常规X光源光栅成像相关方法和技术研究
|
摘要
常规X光源光栅成像技术是当前X射线成像领域里的最新前沿技术和研究热点之一,它在一次成像过程可以同时获得反映物质内部结构的衰减图像、相衬图像和暗场图像,形成“三位一体”的成像模式,即保持了传统X射线衰减成像的优点,又拥有相衬成像和暗场成像两者的优势,因此具有非常重要的科研价值和广阔的应用前景。
本论文依托清华大学工程物理系建立的国内第一套基于经典光学的光栅成像实验平台,深入开展了常规X光源光栅成像技术的建模方法、系统性能与优化设计,信息提取算法与CT重建算法等相关方法和技术研究,为常规X光源光栅成像技术的临床应用奠定坚实的理论基础和技术积累,使我国在该领域的前沿研究中占有一席之地。本论文的研究成果可概述如下:
第一,研究了基于经典光学的X射线光栅成像的建模方法和系统性能优化设计问题。首先,通过在Geant4中实现X射线折射效应来解决X射线相衬成像蒙特卡洛模拟问题,建立了X射线光栅成像蒙特卡洛模拟平台;然后,从多信息提取算法的误差公式、系统敏感度、成像几何条件约束三个方面分析系统性能和优化条件,确立X射线光栅成像系统优化设计方案。
第二,提出了X射线光栅暗场信息定量提取算法和基于三张图的多信息提取算法。首先,暗场信息定量提取算法建立了针对一般高斯散射体的位移曲线对比度退化与散射角分布二阶矩之间的定量关系,将光栅暗场成像中的CT重建问题纳入到传统衰减CT重建的框架中。其次,基于三张图的多信息提取算法解决了光栅成像中快速信息提取问题,在保证图像质量前提下尽可能减少辐射剂量和采集时间。
第三,提出了针对一阶相移信息的少量投影数据DART-CS迭代重建算法。首先,根据一阶相移信息的投影过程的特殊性推导了线性偏导数矩阵,并以此提出了基于ART形式的DART迭代重建算法;然后,以DART为基础,结合Compressed Sensing理论提出了少量投影数据DART-CS迭代重建算法,实现了低剂量条件下从少量折射角投影数据迭代精确重建物体折射率三维空间分布。
Grating-based X-ray imaging with conventional X-ray tube is one of the cutting-edge and hot research fields in X-ray imaging. It can retrieve three different kinds of information of the sample: absorption, refraction and dark-field, from one single scanning. It maintains the advantages of conventional X-ray absorption imaging, and also has the advantages of phase contrast imaging and dark-field imaging, thus it has important research value and a promsing future for practical applications.
Based on the classical-optical grating-based imaging system at the department of Engineering Physics, Tsinghua University, this dissertation investigates several key problems such as the system modeling,analysis and optimization, information retrieving algorithms and imaging reconstruction algorithms. The research in this dissertation makes solid theoretical foundation and technical accumulation for the clinical applications of garting-based imaging and takes our country to the forefront of this area. A series of research results were achieved:
Firstly, the system modeling, performance analysis and design method of the classical-optical grating-based imaging method are investigated. A Monte Carlo simulation platform is built by implementing X-ray refraction process in Geant4. And from the three aspects of the error formula of information retrieving algorithm, the system sensitivity and the system geometric constraints, the optimized system design method is given.
Secondly, a quantitative dark-field information retrieving algorithm and a multiple information retrieving algorithm based on three images are proposed. In the quantitative dark-field information retrieving algorithm, the relationship between the visibility degradation in grating-based dark-field imaging and the general scattering parameter of the sample is deduced. An important conclusion is that, the reconstruction problem of grating-based dark-field computed tomography (CT) can be solved by conventional reconstruction algorithm in absorption CT. The multiple information retrieving algorithm based on three images can reduce the imaging time consuming and the dose delivered to patients in grating-based imaging, while maintain the image quality.
Thirdly, an iterative reconstruction algorithm (DART-CS) which benefits from the Compressed Sensing (CS) theory is proposed for differential phase contrast imaging (DPCI). By discretizing the projection process of DPCI into a linear partial derivative matrix, a differential algebraic reconstruction algorithm (DART) is proposed which can reconstruct the refractive index distribution of the sample from the refraction angle projections directly. Based on DART algorithm, the DART-CS algorithm is proposed by introducing the CS theory into the reconstruction of DPCI. It can accurately reconstruct the refractive index with incomplete projection data in low dose situation.
本论文依托清华大学工程物理系建立的国内第一套基于经典光学的光栅成像实验平台,深入开展了常规X光源光栅成像技术的建模方法、系统性能与优化设计,信息提取算法与CT重建算法等相关方法和技术研究,为常规X光源光栅成像技术的临床应用奠定坚实的理论基础和技术积累,使我国在该领域的前沿研究中占有一席之地。本论文的研究成果可概述如下:
第一,研究了基于经典光学的X射线光栅成像的建模方法和系统性能优化设计问题。首先,通过在Geant4中实现X射线折射效应来解决X射线相衬成像蒙特卡洛模拟问题,建立了X射线光栅成像蒙特卡洛模拟平台;然后,从多信息提取算法的误差公式、系统敏感度、成像几何条件约束三个方面分析系统性能和优化条件,确立X射线光栅成像系统优化设计方案。
第二,提出了X射线光栅暗场信息定量提取算法和基于三张图的多信息提取算法。首先,暗场信息定量提取算法建立了针对一般高斯散射体的位移曲线对比度退化与散射角分布二阶矩之间的定量关系,将光栅暗场成像中的CT重建问题纳入到传统衰减CT重建的框架中。其次,基于三张图的多信息提取算法解决了光栅成像中快速信息提取问题,在保证图像质量前提下尽可能减少辐射剂量和采集时间。
第三,提出了针对一阶相移信息的少量投影数据DART-CS迭代重建算法。首先,根据一阶相移信息的投影过程的特殊性推导了线性偏导数矩阵,并以此提出了基于ART形式的DART迭代重建算法;然后,以DART为基础,结合Compressed Sensing理论提出了少量投影数据DART-CS迭代重建算法,实现了低剂量条件下从少量折射角投影数据迭代精确重建物体折射率三维空间分布。
Grating-based X-ray imaging with conventional X-ray tube is one of the cutting-edge and hot research fields in X-ray imaging. It can retrieve three different kinds of information of the sample: absorption, refraction and dark-field, from one single scanning. It maintains the advantages of conventional X-ray absorption imaging, and also has the advantages of phase contrast imaging and dark-field imaging, thus it has important research value and a promsing future for practical applications.
