19(6):751-753.
[107]徐亚东,介万奇,查刚强,等. CZT平面探测器对低能X/γ射线的光谱响应[J].光学学报,2009,29(11):3072-3077.
[108]王玺,肖沙里,张流强,等.基于CdZnTe晶体的2×2像素阵列探测器研究[J].光电子激光,2010,21(5):639-643.
[109]陈平,潘晋孝,刘宾.连续能谱X-CT投影仿真算法[J].无损检测,2009,31(2):102-104.
[110]蔡彪,潘晋孝,陈平.基于连续X射线谱的CT重建算法仿真[J].计算机仿真,2011,28(4):257-260.
[111] P. He, H. Yu, J. Bennett, et al. Energy-discriminative performance analysis for spectral CT[J].Journal of X-Ray Science and Technology，to appear2013.
[112] MARS-CT Operations Manual.
[113] A. C. Kak and M. Slaney. Principles of Computerized tomographic Imaging[M]. IEEE Press,1998.
[114] J. Fessler. Mean and variance of implicitly defined biased estimators (such as penalizedmaximum likelihood): Applications to tomography[J]. IEEE Transactions on ImageProcessing,1996,5(3):493-506.
[115] E. DiBella, A. Barclay, R. Eisner, et al. A comparison of rotation-based methods for iterativereconstruction algorithms[J]. IEEE Transaction on Nuclear Science,1996,43(6):3370-3376.
[116] W. H. Rucgardson. Bayesian-based iterative method of image restoration[J]. Journal of theOptical Society of America A,1972,62:55-59.
[117] T. Hebert and R. Leahy. Statistic-based MAP image reconstruction from Poisson data usingGibbs priors[J]. IEEE Transaction on Signal Processing,1992,40(9):2290-2303.
[118] H. M. Hudson and R. S. Larkin. Accelerated image reconstruction using ordered subsets ofprojection data[J]. IEEE Transaction on Medical Imaging,1994,13(4):601-609.
[119] J. Browne and A.R. De Pierro. A row-action alternative to the EM algorithm for maximizinglikelihood in emission tomography[J]. IEEE Transaction on Medical Imaging,1996,15(5):687-699.
[120] D. S. Hwang and G. L. Zeng. Convergence study of an accelerated ML-EM algorithm usingbigger step size[J]. Physics in Medicine and Biology,2006,51(2):237-252.
[121] E. Candes and M. Wakin. An introduction to compressive sampling[J]. IEEE SignalProcessing Magazine,2008,25(2):21-30.
[122] E. Candes and J. Romberg. Quantitative robust uncertainty principles and optimally sparsedecompositions[J]. Foundations of Computational Mathematics,2006,6(2):227-254.
[123] http://www.nist.gov/pml/data/xraycoef/index.cfm.
[124] B. Liu, G. Wang, E. L. Ritman, et al. Image reconstruction from limited angle projectionscollected by multisource interior x-ray imaging systems[J]. Physics in Medicine and Biology,2011,56(19):6337-6357.
[125] C. Raven. Numerical removal of ring artifacts in microtomography[J]. Review of ScientificInstruments,1998,69(8):2978-2980.
[126] M. F. Kijewski and P. F. Judy. The noise power spectrum of CT images[J]. Physics inMedicine and Biology,1987,32(8):1049-1058.
[127] I. Cunningham, M. Westmore and A. Fenster. A spatial-frequency dependent quantumaccounting diagram and detective quantum efficiency model of signal and noise propagationin cascaded imaging systems[J]. Medical Physics,1994,21(3):417-427.
[128] M. J. Tapiovaara and R. F. Wagner. SNR and DQE analysis of broad spectrum x-rayimaging[J]. Physics in Medicine and Biology,1985,30(6):519-529.
[129] G. Wang and M. W. Vannier. Helical CT image noise-analytical results[J]. Medical Physics1993,20(6):1635-1640.
