ERT图像重建算法研究及应用软件系统设计
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摘要
电阻层析成像(Electrical Resistance Tomography,简称ERT)技术是上个世纪80年代发展起来的一种高新检测技术,具有非侵入、响应速度快、成本低、安全性能好和可视化等优点,可实现对封闭管道或者过程容器设备内的多相流组分物质参数的可视化测量,具有广阔的应用前景。
图像重建过程是最终实现ERT技术可视化的过程,图像重建的速度和精度是ERT图像重建过程中的两个关键因素。本文从ERT技术的原理出发,对ERT技术的图像重建算法进行了认真的研究,提出了改进方案,并设计了ERT仿真软件包。
在本论文的研究中,作者主要完成了以下工作:
1.对于ERT技术的正问题,用有限元方法对其进行求解,提出了数据存储和场域剖分的优化办法,实现了对场域的剖分,并在剖分的基础上,对正问题进行求解。
2.对于ERT技术的逆问题,即图像重建,从两个方面进行了研究:非迭代图像重建算法和迭代图像重建算法。并分别提出了相应的图像重建算法:在非迭代图像重建算法中,提出了正则化图像重建算法,并提出了修正的正则化图像重建算法;在迭代图像重建算法中,提出了组合型图像重建算法。
3.提出了新的图像重建评价标准,即图像相对误差,对图像重建效果进行评价。
4.用C ++ Builder软件开发系统结合OpenGL开发工具,设计了ERT应用软件系统。该软件系统可以根据不同参数的设置情况,对正问题和逆问题进行分析。即通过设置不同的参数,对不同情况下的场域进行剖分,并对边界测量电压进行求解;通过选择不同的图像重建算法,实现图像重建;并对数据进行存储与显示。
Electrical Resistance Tomography (ERT) technique is a high-new detection technique that has been developed from the eighties last century, it can be applied to measure the material parameters of multi-phase flow in a closed pipe or a process device, and it has a good foreground.
Image reconstruction is the last step to realize visualization for ERT technique, and the reconstruction speed and the quality of the reconstructed images are two key factors. This paper is based on the principle of ERT technique, and carefully research has been made on image reconstruction algorithm, better reconstruction algorithms have been presented, and ERT simulation software kit has been designed.
The main contribution and works are as follow:
(1) For the forward problem of ERT, Finite Element Method is used to solve it. Data storage optimization method and field division optimization method are presented. The field is divided, and on the basic of the field division, the forward problem of ERT is solved.
(2) For the inverse problem of ERT, that is, image reconstruction, research is done from two aspects: non-iterative image reconstruction algorithm and iterative image reconstruction algorithm. For non-iterative image reconstruction algorithm, regularization image reconstruction algorithm is revised and revised regularization image reconstruction algorithm is presented; for iterative image reconstruction algorithm, combined image reconstruction algorithm is presented.
(3). A new evaluation standard for image reconstruction is presented, that is relative resistivity error to evaluate the image reconstruction effect.
(4). An ERT application software system is developed with C++ Builder software development system and OpenGL development tool. The software system can solve the forward problem and the inverse problem according to different given parameter. With different given parameters, the field can be divide differently, and the marginal voltage can be calculated; with different image reconstruction algorithms, the image can be reconstruction differently; and the data can be stored and displayed.