Based on the classical-optical grating-based imaging system at the department of Engineering Physics, Tsinghua University, this dissertation investigates several key problems such as the system modeling,analysis and optimization, information retrieving algorithms and imaging reconstruction algorithms. The research in this dissertation makes solid theoretical foundation and technical accumulation for the clinical applications of garting-based imaging and takes our country to the forefront of this area. A series of research results were achieved:
Firstly, the system modeling, performance analysis and design method of the classical-optical grating-based imaging method are investigated. A Monte Carlo simulation platform is built by implementing X-ray refraction process in Geant4. And from the three aspects of the error formula of information retrieving algorithm, the system sensitivity and the system geometric constraints, the optimized system design method is given.
Secondly, a quantitative dark-field information retrieving algorithm and a multiple information retrieving algorithm based on three images are proposed. In the quantitative dark-field information retrieving algorithm, the relationship between the visibility degradation in grating-based dark-field imaging and the general scattering parameter of the sample is deduced. An important conclusion is that, the reconstruction problem of grating-based dark-field computed tomography (CT) can be solved by conventional reconstruction algorithm in absorption CT. The multiple information retrieving algorithm based on three images can reduce the imaging time consuming and the dose delivered to patients in grating-based imaging, while maintain the image quality.
Thirdly, an iterative reconstruction algorithm (DART-CS) which benefits from the Compressed Sensing (CS) theory is proposed for differential phase contrast imaging (DPCI). By discretizing the projection process of DPCI into a linear partial derivative matrix, a differential algebraic reconstruction algorithm (DART) is proposed which can reconstruct the refractive index distribution of the sample from the refraction angle projections directly. Based on DART algorithm, the DART-CS algorithm is proposed by introducing the CS theory into the reconstruction of DPCI. It can accurately reconstruct the refractive index with incomplete projection data in low dose situation.
引文
[1] Pisano E D, Johnston R E, Chapman D, et al. Human breast cancer specimens: Diffraction-enhanced imaging with histologic correlation -- Improved conspicuity of lesion detail compared with digital radiography. Radiology, 2000, 214(3):895-901.
[2] Momose A. Recent advances in x-ray phase imaging. Japanese Journal of Applied Physics, 2005, 44(9A):6355.
[3] Momose A, Fukuda J. Phase-contrast radiographs of nonstained rat cerebellar specimen. Medical Physics, 1995, 22(4):375-379.
[4] Chapman D, Nesch I, Hasnah M O, et al. X-ray optics for emission line X-ray source diffraction enhanced systems. Nuclear Instruments and Methods in Physics Research Section A, 2006, 562(1):461-467.
[5] Momose A. Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer. Nuclear Instruments and Methods in Physics Research A, 1995, 352(3): 622-628.
[6] Beckmann F, Bonse U, Busch F, et al. X-ray microtomography ([mu] CT) using phase contrast for the investigation of organic matter. Journal of computer assisted tomography, 1997, 21(4):539.
[7] Snigirev A, Snigireva I, Kohn V, et al. On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation. Review of Scientific Instruments, 1995, 66(12):5486-5492.
[8] Wilkins S W, Gureyev T E, Gao D, et al. Phase-contrast imaging using polychromatic hard X-rays. Nature, 1996, 384(6607):335-338.
[9] Mayo S, Miller P, Wilkins S, et al. Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging. Journal of microscopy, 2002, 207(2):79-96.
[10] Davis T J, Gao D, Gureyev T E, et al. Phase-contrast imaging of weakly absorbing materials using hard X-rays. Nature, 1995, 373(6515):595-598.
[11] Chapman D, Thomlinson W, Johnston R E, et al. Diffraction enhanced x-ray imaging. Physics in Medicine and Biology, 1997, 42(11):2015-2025.
[12] Hirano K. Angle-resolved x-ray imaging using a resolution-tunable double-crystal analyser. Journal of Physics D: Applied Physics, 2003, 36(13):1469.
[13] Ingal V N, Beliaevskaya E A, Brianskaya A P, et al. Phase mammography - a new technique for breast investigation. Physics in Medicine and Biology, 1998, 43:2555-2567.
[14] Keyril?inen J, Fernández M, Suortti P. Refraction contrast in X-ray imaging. Nuclear Instruments and Methods in Physics Research Section A, 2002, 488(1-2):419-427.
[15] Vine D, Paganin D, Pavlov K, et al. Analyzer-based phase contrast imaging and phase retrieval using a rotating anode x-ray source. Applied Physics Letters, 2007, 91:254110.
[16] Murphy D B. Fundamentals of light microscopy and electronic imaging. Wiley-Liss, 2002.
[17] Suzuki Y, Uchida F. Dark-field imaging in hard x-ray scanning microscopy. Review of Scientific Instruments, 1995, 66:1468.
[18] Ando M, Hashimoto E, Hashizume H, et al. Clinical step onward with X-ray dark-field imaging and perspective view of medical applications of synchrotron radiation in Japan. Nuclear Instruments and Methods in Physics Research Section A, 2005, 548(1-2):1-16.
[19] Shimao D, Sugiyama H, Kunisada T, et al. Articular cartilage depicted at optimized angular position of Laue angular analyzer by X-ray dark-field imaging. Applied Radiation and Isotopes, 2006, 64(8):868-874.
[20] Ando M, Bando H, Chen Z, et al. 2D and 3D Refraction Based X-ray Imaging Suitable for Clinical and Pathological Diagnosis. AIP Conference Proceedings, 2007, 879: 1899-1902.
[21] Shimao D, Kunisada T, Sugiyama H, et al. Shift-and-add tomosynthesis of a finger joint by X-ray dark-field imaging: Difference due to tomographic angle. European Journal of Radiology, 2008, 68(3):S27-S31.
[22] Yin G C, Duewer F, Zeng X, et al. Dark-field image of full-field transmission hard x-ray microscope in 8-11 keV. Proceedings of SPIE. 2006, 6317:631703.
[23] Pfeiffer F, Bech M, Bunk O, et al. Hard-X-ray dark-field imaging using a grating interferometer. Nat Mater, 2008, 7(2):134-137.
[24] Talbot H. LXXVI. Facts relating to optical science. No. IV. Philosophical Magazine Series 3, 1836, 9(56):401-407.
[25] David C, Nohammer B, Solak H H, et al. Differential x-ray phase contrast imaging using a shearing interferometer. Applied Physics Letters, 2002, 81(17):3287-3289.
[26] Momose A, Kawamoto S, Koyama I, et al. Demonstration of X-ray Talbotinterferometry. Japanese Journal of Applied Physics, 2003, 42(7B):866-868.
[27] Takeda Y, Yashiro W, Suzuki Y, et al. X-Ray Phase Imaging with Single Phase Grating. Japanese Journal of Applied Physics, 2007, 46(3):L89-L91.
[28] Weitkamp T, Diaz A, David C, et al. X-ray phase imaging with a grating interferometer. Opt. Express, 2005, 13(16):6296-6304.
[29] Pfeiffer F., Bunk O, Schulze-Briese C, et al. Shearing interferometer for quantifying the coherence of hard X-ray beams. Physical review letters, 2005, 94(16):164801.