[130] E. Dizendorf, H. Hany, A. Buck, et al. Cause and magnitude of the error induced by oral CTcontrast agent in CT-based attenuation correction of PET emission studies[J]. Journal ofNuclear Medicine,2003,44(5):732-738.
[131] H. Gao, H. Yu, S. Osher, et al. Multi-energy CT based on a prior rank, intensity and sparsitymodel (PRISM)[J]. Inverse Problems,2011,27(11).11502.
[132] M. Depypere, J. Nuyts, N. Gastel, et al. An iterative dual energy CT reconstruction methodfor a K-edge contrast material[J]. Proceedings of SPIE,2011,7916,79610M.
[133] E. Sato, Y. Oda, A. Abudurexiti, et al. Demonstration of enhanced iodine K-edge imagingusing an energy-dispersive X-ray computed tomography system with a25mm/s-scan linearcadmium telluride detector and a single comparator[J]. Applied Radiation and Isotopes,2012,70(5):831–836.
[134] D. S. Gierada and K. T. Bae. Gadolinium as a CT contrast agent: Assessment in a porcinemodel[J]. Radiology,1999,210(3):829-834.
[135] http://www.imp.uni-erlangen.de/forbild.
[2] G.T. Herman著,王洪范等译.由投影重建图像[M].北京:科学出版社,1985.
[3] H.H.巴雷特, W.斯温德尔著,庄天戈,周松凯译.放射成像——图像形成、检测和处理理论[M].第二卷.北京:科学出版社,1988.
[4]吴世法.中国工程物理研究院科技丛书——近代成像技术与图像处理[M].北京:国防工业出版社,1997.
[5] Hsieh Jiang. Computed Tomography：Principle, Design, Artifacts and Recent Advances[M].第一版.北京:科学出版社,2006.
[6] G. Dichiro and R. A. Brooks.1979Nobel-Prize in Physiology or Medicine[J]. Science,1979,206(4422):1060-1062.
[7] R. E. Alvarez and A. Macovski. Energy-selective reconstructions in x-ray computerizedtomography[J]. Physics in Medicine and Biology,1976,21(5):733-744.
[8] J. L. Ducote, Y. Alivov and S. Molloi. Imaging of nanoparticles with dual-energy computedtomography[J]. Physics in Medicine and Biology,2011,56(7):2031-2044.
[9] A. Graser, T. R. Johnson, H. Chandarana, et al. Dual energy CT: preliminary observations andpotential clinical applications in the abdomen[J]. European Radiology,2009,19(1):13–23.
[10] C. Baumer, G. Martens, B. Menser, et al. Testing an energy-dispersive counting-mode detectorwith hard x-rays from a synchrotron source[J]. IEEE Transactions on Nuclear Science,2008,55(3):1785-1790.
[11] J. H. Kinney and M. C. Nichols. X-ray tomographic microscopy (XTM) using synchrotronradiation[J]. Annual Review of Materials Science,1992,22:121-152.
[12] E. Schultke, S. Fiedler, C. Nemoz, et al. Synchrotron-based intra-venous K-edge digitalsubtraction angiography in a pig model: A feasibility study[J]. European Journal ofRadiology,2010,73(3):677-681.
[13] M. Campbell, E. H. M Heijne, G. Meddeler, et al. A readout chip for a64×64pixel matrixwith15-bit single Photon Counting[J]. IEEE Transactions on Nuclear Science,1998,45(3):751-753.
[14] C. Ponchut and F. Zontone. Evaluation of medipix-1in X-ray scattering and X-ray diffractionapplications[J]. Nuclear Instruments and Methods in Physics Research A,2003,510(1-2):29-34.
[15] A. Manuilskiy, B. Norlin, H. E. Nilsson, et al. Spectroscopy applications for the Medipixphoton counting X-ray system[J]. Nuclear Instruments and Methods in Physics Research A,2004,531(1-2):251-257.
[16] X. Llopart, M. Campbell, D. S. Segundo, et al. Medipix2: a64-k pixel readout chip with55-μm square elements working in single photon counting mode[J]. IEEE Transactions onNuclear Science,2002,49(5):2279-2283.
[17] M. Fiederle, D. Greiffenberg, J. Idarraga, et al. Energy calibration measurements ofMedipix2[J]. Nuclear Instruments and Methods in Physics Research A,2008,591(1):75-79.
[18] R. Ballabriga, M. Campbell, E. Heijne, et al. Medipix3: A64k pixel detector readout chipworking in single photon counting mode with improved spectrometric performance[J].Nuclear Instruments and Methods in Physics Research A,2011,633(1):15-18.
[19] R. Ballabriga, G. Blaj, M. Campbell, et al. Characterization of the Medipix3pixel readoutchip[J]. Journal of Instrumentation,2011,6(1):1052-1058.
[20] R. Ballabriga, M. Campbell, E. Heijne, et al. The Medipix3Prototype, a Pixel Readout ChipWorking in Single Photon Counting Mode With Improved Spectrometric Performance[J].IEEE Transaction on Nuclear Science,2007,54(5):1824-1829.
[21] A. S. Wang and N. J. Pelc. Sufficient Statistics as a Generalization of Binning in SpectralX-ray Imaging[J]. IEEE Transaction on Medical Imaging,2011,30(1):84-93.
[22] K. Taguchi, E. C. Frey and X. Wang. An analytical model of the effects of pulse pileup on theenergy spectrum recorded by energy resolved photon counting x-ray detectors[J]. MedicalPhysics,2010,37(8):3957-3969.
[23] X. Wang, D. Meier, S. Mikkelsen, et al. MicroCT with energy-resolved photon-countingDetectors[J]. Physics in Medicine and Biology,2011,56(9):2791-2816.
[24] J. Giersch, M. Firsching, D. Niederlohner, et al. Material reconstruction with spectroscopicpixel X-ray detectors[J]. Nuclear Instruments and Methods in Physics Research Section A,2005,546(1-2):125-130.
[25] M. Firsching, P. T. Talla, T. Michel, et al. Material resolving X-ray imaging using spectrumreconstruction with Medipix2[J]. Nuclear Instruments and Methods in Physics Research A,2008,591(1):19-23.
[26] M. Firsching, A. P. Butler, N. Scott, et al. Contrast agent recognition in small animal CT usingthe Medipix2detector[J]. Nuclear Instruments and Methods in Physics Research Section A,2009,607(1):179-192.
[27] Q. Xu, H. Yu, J. Bennett, et al. Image reconstruction for hybrid true-color micro-CT[J]. IEEETransactions on Biomedical Engineering,2012,59,1711-1719.
[28] P. M. Frallicciardi, J. Jakubek, D. Vavrik, et al. Comparison of single-photon counting andcharge-integrating detectors for X-ray high-resolution imaging of small biological objects[J].Nuclear Instruments and Methods in Physics Research A: Accelerators SpectrometersDetectors and Associated Equipment,2009,607(1):221-222.
[29] J. Dammer, P. M. Frallicciardi, J. Jakubek, et al. Real-time in-vivo mu-imaging withMedipix2[J]. Nuclear Instruments and Methods in Physics Research A: AcceleratorsSpectrometers Detectors and Associated Equipment,2009,607(1):205-207.
[30] N. G. Anderson, A. Butler, N. Scott, et al. Spectroscopic (multi-energy) CT distinguishesiodine and barium contrast material in MICE[J]. European Radiology,20(9)(2010):2126-2134.
[31]郝佳,张丽,陈志强,等.多能谱X射线成像技术及其在CT中的应用[J]. CT理论与应用研究,2011,20(1):141-150.
[32] L. Tlustos, M. Campbell, E. Heijne, et al. Signal variations in high-granularity Si pixeldetectors[J]. IEEE Transaction on Nuclear Science,2004,51(6):3006-3012.
[33] G. Mettivier, M. C. Montesi and P. Russo. First images of a digital autoradiography systembased on a Medipix2hybrid silicon pixel detector[J]. Physics in Medicine and Biology,2003,48(12):173-181.