[30] Weitkamp T, Nohammer B, Diaz A, et al. X-ray wavefront analysis and optics characterization with a grating interferometer. Applied Physics Letters, 2005, 86(5): 054101-3.
[31] Momose A, Kawamot S. X-ray Talbot interferometry with capillary plates. Japanese Journal of Applied Physics, 2006, 45(1A):314-316.
[32] Jiang M, Wyatt C L, Wang Ge. X-Ray Phase-Contrast Imaging with Three 2D Gratings. International Journal of Biomedical Imaging, 2008, 2008:827152.
[33] Kottler C, David C, Pfeiffer F, et al. A two-directional approach for grating based differential phase contrast imaging using hard x-rays. Opt. Express, 2007, 15(3): 1175-1181.
[34] Pfeiffer F, Bunk O, David C, et al. Advances in the visualization of unstained brain tumors using grating-based x-ray phase-contrast tomography. Developments in X-Ray Tomography VI, San Diego, CA, USA, 2008, 707815-10.
[35] Pfeiffer F, Bunk O, David C, et al. High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography. Physics in Medicine and Biology, 2007, 52(23):6923-6930.
[36] Bech M., Bunk O, David C, et al. Hard X-ray phase-contrast imaging with the Compact Light Source based on inverse Compton X-rays. Journal of Synchrotron Radiation, 2009, 16:43-47.
[37] Pfeiffer F, Weitkamp T, Bunk O, et al. Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources. Nat Phys, 2006, 2(4):258-261.
[38] Nesterets Y I, Wilkins S W. Phase-contrast imaging using a scanning-double grating configuration. Opt. Express, 2008, 16(8):5849-5867.
[39] Kottler C, Pfeiffer F, Bunk O, et al. Phase contrast X-ray imaging of large samples using an incoherent laboratory source. Physica Status Solidi(a), 2007, 204(8):2728-2733.
[40] Donath T, Chabior M, Pfeiffer F, et al. Inverse geometry for grating-based x-ray phase-contrast imaging. Journal of Applied Physics, 2009, 106:054703.
[41] Kottler C, Pfeiffer F, Bunk O, et al. Grating interferometer based scanning setup for hard x-ray phase contrast imaging. Review of Scientific Instruments, 2007, 78:043710.
[42] Strobl M., Treimer W, Hilger A. Small angle scattering signals for (neutron) computerized tomography. Applied Physics Letters, 2004, 85(3):488-490.
[43] Grunzweig C, David C, Bunk O, et al. Neutron Decoherence Imaging for Visualizing Bulk Magnetic Domain Structures. Physical Review Letters, 2008, 101(2):025504-4.
[44] Strobl M, Grünzweig C, Hilger A, et al. Neutron Dark-Field Tomography. Physical Review Letters, 2008, 101(12):123902.
[45]黄万霞,田玉莲,朱佩平,等.北京同步辐射装置上的位相衬度成像.物理学报, 2002, 51(5):1040-1043.
[46]朱佩平,袁清习,黄万霞,等.衍射增强成像原理.物理学报, 2006, 55(3):1089-1098.
[47]肖体乔,徐洪杰,陈敏,等.一种新型X射线相衬成像实验室系统.核技术, 2003, 26(10):743-747.
[48] Liu X, Guo J C, Peng X, et al. Visibility in differential phase-contrast imaging with partial coherence source. Chinese Physics, 2007, 16(6):1632.
[49]尹红霞,刘波,高欣,等.基于同步辐射光源的DEI技术在豚鼠耳蜗成像中的应用.自然科学进展, 2006, 16(10):1230-1237.
[50]姜庆军,肖湘生,刘士远,等.相干X线相衬成像的初步研究:离体大白鼠肝脏、肺脏成像实验.中国医学影像技术, 2003, 19(9):1116-1117.
[51]陈志华,潘琳,黎刚,等.大鼠肾X线衍射增强成像.中国医学影像技术, 2005, 21(9):1345-1348.
[52] Ando M, Maksimenko A, Ichihara S, et al. X-ray System for Early Diagnosis of Breast Cancer. AIP Conference Proceedings. 2007, 902:37.
[53] Wang Z T, Huang Z F, Zhang L, et al. Fast X-Ray Phase-Contrast Imaging Using High Resolution Detector. IEEE Transactions on Nuclear Science, 2009, 56(3):1383-1388.
[54] Huang Z F, Kang K J, Zhang L, et al. Alternative method for differential phase-contrast imaging with weakly coherent hard x rays. Physical Review A 2009, 79(1):013815-6.
[55] Wang Z T, Huang Z F, Xiao Y S, et al. Multiple information tomosynthesis with grating-based phase contrast imaging. SPIE Medical Imaging 2009, Lake BuenaVista, FL, USA, 2009, 72581N-7.
[56] Chapman D., Pisanob E, Thomlinsonc W, et al. Medical applications of diffraction enhanced imaging. Breast disease, 1998, 10(3):197-207.
[57] Arfelli F, Rigon L, Menk R H, et al. On the possibility of utilizing scattering-based contrast agents in combination with diffraction-enhanced imaging. SPIE Medical Imaging 2003, San Diego, CA, USA, 2003, 274-283.
[58] Lewis R, Rogers K, Hall C, et al. Breast cancer diagnosis using scattered X-rays. Journal of synchrotron radiation, 2000, 7(5):348-352.
[59] Changizi V, Oghabian M A, Speller R, et al. Application of small angle X-ray scattering (SAXS) for differentiation between normal and cancerous breast tissue. International journal of medical sciences, 2005, 2(3):118.
[60] Fernández M, Suhonen H, Keyril?inen et al. USAXS and SAXS from cancer-bearing breast tissue samples. European Journal of Radiology, 2008, 68(3, Supplement 1):S89-S94.
[61] http://www.xrt.com.au/
[62] http://www.konicaminolta.eu/healthcare/technology/phase-contrast.html.
[63] Bragg W. X-rays and Crystals. Nature, 1912, 90(2243):219.
[64] Cullity B D, Stock S R. Elements of X-ray Diffraction. Addison-Wesley Reading,1978.
[65] Authier A. Dynamical theory of X-ray diffraction. Oxford University Press, USA, 2001.
[66] Michette A G, Buckley C J. X-ray Science and Technology. Institute of Physics Publishing, 1993.
[67] Ebel H. Quantification of the monochromatic photon flux of refractive x-ray monochromators in the energy range from 10 to 30 keV. X-Ray Spectrometry, 2002, 31(5):368-372.
[68] Als-Nielsen J, McMorrow D. Elements of modern X-ray physics. Wiley Chichester, 2001.
[69] Rigon L, Arfelli F, Menk R H. Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects. Journal of Physics D: Applied Physics, 2007, 40(10):3077-3089.
[70] Rigon L, Arfelli F, Menk R H. Three-image diffraction enhanced imaging algorithm to extract absorption, refraction, and ultra small-angle scattering. Applied Physics Letters, 2007, 90(11):114102-3.
[71] Glatter O, Kratky O. Small angle X-ray scattering. Academic Press London, 1982.
[72] Stribeck N. X-ray scattering of soft matter. New York :Springer Heidelberg, 2007.
[73] Takeda M, Ina H, Kobayashi S. Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry. J. Opt. Soc. Am., 1982, 72(1):156.
[74] Kafri O, Glatt I. The physics of moirémetrology. Wiley-Interscience, 1990.
[75] Momose A, Kawamoto S, Koyama I. Phase tomography using an x-ray Talbot interferometer. Developments in X-Ray Tomography IV, Denver, CO, USA, 2004, 352-360.
[76] Berry M V, Klein S, Integer, fractional and fractal Talbot effects. 1996, 43:2139-2164.
[77] Yokozeki S, Suzuki T. Shearing interferometer using the grating as the beam splitter. Applied optics, 1971, 10(7):1575-1580.
[78] Nakano Y, Murata K. Measurements of phase objects using the Talbot effect and moirétechniques. Applied optics, 1984, 23(14):2296-2299.
[79] Matsumoto M., Takiguchi K, Tanaka M, et al. Fabrication of diffraction grating for X-ray Talbot interferometer. Microsystem Technologies, 2007, 13(5):543-546.
[80] David C, Bruder J, Rohbeck T, et al Fabrication of diffraction gratings for hard X-ray phase contrast imaging. Microelectronic Engineering, 2007, 84(5-8):1172-1177.
[81] Noda D, Tanaka M, Shimada K, et al. Fabrication of diffraction grating with high aspect ratio using X-ray lithography technique for X-ray phase imaging. Japanese Journal of Applied Physics, 2007, 46(2):849-851.
[82] Teng S, Liu L, Zu J, et al. Uniform theory of the Talbot effect with partially coherent light illumination. Journal of the Optical Society of America A, 2003, 20(9):1747-1754.
[83] Swanson G J, Leith E N. Lau effect and grating imaging. J. Opt. Soc. Am., 1982, 72(5):552-555.
[84] Sudol R, Thompson B. Lau effect: theory and experiment. Applied Optics, 1981, 20(6):1107-1116.
[85] Liu L. Partially coherent diffraction effect between Lau and Talbot effects. J. Opt. Soc. Am. A, 1988, 5(10):1709-1716.
[86] Koo B, Jiang M, Wyatt C L, et al. Parameter optimization for a grating-based phase contrast x-ray system. SPIE Medical Imaging 2008, San Diego, CA, USA, 2008, 691348-9.
[87] Weitkamp T, Diaz A, Nohammer B, et al. Hard x-ray phase imaging and tomography with a grating interferometer. Developments in X-Ray Tomography IV, Denver, CO, USA, 2004, 137-142.
[88] Born M, Wolf E. Principles of Optics. Oxford:Pergamon Press, 1980.
[89] Kafri O. Noncoherent method for mapping phase objects. Opt. Lett., 1980, 5(12):555.
[90] Kafri O, Livnat A, Keren E. Infinite fringe moire deflectometry. Appl. Opt., 1982, 21(21):3884-3886.
[91] Keren E, Kafri O. Diffraction effects in moire deflectometry. J. Opt. Soc. Am. A, 1985, 2(2):111-120.
[92] Krasinski J, Heller D F, Kafri O. Phase object microscopy using moire deflectometry. Appl. Opt., 1985, 24(18):3032-3036.
[93] Livnat A, Kafri O. Finite fringe shadow moire slope mapping of diffusive objects. Appl. Opt., 1983, 22(20):3232-3235.
[94] Keprt S J, Bartonek L. Moire deflectometry used for refractive index measurements. 15th Czech-Polish-Slovak Conference on Wave and Quantum Aspects of Contemporary Optics, 2007, 66090Z-11.
[95] Kafri O Margalit E. Double exposure moire deflectometry for removing noise. Appl. Opt., 1981, 20(14):2344-2345.
[96] Huang Z F, Kang K J, Zhang L, et al. Differential Phase-Contrast Imaging Experimental System Under the Incoherent Condition With Conventional X-Ray Tubes. IEEE Transactions on Nuclear Science,2009, 56(3):1438-1443.
[97] Huang Z F, Kang K J, Zhang L, et al. X-ray phase contrast computed tomographic elementary experiments under incoherent conditions. Nuclear Science Symposium Conference Record, 2008. NSS '08. IEEE, 2008, 593-596.
[98] Momose A, Yashiro W, Takeda Y, et al. Phase tomography by X-ray Talbot interferometry for biological imaging. Japanese Journal of Applied Physics, 2006, 45:5254-5262.
[99] Wang Z T, Kang K J, Huang Z F, et al. Quantitative grating-based x-ray dark-field computed tomography. Applied Physics Letters, 2009, 95(9):094105.
[100] Bruning J, Herriott D, Gallagher J, et al. Digital wavefront measuring interferometer for testing optical surfaces and lenses. Appl. Opt, 1974, 13:2693-2703.
[101] Stampanoni M, Groso A, Isenegger A, et al. Trends in synchrotron-based tomographic imaging: The SLS experience. Proc. of SPIE, 2006, 6318:63180M-1.
[102] McDonald S, Marone F, Hintermuller C, et al. Advanced phase-contrast imaging using a grating interferometer. Journal of Synchrotron Radiation, 2009, 16(4):562-572.
[103] Giersch J, Weidemann A, Anton G. ROSI--an object-oriented and parallel-computing Monte Carlo simulation for X-ray imaging. Nuclear Instruments and Methods in Physics Research Section A, 2003, 509(1-3):151-156.
[104] Agostinelli S, Allison J, Amako K, et al. G4--a simulation toolkit. Nuclear Instruments and Methods in Physics Research Section A, 2003, 506(3):250-303.
[105] Briesmeister J F. MCNP-A general Monte Carlo N-Particle transport code, version 4C. Los Alamos National Laboratory, LA-13709-M, 2000.
[106] Rigon L, Zhong Z, Arfelli F. Diffraction-enhanced imaging utilizing different crystal reflections at Elettra and NSLS. SPIE Medical Imaging 2002, San Diego, CA, USA, 2002, 255-266.
[107] Chauvie S, Guatelli S, Ivanchenko V, et al. Geant4 low energy electromagnetic physics. Nuclear Science Symposium Conference Record, 2004 IEEE, 2004, 3:1881-1885.
[108] Ferguson C. General purpose source particle module for Geant4 SPARSET. Technical Note, Uos-GSPM-Tech, 2000.
[109] Liu Y J, Zhu P P, Chen B, et al. Edge enhanced X-ray phase tomography. Nuclear Instruments and Methods in Physics Research Section A, 2007, 580(1):617-620.