[34] L. Tlustos, R. Ballabriga, M. Campbell, et al. Imaging properties of the Medipix2systemexploiting single and dual energy thresholds[J]. IEEE Transaction on Nuclear Science,2005,53(1):367-372.
[35] P. Fischer, J.Hausmann, A. Helmich, et al. Counting pixel chip and sensor system for X-rayimaging[J]. IEEE Transactions on Nuclear Science,1999,46(4):1070-1074.
[36] T. Kubicki, K. Lubelsmeyer, J. Ortmanns, et al. Calculation of the electric field in GaAsparticle detectors[J]. Nuclear Instruments and Methods in Physics Research A,1994,345(3):468-473.
[37] J. W. Chen, T. Frommichen, J. Ludwig, et al. Evaluation of active layer properties and chargecollection efficiency of GaAs particle detectors[J]. Nuclear Instruments and Methods inPhysics Research A,1995,365(2-3):273-284.
[38] A. Cola, F. Quaranta, M. A. Ciocci, et al. Fantacci. A study of the electrical andcharge-collection properties of semi-insulating GaAs detectors[J]. Nuclear Instruments andMethods in Physics Research A: Accelerators, Spectrometers, Detectors and AssociatedEquipment,1996,380(1-2):66-69.
[39] R. Irsigler, J. Andersson, J. Alverbro, et al. X-ray imaging using a320×240hybrid gaas pixeldetector[J]. IEEE Transactions on Nuclear Science,1999,46(2-3):507-512.
[40] P. Fischer, J. Hausmann, M. Overdick, et al. A counting pixel readout chip for imagingapplications[J]. Nuclear Instruments and Methods in Physics Research A: Accelerators,Spectrometers, Detectors and Associated Equipment,1998,405(1):53-59.
[41] C. Schwarz, M. Campbell, R. Goeppert, et al. Measurements with Si and GaAs pixeldetectors bonded to photon counting readout chips[J]. Nuclear Instruments and Methods inPhysics Research A,2001,466:87-94.
[42] M. Lindner, P. Fischer, S. Florin, et al. Comparison of hybrid pixel detectors with Si andGaAs sensors[J]. Nuclear Instruments and Methods in Physics Research A,2001,466:63-73.
[43] H. Tajima, T. Kamae, G. Madejski, et al. Application of CdTe for the NeXT mission[J].Nuclear Instruments and Methods in Physics Research A,2005,541:332-341.
[44] G. Sato, A. Parsons, D. Hullinger, et al. Development of a spectral model based on chargetransport for the swift/BAT32K CdZnTe detector array[J]. Nuclear Instruments and Methodsin Physics Research A,2005,541:372-384.
[45] V. B. Cajipe, R. F. Calderwood, M. Clajus, et al. Multi-energy x-ray imaging with linear CZTpixel arrays and integrated electronics[J]. IEEE Nuclear Science Symposium ConferenceRecord,2004,7:4548-4551.
[46] P. M. Shikhaliev. Computed tomography with energy resolved detection: a feasibility study[J].Physics in Medicine and Biology,2008,53(5):1475-1495.
[47] P. M. Shikhaliev. Energy resolved computed tomography: first experimental results[J].Physics in Medicine and Biology,2008,53(20):5595-5613.
[48] P. M. Shikhaliev. Projection x-ray imaging with photon energy weighting: experimentalevaluation with a prototype detector[J]. Physics in Medicine and Biology,2008,54(16):4971-4992.
[49] J. P. Schlomka, E. Roessl, R. Dorscheid, et al. Experimental feasibility of multi-energyphoton-counting K-edge imaging in pre-clinical computed tomography[J]. Physics inMedicine and Biology,2008,53(15):4031–4047
[50] P. M. Shikhaliev and S. G. Fritz. Photon counting spectral CT versus conventional CT:comparative evaluation for breast imaging application[J]. Physics in Medicine and Biology,2011,56(7):1905-1930.