[110] Yashiro W, Takeda Y, Momose A. Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry. J. Opt. Soc. Am. A, 2008, 25(8):2025-2039.
[111] Khelashvili G, Brankov J G, Chapman D, et al. A physical model of multiple-image radiography. Physics in Medicine and Biology, 2006, 51(2):221-236.
[112] Brankov J G, Khelashvili G, Chapman D, et al. Physical model of image formation in multiple-image radiography. Nuclear Science Symposium Conference Record, 2005 IEEE, 2005, 2320-2322.
[113] Momose A, Yashiro W, Moritake M, et al. Biomedical imaging by Talbot-type x-ray phase tomography. Developments in X-Ray Tomography V, San Diego, CA, USA, 2006, 63180T-10.
[114] Malacara D, Servín M, Malacara Z, Interferogram analysis for optical testing. CRC, 2005.
[115] Kak A C, Slaney M. Principles of Computerized Tomographic Imaging. New York: IEEE Press, 1988.
[116] Lange K, Carson R. EM reconstruction algorithms for emission and transmission tomography. J. Comput. Assist. Tomogr. , 1984, 8:306-316.
[117] Candes E J, Romberg K, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 2006, 52(2):489-509.
[118]Donoho D. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4):1289-1306.
[119] Lustig M, Donoho D, Santos J M, et al. Compressed sensing MRI. IEEE Signal Processing Magazine, 2008, 25(2):72-82.
[120] Gamper U, Boesiger P, Kozerke S. Compressed sensing in dynamic MRI. Magnetic Resonance in Medicine, 2008, 59(2):365-373.
[121] Sidky E Y, Kao C M, Pan X. Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT. Journal of X-Ray Science and Technology, 2006, 14(2):119-139.
[122]Chen G H, Tang J, Leng S. Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets. Medical Physics, 2008, 35(2):660-663.
[123] Pavlov K, Kewish C, Davis J. A variant on the geometrical optics approximation in diffraction enhanced tomography. Journal of physics D: Applied physics,2001, 34(10; SPI/A):168-172.
[124] Zhu P P, Wang J Y, Yuan Q X, et al. Computed tomography algorithm based on diffraction-enhanced imaging setup. Applied Physics Letters, 2005, 87(26):264101-3.
[125] Maksimenko A, Ando M, Hiroshi S, et al. Computed tomographic reconstruction based on x-ray refraction contrast. Applied Physics Letters, 2005, 86:124105.
[126] Wang Z T, Zhang L, Huang Z F, et al. An ART iterative reconstruction algorithm for computed tomography of diraction enhanced imaging. CPC(HEP & NP), 2009, 33(11): 975-980, 2009.
[127] Huang Z F, Kang K J, Zhang L, et al. Direct computed tomographic reconstruction for directional-derivative projections of computed tomography of diffraction enhanced imaging. Applied Physics Letters, 2006, 89(4):041124-3.
[128] Pfeiffer F, Kottler C, Bunk O, et al. Hard X-Ray Phase Tomography with Low-Brilliance Sources. Physical Review Letters, 2007, 98(10):108105.
[129] Chen G H, Qi Z. Image reconstruction for fan-beam differential phase contrastcomputed tomography. Physics in Medicine and Biology, 2008, 53(4):1015-1025.
[130] Zhang L, Fang Q G Huang Z F. 3D reconstruction algorithm for cone-beam differential phase contrast computed tomography. Nuclear Science Symposium Conference Record, 2008. NSS '08. IEEE, 2008, 4193-4197.
[131] Qi Z, Chen G H. A local region of interest image reconstruction via filtered backprojection for fan-beam differential phase-contrast computed tomography. Physics in medicine and biology, 2007, 52:N417.
[132]方侨光,张丽,黄志峰,等.一阶相衬CT重建算法的最新进展. CT理论与应用研究, 2008, 17(4):23-31.
[133] Liu Y J, Zhu P P, Chen B, et al. A new iterative algorithm to reconstruct the refractive index. Physics in Medicine and Biology, 2007, 52(12):L5-L13.
[134] Gonzalez R C, Richard E. Digital image processing. Addison Wisley, 1992.
[2] Momose A. Recent advances in x-ray phase imaging. Japanese Journal of Applied Physics, 2005, 44(9A):6355.
[3] Momose A, Fukuda J. Phase-contrast radiographs of nonstained rat cerebellar specimen. Medical Physics, 1995, 22(4):375-379.
[4] Chapman D, Nesch I, Hasnah M O, et al. X-ray optics for emission line X-ray source diffraction enhanced systems. Nuclear Instruments and Methods in Physics Research Section A, 2006, 562(1):461-467.
[5] Momose A. Demonstration of phase-contrast X-ray computed tomography using an X-ray interferometer. Nuclear Instruments and Methods in Physics Research A, 1995, 352(3): 622-628.
[6] Beckmann F, Bonse U, Busch F, et al. X-ray microtomography ([mu] CT) using phase contrast for the investigation of organic matter. Journal of computer assisted tomography, 1997, 21(4):539.
[7] Snigirev A, Snigireva I, Kohn V, et al. On the possibilities of x-ray phase contrast microimaging by coherent high-energy synchrotron radiation. Review of Scientific Instruments, 1995, 66(12):5486-5492.
[8] Wilkins S W, Gureyev T E, Gao D, et al. Phase-contrast imaging using polychromatic hard X-rays. Nature, 1996, 384(6607):335-338.
[9] Mayo S, Miller P, Wilkins S, et al. Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging. Journal of microscopy, 2002, 207(2):79-96.
[10] Davis T J, Gao D, Gureyev T E, et al. Phase-contrast imaging of weakly absorbing materials using hard X-rays. Nature, 1995, 373(6515):595-598.
[11] Chapman D, Thomlinson W, Johnston R E, et al. Diffraction enhanced x-ray imaging. Physics in Medicine and Biology, 1997, 42(11):2015-2025.
[12] Hirano K. Angle-resolved x-ray imaging using a resolution-tunable double-crystal analyser. Journal of Physics D: Applied Physics, 2003, 36(13):1469.
[13] Ingal V N, Beliaevskaya E A, Brianskaya A P, et al. Phase mammography - a new technique for breast investigation. Physics in Medicine and Biology, 1998, 43:2555-2567.
[14] Keyril?inen J, Fernández M, Suortti P. Refraction contrast in X-ray imaging. Nuclear Instruments and Methods in Physics Research Section A, 2002, 488(1-2):419-427.
[15] Vine D, Paganin D, Pavlov K, et al. Analyzer-based phase contrast imaging and phase retrieval using a rotating anode x-ray source. Applied Physics Letters, 2007, 91:254110.
[16] Murphy D B. Fundamentals of light microscopy and electronic imaging. Wiley-Liss, 2002.
[17] Suzuki Y, Uchida F. Dark-field imaging in hard x-ray scanning microscopy. Review of Scientific Instruments, 1995, 66:1468.
[18] Ando M, Hashimoto E, Hashizume H, et al. Clinical step onward with X-ray dark-field imaging and perspective view of medical applications of synchrotron radiation in Japan. Nuclear Instruments and Methods in Physics Research Section A, 2005, 548(1-2):1-16.
[19] Shimao D, Sugiyama H, Kunisada T, et al. Articular cartilage depicted at optimized angular position of Laue angular analyzer by X-ray dark-field imaging. Applied Radiation and Isotopes, 2006, 64(8):868-874.
[20] Ando M, Bando H, Chen Z, et al. 2D and 3D Refraction Based X-ray Imaging Suitable for Clinical and Pathological Diagnosis. AIP Conference Proceedings, 2007, 879: 1899-1902.
[21] Shimao D, Kunisada T, Sugiyama H, et al. Shift-and-add tomosynthesis of a finger joint by X-ray dark-field imaging: Difference due to tomographic angle. European Journal of Radiology, 2008, 68(3):S27-S31.
[22] Yin G C, Duewer F, Zeng X, et al. Dark-field image of full-field transmission hard x-ray microscope in 8-11 keV. Proceedings of SPIE. 2006, 6317:631703.
[23] Pfeiffer F, Bech M, Bunk O, et al. Hard-X-ray dark-field imaging using a grating interferometer. Nat Mater, 2008, 7(2):134-137.
[24] Talbot H. LXXVI. Facts relating to optical science. No. IV. Philosophical Magazine Series 3, 1836, 9(56):401-407.
[25] David C, Nohammer B, Solak H H, et al. Differential x-ray phase contrast imaging using a shearing interferometer. Applied Physics Letters, 2002, 81(17):3287-3289.
[26] Momose A, Kawamoto S, Koyama I, et al. Demonstration of X-ray Talbotinterferometry. Japanese Journal of Applied Physics, 2003, 42(7B):866-868.
[27] Takeda Y, Yashiro W, Suzuki Y, et al. X-Ray Phase Imaging with Single Phase Grating. Japanese Journal of Applied Physics, 2007, 46(3):L89-L91.
[28] Weitkamp T, Diaz A, David C, et al. X-ray phase imaging with a grating interferometer. Opt. Express, 2005, 13(16):6296-6304.
[29] Pfeiffer F., Bunk O, Schulze-Briese C, et al. Shearing interferometer for quantifying the coherence of hard X-ray beams. Physical review letters, 2005, 94(16):164801.
[30] Weitkamp T, Nohammer B, Diaz A, et al. X-ray wavefront analysis and optics characterization with a grating interferometer. Applied Physics Letters, 2005, 86(5): 054101-3.
[31] Momose A, Kawamot S. X-ray Talbot interferometry with capillary plates. Japanese Journal of Applied Physics, 2006, 45(1A):314-316.
[32] Jiang M, Wyatt C L, Wang Ge. X-Ray Phase-Contrast Imaging with Three 2D Gratings. International Journal of Biomedical Imaging, 2008, 2008:827152.
[33] Kottler C, David C, Pfeiffer F, et al. A two-directional approach for grating based differential phase contrast imaging using hard x-rays. Opt. Express, 2007, 15(3): 1175-1181.
[34] Pfeiffer F, Bunk O, David C, et al. Advances in the visualization of unstained brain tumors using grating-based x-ray phase-contrast tomography. Developments in X-Ray Tomography VI, San Diego, CA, USA, 2008, 707815-10.
[35] Pfeiffer F, Bunk O, David C, et al. High-resolution brain tumor visualization using three-dimensional x-ray phase contrast tomography. Physics in Medicine and Biology, 2007, 52(23):6923-6930.
[36] Bech M., Bunk O, David C, et al. Hard X-ray phase-contrast imaging with the Compact Light Source based on inverse Compton X-rays. Journal of Synchrotron Radiation, 2009, 16:43-47.
[37] Pfeiffer F, Weitkamp T, Bunk O, et al. Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources. Nat Phys, 2006, 2(4):258-261.
[38] Nesterets Y I, Wilkins S W. Phase-contrast imaging using a scanning-double grating configuration. Opt. Express, 2008, 16(8):5849-5867.
[39] Kottler C, Pfeiffer F, Bunk O, et al. Phase contrast X-ray imaging of large samples using an incoherent laboratory source. Physica Status Solidi(a), 2007, 204(8):2728-2733.
[40] Donath T, Chabior M, Pfeiffer F, et al. Inverse geometry for grating-based x-ray phase-contrast imaging. Journal of Applied Physics, 2009, 106:054703.
[41] Kottler C, Pfeiffer F, Bunk O, et al. Grating interferometer based scanning setup for hard x-ray phase contrast imaging. Review of Scientific Instruments, 2007, 78:043710.
[42] Strobl M., Treimer W, Hilger A. Small angle scattering signals for (neutron) computerized tomography. Applied Physics Letters, 2004, 85(3):488-490.
[43] Grunzweig C, David C, Bunk O, et al. Neutron Decoherence Imaging for Visualizing Bulk Magnetic Domain Structures. Physical Review Letters, 2008, 101(2):025504-4.
[44] Strobl M, Grünzweig C, Hilger A, et al. Neutron Dark-Field Tomography. Physical Review Letters, 2008, 101(12):123902.
[45]黄万霞,田玉莲,朱佩平,等.北京同步辐射装置上的位相衬度成像.物理学报, 2002, 51(5):1040-1043.
[46]朱佩平,袁清习,黄万霞,等.衍射增强成像原理.物理学报, 2006, 55(3):1089-1098.
[47]肖体乔,徐洪杰,陈敏,等.一种新型X射线相衬成像实验室系统.核技术, 2003, 26(10):743-747.
[48] Liu X, Guo J C, Peng X, et al. Visibility in differential phase-contrast imaging with partial coherence source. Chinese Physics, 2007, 16(6):1632.
[49]尹红霞,刘波,高欣,等.基于同步辐射光源的DEI技术在豚鼠耳蜗成像中的应用.自然科学进展, 2006, 16(10):1230-1237.
[50]姜庆军,肖湘生,刘士远,等.相干X线相衬成像的初步研究:离体大白鼠肝脏、肺脏成像实验.中国医学影像技术, 2003, 19(9):1116-1117.
[51]陈志华,潘琳,黎刚,等.大鼠肾X线衍射增强成像.中国医学影像技术, 2005, 21(9):1345-1348.
[52] Ando M, Maksimenko A, Ichihara S, et al. X-ray System for Early Diagnosis of Breast Cancer. AIP Conference Proceedings. 2007, 902:37.
[53] Wang Z T, Huang Z F, Zhang L, et al. Fast X-Ray Phase-Contrast Imaging Using High Resolution Detector. IEEE Transactions on Nuclear Science, 2009, 56(3):1383-1388.