[51] M. Hurrell, A. Butler, N. Cook, et al. Spectral Hounsfield units: a new radiological concept[J].European Radiology,2012,22(5):1008-1013.
[52] R. Carmi, A. Livne, A. Gringauz, et al. Experimental Evaluation of Image-Based SpectralAnalysis Method for Multi Energy Window Photon Counting X-Ray CT[J]. IEEE NuclearScience Symposium and Medical Imaging Conference,2009,1-9:3178-3180.
[53] S. Gleason, H. Sari-Sarraf, M. Paulus, et al. Reconstruction of multi-energy x-ray computedtomography images of laboratory mice[J]. IEEE Transactions on Nuclear Science,1999,46(4):1081-1086.
[54] E. Roessl and R. Proksa. K-edge imaging in x-ray computed tomography using multi-binphoton counting detectors[J]. Physics in Medicine and Biology,2007,52(15):4679-4696.
[55] P. He, H. Yu, P. Thayer, X. Jin, Q. Xu, J. Bennett, R. Tappenden, B. Wei, A. Goldstein, P.Renaud, A. Butler, P. Butler and G. Wang. Preliminary Experimental Results from a MARSMicro-CT System[J]. Journal of X-ray Science and Technology,2012,20,199-211.
[56] R. Gordon, R. Bender and G.T. Herman. Algebraic reconstruction techniques (ART) forthree-dimensional electron microscopy and x-ray photography[J]. Journal of TheoreticalBiology,1970,29(3):471-482.
[57] A.H. Andersen and A. C. Kak. Simultaneous Algebraic Reconstruction Technique (SART): asuperior implementation of the ART algorithm[J]. Ultrasonic Imaging,1984,6(1):81-94.
[58] G. Wang and M. Jiang. Ordered-Subset Simultaneous Algebraic Reconstruction Techniques(OS-SART)[J]. Journal of X-ray Science and Technology,2004,12(3):169-177.
[59] M. Jiang and G. Wang. Convergence studies on iterative algorithms for imagereconstruction[J]. IEEE Transaction on Medical Imaging,2003,22(5):569-579.
[60] D. L. Donoho. Compressed sensing[J]. IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[61] E. J. Candes, J. Romberg and T. Tao. Robust uncertainty principles: exact signalreconstruction from highly incomplete frequency information[J]. IEEE Transactions onInformation Theory,2006,52(2):489-509.
[62] G. Wang, H. Yu and B. DeMan. An outlook on x-ray CT research and development[J].Medical Physics,2008,35(3):1051-1064.
[63] G. H. Chen, J. Tang and S. Leng. Prior image constrained compressed sensing (PICCS): Amethod to accurately reconstruct dynamic CT images from highly undersampled projectiondatasets[J]. Medical Physics,2008,35(2):660-663.
[64] H. Yu and G. Wang. Compressed sensing based interior tomography[J]. Physics in Medicineand Biology,2009,54(9):2791-2805.
[65] E. Y. Sidky, C. M. Kao and X. Pan. Accurate image reconstruction from few-views andlimited-angle data in divergent-beam CT[J]. Journal of X-ray Science and Technology,2006,14:119-139.
[66] Y. Ye, H. Yu, Y. Wei, et al. A general local reconstruction approach based on a truncatedHilbert transform[J]. International journal of biomedical imaging,2007:1-8.
[67] H. Kudo, M. Courdurier, F. Noo, et al. Tiny a priori knowledge solves the interior problem incomputed tomography[J]. Physics in Medicine and Biology,2008,53:2207-2231.
[68] M. Courdurier, F. Noo, M. Defrise, et al. Solving the interior problem of computedtomography using a priori knowledge[J]. Inverse Problems,2008,24,065001.
[69] H. Yu and G. Wang, A soft-threshold filtering approach for reconstruction from a limitednumber of projections[J]. Physics in Medicine and Biology,2010,55(13):3905-3916.
[70] J.S. Yang, H. Yu, M. Jiang, et al, High-order total variation minimization for interiortomography[J]. Inverse Problems,2010,26,035013.