[54] Huang Z F, Kang K J, Zhang L, et al. Alternative method for differential phase-contrast imaging with weakly coherent hard x rays. Physical Review A 2009, 79(1):013815-6.
[55] Wang Z T, Huang Z F, Xiao Y S, et al. Multiple information tomosynthesis with grating-based phase contrast imaging. SPIE Medical Imaging 2009, Lake BuenaVista, FL, USA, 2009, 72581N-7.
[56] Chapman D., Pisanob E, Thomlinsonc W, et al. Medical applications of diffraction enhanced imaging. Breast disease, 1998, 10(3):197-207.
[57] Arfelli F, Rigon L, Menk R H, et al. On the possibility of utilizing scattering-based contrast agents in combination with diffraction-enhanced imaging. SPIE Medical Imaging 2003, San Diego, CA, USA, 2003, 274-283.
[58] Lewis R, Rogers K, Hall C, et al. Breast cancer diagnosis using scattered X-rays. Journal of synchrotron radiation, 2000, 7(5):348-352.
[59] Changizi V, Oghabian M A, Speller R, et al. Application of small angle X-ray scattering (SAXS) for differentiation between normal and cancerous breast tissue. International journal of medical sciences, 2005, 2(3):118.
[60] Fernández M, Suhonen H, Keyril?inen et al. USAXS and SAXS from cancer-bearing breast tissue samples. European Journal of Radiology, 2008, 68(3, Supplement 1):S89-S94.
[61] http://www.xrt.com.au/
[62] http://www.konicaminolta.eu/healthcare/technology/phase-contrast.html.
[63] Bragg W. X-rays and Crystals. Nature, 1912, 90(2243):219.
[64] Cullity B D, Stock S R. Elements of X-ray Diffraction. Addison-Wesley Reading,1978.
[65] Authier A. Dynamical theory of X-ray diffraction. Oxford University Press, USA, 2001.
[66] Michette A G, Buckley C J. X-ray Science and Technology. Institute of Physics Publishing, 1993.
[67] Ebel H. Quantification of the monochromatic photon flux of refractive x-ray monochromators in the energy range from 10 to 30 keV. X-Ray Spectrometry, 2002, 31(5):368-372.
[68] Als-Nielsen J, McMorrow D. Elements of modern X-ray physics. Wiley Chichester, 2001.
[69] Rigon L, Arfelli F, Menk R H. Generalized diffraction enhanced imaging to retrieve absorption, refraction and scattering effects. Journal of Physics D: Applied Physics, 2007, 40(10):3077-3089.
[70] Rigon L, Arfelli F, Menk R H. Three-image diffraction enhanced imaging algorithm to extract absorption, refraction, and ultra small-angle scattering. Applied Physics Letters, 2007, 90(11):114102-3.
[71] Glatter O, Kratky O. Small angle X-ray scattering. Academic Press London, 1982.
[72] Stribeck N. X-ray scattering of soft matter. New York :Springer Heidelberg, 2007.
[73] Takeda M, Ina H, Kobayashi S. Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry. J. Opt. Soc. Am., 1982, 72(1):156.
[74] Kafri O, Glatt I. The physics of moirémetrology. Wiley-Interscience, 1990.
[75] Momose A, Kawamoto S, Koyama I. Phase tomography using an x-ray Talbot interferometer. Developments in X-Ray Tomography IV, Denver, CO, USA, 2004, 352-360.
[76] Berry M V, Klein S, Integer, fractional and fractal Talbot effects. 1996, 43:2139-2164.
[77] Yokozeki S, Suzuki T. Shearing interferometer using the grating as the beam splitter. Applied optics, 1971, 10(7):1575-1580.
[78] Nakano Y, Murata K. Measurements of phase objects using the Talbot effect and moirétechniques. Applied optics, 1984, 23(14):2296-2299.
[79] Matsumoto M., Takiguchi K, Tanaka M, et al. Fabrication of diffraction grating for X-ray Talbot interferometer. Microsystem Technologies, 2007, 13(5):543-546.
[80] David C, Bruder J, Rohbeck T, et al Fabrication of diffraction gratings for hard X-ray phase contrast imaging. Microelectronic Engineering, 2007, 84(5-8):1172-1177.
[81] Noda D, Tanaka M, Shimada K, et al. Fabrication of diffraction grating with high aspect ratio using X-ray lithography technique for X-ray phase imaging. Japanese Journal of Applied Physics, 2007, 46(2):849-851.
[82] Teng S, Liu L, Zu J, et al. Uniform theory of the Talbot effect with partially coherent light illumination. Journal of the Optical Society of America A, 2003, 20(9):1747-1754.
[83] Swanson G J, Leith E N. Lau effect and grating imaging. J. Opt. Soc. Am., 1982, 72(5):552-555.
[84] Sudol R, Thompson B. Lau effect: theory and experiment. Applied Optics, 1981, 20(6):1107-1116.
[85] Liu L. Partially coherent diffraction effect between Lau and Talbot effects. J. Opt. Soc. Am. A, 1988, 5(10):1709-1716.
[86] Koo B, Jiang M, Wyatt C L, et al. Parameter optimization for a grating-based phase contrast x-ray system. SPIE Medical Imaging 2008, San Diego, CA, USA, 2008, 691348-9.
[87] Weitkamp T, Diaz A, Nohammer B, et al. Hard x-ray phase imaging and tomography with a grating interferometer. Developments in X-Ray Tomography IV, Denver, CO, USA, 2004, 137-142.
[88] Born M, Wolf E. Principles of Optics. Oxford:Pergamon Press, 1980.
[89] Kafri O. Noncoherent method for mapping phase objects. Opt. Lett., 1980, 5(12):555.
[90] Kafri O, Livnat A, Keren E. Infinite fringe moire deflectometry. Appl. Opt., 1982, 21(21):3884-3886.
[91] Keren E, Kafri O. Diffraction effects in moire deflectometry. J. Opt. Soc. Am. A, 1985, 2(2):111-120.
[92] Krasinski J, Heller D F, Kafri O. Phase object microscopy using moire deflectometry. Appl. Opt., 1985, 24(18):3032-3036.
[93] Livnat A, Kafri O. Finite fringe shadow moire slope mapping of diffusive objects. Appl. Opt., 1983, 22(20):3232-3235.
[94] Keprt S J, Bartonek L. Moire deflectometry used for refractive index measurements. 15th Czech-Polish-Slovak Conference on Wave and Quantum Aspects of Contemporary Optics, 2007, 66090Z-11.
[95] Kafri O Margalit E. Double exposure moire deflectometry for removing noise. Appl. Opt., 1981, 20(14):2344-2345.
[96] Huang Z F, Kang K J, Zhang L, et al. Differential Phase-Contrast Imaging Experimental System Under the Incoherent Condition With Conventional X-Ray Tubes. IEEE Transactions on Nuclear Science,2009, 56(3):1438-1443.