[71] Q. Xu, X. Mou, G. Wang, et al. Statistical Interior Tomography[J]. IEEE Transactions onMedical Imaging,2011,30(5):1116-1128.
[72] E. C. Frey, X. Wang, Y. Du, et al. Investigation of the use of Photon Counting X-RayDetectors with Energy Discrimination Capability for Material Decomposition inMicro-Computed Tomography[J]. Physics of Medical Imaging,2007,6510:93-103.
[73] S. J. Nik，J. Meyer and R. Watts. Optimal material discrimination using spectral x-rayimaging[J]. Physics in Medicine and Biology,2011,56(18):5969-5983.
[74] B. Norlin, A. Manuilskiy, H. Nilsson, et al. Material recognition with the Medipix photoncounting colour X-ray system[J]. Nuclear Instruments and Methods in Physics Research A,2004,531(1-2):265-269.
[75] H. Le and S. Molloi. Least squares parameter estimation methods for material decompositionwith energy discriminating detectors[J]. Medical Physics,2010,38:245-55.
[76] M. Firsching, D. Niederlohner, T. Michel, et al. Quantitative material reconstruction in CTwith spectroscopic x-ray pixel detectors—a simulation study[J]. IEEE Nuclear ScienceSymposium Conference Record,2006,4:2257-2259.
[77] L. A. Lehmann, R. E. Alvarez, A. Macovski, et al. Generalized image combinations in dualKVP digital radiography[J]. Medical Physics,1981,8(5):659-667.
[78] W. H. Marshall, R. E. Alvarez and A. Macovski. Initial results with prereconstructiondual-energy computed tomography (PREDECT)[J]. Radiology,1981,140(2):421-430.
[79] J. P. Stonestrom, R. E. Alvarez and A. Macovski. A framework for spectral artifact correctionsin x-ray CT[J]. IEEE Transactions on Biomedical Engineering,1981,28(2):128-41.
[80] R. A. Brooks. A quantitative theory of the Hounsfield unit and its application to dual energyscanning[J]. Journal of Computer Assisted Tomography,1977,1(4):487-93.
[81] H. J. Vinegar and S. L. Wellington. Method of Imaging the Atomic Number of a Sample.1986,US Patent4571491.
[82] G. Christ. Exact treatment of the dual-energy method in CT using polyenergetic X-rayspectra[J]. Physics in Medicine and Biology,1984,29(12):1501-1510.
[83] D. J. Drost and A. Fenster. Experimental dual xenon detectors for quantitative CT and spectralartifact correction[J]. Medical Physics,1980,7(2):101-107.
[84] M. van Straten, M. Schaap, M. L. Dijkshoorn, et al. Automated bone removal in CTangiography: Comparison of methods based on single energy and dual energy scans[J].Medical Physics,2011,38(11):6128-6137.
[85] B. M. Yeh, J. A. Shepherd, Z. J. Wang, et al. Dual-energy and low-kVp CT in the abdomen[J].American Journal of Roentgenology,2009,193(1):47-54.
[86] D. N. Tran, M. Straka, J. E. Roos, et al. Dual-energy CT discrimination of iodine and calcium:Experimental results and implications for lower extremity CT angiography[J]. AcademicRadiology,2009,16(2):160-171.
[87] I. T. Jolliffe. Principal Components Analysis[M]. New York: Springer-Verlag,1986.
[88] H. Hotelling. Analysis of a complex of statistical variables into principal components[J].Journal of Educational Psychology,1933,24:417-441and498-520.
[89] L. Sirovich and M. Kirby. Low-dimensional procedure for the characterization of humanfaces[J]. Journal of the Optical Society of America A,1987,4(3):519-524.
[90] A. R. Kalukin, M.Van Geet and R. Swennen, Principal components analysis of multienergyx-ray computed tomography of mineral samples[J]. IEEE Transaction on Nuclear Science,2000,47(5):1729-1736.
[91] A. P. Butler, J. Butzer, N. Schleich, et al, Processing of spectral X-ray data with principalcomponents analysis[J]. Nuclear Instruments and Methods in Physics Research A,2011,633(1):140-142.
[92] J.S. Butzer, A. P. Butler, P. H. Butler, et al. Medipix imaging—evaluation of datasets withPCA[J]. Proceedings of the23rd International Conference on Image and Vision ComputingNew Zealand,2008:1-6.
[93] S. Feuerlein, E. Roessl, R. Proksa, et al. Multienergy Photon-counting K-edge Imaging:Potential for Improved Luminal Depiction in Vascular Imaging[J]. Radiology,2008,249(3):1010-1016.
[94] P. He, B. Wei, W.X. Cong and G. Wang, Optimization of K-edge Imaging with Spectral CT[J].Medical Physics,2012,39(11):6572-6579.
[95] E. Roessl, B. Brendel, K. J. Engel, et al. Sensitivity of Photon-Counting Based K-edgeImaging in X-ray Computed Tomography[J]. IEEE Transactions on Medical Imaging,2011,30(9):1678-1690.
[96] A. Abudurexiti, M. Kameda, E. Sato, et al. Demonstration of iodine K-edge imaging by use ofan energy-discrimination X-ray computed tomography system with a cadmium telluridedetector[J]. Radiological physics and technology,2010,3(2):127-135.
[97]何鹏,魏彪,冯鹏,等. Color-CT技术研究简述[J].2012年全国射线数字成像与CT新技术研讨会论文集,2012,07.
[98]郝佳,张丽,陈志强,等.彩色X射线成像技术新进展[J].中国体视学与图像分析,2011,16(2):203-208
[99]陈克敏,林晓珠. CT能谱成像临床应用与研究价值及展望[J].现代实用医学,2011,23(8):841-844.
[100]李小虎,刘斌,余永强,等.能谱CT的基本原理与临床应用[J].中国医疗器械信息,2011,10:1-5.
[101]孙丛,柳澄,王锡明,等.双能CT成像在显示膝关节韧带中的价值[J].中国医学影像技术,2008,24(9):1323-1325.
[102]邓凯,张成琪,李伟,等.宝石能谱CT的特点及临床应用价值[J].中国医药导报,2011,25(8):16-17.
[103]汤昕烨,张丽,陈志强,等.双能DR物质识别算法在CT成像系统中的应用[J].中国体视学与图像分析,2007,12(2):88-92.
[104]郝佳,张丽,邢宇翔,等.双能量CT技术在电子密度测量中的应用[J].核电子学与探测技术,2011，31(10):1082-1085.
[105]张岚,李元景,郑晓翠,等.线阵计数型多能CZT成像系统的性能研究[J].第十五届全国核电子学与核探测技术学术年会论文集，2010,08.
[106]李霞,褚君浩,李陇遐,等.室温核辐射CdZnTe像素阵列探测器的研制[J].光电子激光,2008,19(6):751-753.
[107]徐亚东,介万奇,查刚强,等. CZT平面探测器对低能X/γ射线的光谱响应[J].光学学报,2009,29(11):3072-3077.
[108]王玺,肖沙里,张流强,等.基于CdZnTe晶体的2×2像素阵列探测器研究[J].光电子激光,2010,21(5):639-643.
[109]陈平,潘晋孝,刘宾.连续能谱X-CT投影仿真算法[J].无损检测,2009,31(2):102-104.
[110]蔡彪,潘晋孝,陈平.基于连续X射线谱的CT重建算法仿真[J].计算机仿真,2011,28(4):257-260.
[111] P. He, H. Yu, J. Bennett, et al. Energy-discriminative performance analysis for spectral CT[J].Journal of X-Ray Science and Technology，to appear2013.
[112] MARS-CT Operations Manual.
[113] A. C. Kak and M. Slaney. Principles of Computerized tomographic Imaging[M]. IEEE Press,1998.
[114] J. Fessler. Mean and variance of implicitly defined biased estimators (such as penalizedmaximum likelihood): Applications to tomography[J]. IEEE Transactions on ImageProcessing,1996,5(3):493-506.