[97] Huang Z F, Kang K J, Zhang L, et al. X-ray phase contrast computed tomographic elementary experiments under incoherent conditions. Nuclear Science Symposium Conference Record, 2008. NSS '08. IEEE, 2008, 593-596.
[98] Momose A, Yashiro W, Takeda Y, et al. Phase tomography by X-ray Talbot interferometry for biological imaging. Japanese Journal of Applied Physics, 2006, 45:5254-5262.
[99] Wang Z T, Kang K J, Huang Z F, et al. Quantitative grating-based x-ray dark-field computed tomography. Applied Physics Letters, 2009, 95(9):094105.
[100] Bruning J, Herriott D, Gallagher J, et al. Digital wavefront measuring interferometer for testing optical surfaces and lenses. Appl. Opt, 1974, 13:2693-2703.
[101] Stampanoni M, Groso A, Isenegger A, et al. Trends in synchrotron-based tomographic imaging: The SLS experience. Proc. of SPIE, 2006, 6318:63180M-1.
[102] McDonald S, Marone F, Hintermuller C, et al. Advanced phase-contrast imaging using a grating interferometer. Journal of Synchrotron Radiation, 2009, 16(4):562-572.
[103] Giersch J, Weidemann A, Anton G. ROSI--an object-oriented and parallel-computing Monte Carlo simulation for X-ray imaging. Nuclear Instruments and Methods in Physics Research Section A, 2003, 509(1-3):151-156.
[104] Agostinelli S, Allison J, Amako K, et al. G4--a simulation toolkit. Nuclear Instruments and Methods in Physics Research Section A, 2003, 506(3):250-303.
[105] Briesmeister J F. MCNP-A general Monte Carlo N-Particle transport code, version 4C. Los Alamos National Laboratory, LA-13709-M, 2000.
[106] Rigon L, Zhong Z, Arfelli F. Diffraction-enhanced imaging utilizing different crystal reflections at Elettra and NSLS. SPIE Medical Imaging 2002, San Diego, CA, USA, 2002, 255-266.
[107] Chauvie S, Guatelli S, Ivanchenko V, et al. Geant4 low energy electromagnetic physics. Nuclear Science Symposium Conference Record, 2004 IEEE, 2004, 3:1881-1885.
[108] Ferguson C. General purpose source particle module for Geant4 SPARSET. Technical Note, Uos-GSPM-Tech, 2000.
[109] Liu Y J, Zhu P P, Chen B, et al. Edge enhanced X-ray phase tomography. Nuclear Instruments and Methods in Physics Research Section A, 2007, 580(1):617-620.
[110] Yashiro W, Takeda Y, Momose A. Efficiency of capturing a phase image using cone-beam x-ray Talbot interferometry. J. Opt. Soc. Am. A, 2008, 25(8):2025-2039.
[111] Khelashvili G, Brankov J G, Chapman D, et al. A physical model of multiple-image radiography. Physics in Medicine and Biology, 2006, 51(2):221-236.
[112] Brankov J G, Khelashvili G, Chapman D, et al. Physical model of image formation in multiple-image radiography. Nuclear Science Symposium Conference Record, 2005 IEEE, 2005, 2320-2322.
[113] Momose A, Yashiro W, Moritake M, et al. Biomedical imaging by Talbot-type x-ray phase tomography. Developments in X-Ray Tomography V, San Diego, CA, USA, 2006, 63180T-10.
[114] Malacara D, Servín M, Malacara Z, Interferogram analysis for optical testing. CRC, 2005.
[115] Kak A C, Slaney M. Principles of Computerized Tomographic Imaging. New York: IEEE Press, 1988.
[116] Lange K, Carson R. EM reconstruction algorithms for emission and transmission tomography. J. Comput. Assist. Tomogr. , 1984, 8:306-316.
[117] Candes E J, Romberg K, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Transactions on Information Theory, 2006, 52(2):489-509.
[118]Donoho D. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4):1289-1306.
[119] Lustig M, Donoho D, Santos J M, et al. Compressed sensing MRI. IEEE Signal Processing Magazine, 2008, 25(2):72-82.
[120] Gamper U, Boesiger P, Kozerke S. Compressed sensing in dynamic MRI. Magnetic Resonance in Medicine, 2008, 59(2):365-373.
[121] Sidky E Y, Kao C M, Pan X. Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT. Journal of X-Ray Science and Technology, 2006, 14(2):119-139.
[122]Chen G H, Tang J, Leng S. Prior image constrained compressed sensing (PICCS): A method to accurately reconstruct dynamic CT images from highly undersampled projection data sets. Medical Physics, 2008, 35(2):660-663.
[123] Pavlov K, Kewish C, Davis J. A variant on the geometrical optics approximation in diffraction enhanced tomography. Journal of physics D: Applied physics,2001, 34(10; SPI/A):168-172.
[124] Zhu P P, Wang J Y, Yuan Q X, et al. Computed tomography algorithm based on diffraction-enhanced imaging setup. Applied Physics Letters, 2005, 87(26):264101-3.
[125] Maksimenko A, Ando M, Hiroshi S, et al. Computed tomographic reconstruction based on x-ray refraction contrast. Applied Physics Letters, 2005, 86:124105.
[126] Wang Z T, Zhang L, Huang Z F, et al. An ART iterative reconstruction algorithm for computed tomography of diraction enhanced imaging. CPC(HEP & NP), 2009, 33(11): 975-980, 2009.
[127] Huang Z F, Kang K J, Zhang L, et al. Direct computed tomographic reconstruction for directional-derivative projections of computed tomography of diffraction enhanced imaging. Applied Physics Letters, 2006, 89(4):041124-3.
[128] Pfeiffer F, Kottler C, Bunk O, et al. Hard X-Ray Phase Tomography with Low-Brilliance Sources. Physical Review Letters, 2007, 98(10):108105.
[129] Chen G H, Qi Z. Image reconstruction for fan-beam differential phase contrastcomputed tomography. Physics in Medicine and Biology, 2008, 53(4):1015-1025.
[130] Zhang L, Fang Q G Huang Z F. 3D reconstruction algorithm for cone-beam differential phase contrast computed tomography. Nuclear Science Symposium Conference Record, 2008. NSS '08. IEEE, 2008, 4193-4197.
[131] Qi Z, Chen G H. A local region of interest image reconstruction via filtered backprojection for fan-beam differential phase-contrast computed tomography. Physics in medicine and biology, 2007, 52:N417.
[132]方侨光,张丽,黄志峰,等.一阶相衬CT重建算法的最新进展. CT理论与应用研究, 2008, 17(4):23-31.
[133] Liu Y J, Zhu P P, Chen B, et al. A new iterative algorithm to reconstruct the refractive index. Physics in Medicine and Biology, 2007, 52(12):L5-L13.
[134] Gonzalez R C, Richard E. Digital image processing. Addison Wisley, 1992.