[115] E. DiBella, A. Barclay, R. Eisner, et al. A comparison of rotation-based methods for iterativereconstruction algorithms[J]. IEEE Transaction on Nuclear Science,1996,43(6):3370-3376.
[116] W. H. Rucgardson. Bayesian-based iterative method of image restoration[J]. Journal of theOptical Society of America A,1972,62:55-59.
[117] T. Hebert and R. Leahy. Statistic-based MAP image reconstruction from Poisson data usingGibbs priors[J]. IEEE Transaction on Signal Processing,1992,40(9):2290-2303.
[118] H. M. Hudson and R. S. Larkin. Accelerated image reconstruction using ordered subsets ofprojection data[J]. IEEE Transaction on Medical Imaging,1994,13(4):601-609.
[119] J. Browne and A.R. De Pierro. A row-action alternative to the EM algorithm for maximizinglikelihood in emission tomography[J]. IEEE Transaction on Medical Imaging,1996,15(5):687-699.
[120] D. S. Hwang and G. L. Zeng. Convergence study of an accelerated ML-EM algorithm usingbigger step size[J]. Physics in Medicine and Biology,2006,51(2):237-252.
[121] E. Candes and M. Wakin. An introduction to compressive sampling[J]. IEEE SignalProcessing Magazine,2008,25(2):21-30.
[122] E. Candes and J. Romberg. Quantitative robust uncertainty principles and optimally sparsedecompositions[J]. Foundations of Computational Mathematics,2006,6(2):227-254.
[123] http://www.nist.gov/pml/data/xraycoef/index.cfm.
[124] B. Liu, G. Wang, E. L. Ritman, et al. Image reconstruction from limited angle projectionscollected by multisource interior x-ray imaging systems[J]. Physics in Medicine and Biology,2011,56(19):6337-6357.
[125] C. Raven. Numerical removal of ring artifacts in microtomography[J]. Review of ScientificInstruments,1998,69(8):2978-2980.
[126] M. F. Kijewski and P. F. Judy. The noise power spectrum of CT images[J]. Physics inMedicine and Biology,1987,32(8):1049-1058.
[127] I. Cunningham, M. Westmore and A. Fenster. A spatial-frequency dependent quantumaccounting diagram and detective quantum efficiency model of signal and noise propagationin cascaded imaging systems[J]. Medical Physics,1994,21(3):417-427.
[128] M. J. Tapiovaara and R. F. Wagner. SNR and DQE analysis of broad spectrum x-rayimaging[J]. Physics in Medicine and Biology,1985,30(6):519-529.
[129] G. Wang and M. W. Vannier. Helical CT image noise-analytical results[J]. Medical Physics1993,20(6):1635-1640.
[130] E. Dizendorf, H. Hany, A. Buck, et al. Cause and magnitude of the error induced by oral CTcontrast agent in CT-based attenuation correction of PET emission studies[J]. Journal ofNuclear Medicine,2003,44(5):732-738.
[131] H. Gao, H. Yu, S. Osher, et al. Multi-energy CT based on a prior rank, intensity and sparsitymodel (PRISM)[J]. Inverse Problems,2011,27(11).11502.
[132] M. Depypere, J. Nuyts, N. Gastel, et al. An iterative dual energy CT reconstruction methodfor a K-edge contrast material[J]. Proceedings of SPIE,2011,7916,79610M.
[133] E. Sato, Y. Oda, A. Abudurexiti, et al. Demonstration of enhanced iodine K-edge imagingusing an energy-dispersive X-ray computed tomography system with a25mm/s-scan linearcadmium telluride detector and a single comparator[J]. Applied Radiation and Isotopes,2012,70(5):831–836.
[134] D. S. Gierada and K. T. Bae. Gadolinium as a CT contrast agent: Assessment in a porcinemodel[J]. Radiology,1999,210(3):829-834.
[135] http://www.imp.uni-erlangen.de/forbild.