图像重建过程是最终实现ERT技术可视化的过程,图像重建的速度和精度是ERT图像重建过程中的两个关键因素。本文从ERT技术的原理出发,对ERT技术的图像重建算法进行了认真的研究,提出了改进方案,并设计了ERT仿真软件包。
在本论文的研究中,作者主要完成了以下工作:
1.对于ERT技术的正问题,用有限元方法对其进行求解,提出了数据存储和场域剖分的优化办法,实现了对场域的剖分,并在剖分的基础上,对正问题进行求解。
2.对于ERT技术的逆问题,即图像重建,从两个方面进行了研究:非迭代图像重建算法和迭代图像重建算法。并分别提出了相应的图像重建算法:在非迭代图像重建算法中,提出了正则化图像重建算法,并提出了修正的正则化图像重建算法;在迭代图像重建算法中,提出了组合型图像重建算法。
3.提出了新的图像重建评价标准,即图像相对误差,对图像重建效果进行评价。
4.用C ++ Builder软件开发系统结合OpenGL开发工具,设计了ERT应用软件系统。该软件系统可以根据不同参数的设置情况,对正问题和逆问题进行分析。即通过设置不同的参数,对不同情况下的场域进行剖分,并对边界测量电压进行求解;通过选择不同的图像重建算法,实现图像重建;并对数据进行存储与显示。
Electrical Resistance Tomography (ERT) technique is a high-new detection technique that has been developed from the eighties last century, it can be applied to measure the material parameters of multi-phase flow in a closed pipe or a process device, and it has a good foreground.
Image reconstruction is the last step to realize visualization for ERT technique, and the reconstruction speed and the quality of the reconstructed images are two key factors. This paper is based on the principle of ERT technique, and carefully research has been made on image reconstruction algorithm, better reconstruction algorithms have been presented, and ERT simulation software kit has been designed.
The main contribution and works are as follow:
(1) For the forward problem of ERT, Finite Element Method is used to solve it. Data storage optimization method and field division optimization method are presented. The field is divided, and on the basic of the field division, the forward problem of ERT is solved.
(2) For the inverse problem of ERT, that is, image reconstruction, research is done from two aspects: non-iterative image reconstruction algorithm and iterative image reconstruction algorithm. For non-iterative image reconstruction algorithm, regularization image reconstruction algorithm is revised and revised regularization image reconstruction algorithm is presented; for iterative image reconstruction algorithm, combined image reconstruction algorithm is presented.
(3). A new evaluation standard for image reconstruction is presented, that is relative resistivity error to evaluate the image reconstruction effect.
(4). An ERT application software system is developed with C++ Builder software development system and OpenGL development tool. The software system can solve the forward problem and the inverse problem according to different given parameter. With different given parameters, the field can be divide differently, and the marginal voltage can be calculated; with different image reconstruction algorithms, the image can be reconstruction differently; and the data can be stored and displayed.
引文
[1]徐苓安,过程层析成像技术的最新进展-记第一届世界工业过程层析成像技术会议,世界仪表与自动化,1999,3(5):34～37
[2]董峰,崔晓会,电阻层析成像技术的发展,仪器仪表学报,2003,24(2):23～27
[3]吴小平,汪彤彤,电阻率三维反演方法研究进展,地球物理学进展,2002,17(1):156～162
[4]任超世,生物电阻抗测量技术,中国医疗器械信息,2004,10(1):21～25
[5]Dickin F., Wang M., Electrical Resistance Tomography for Process Application, Measurement Science &Technology, 1996, 7(3):247～260
[6]Wang M, Dickin D J, Williams R A, Electrical resistance tomography of metal walled vessels and pipelines, 1994, 30(10):771～773
[7]Xu L A, Jiang Z C, Performance Analysis of the UMIST MK1b Electrical Impedance Tomography System, ECAPT’94, 1994. 114～119
[8]Cillierts J.J., Xie W. ,Neethling S.J., et al. , Electrical resistance tomography using a bi-directional current pulse technique, Measurement Science and Technology, 2001, l2(8) : 997～1001
[9]Primrose K, Qiu C, Performance and Application Studies of an Electrical Resistance Tomography System, 1st World Congress on Industrial Process Tomography, 1999, 133～139
[10]Y Ma, N Holliday, Y Dai et al., A High Performance Online Data Processing EIT System, 3rd World Congress on Industrial Process Tomography, Banff, Canada, 2003. 27～32
[11] Deng X, Dong F, Xu L J, et al., The design of a dual-plane ERT system for cross correlation measurement of bubbly gas/liquid pipe flow, Measurement Science and Technology 2001, 12(8):1024～1031
[12] Wang Wenhui, Dong Feng Xie Lipeng, The Study of ERT System Performance Improvement, The 4th International Symposium on Measurement Technique for Multiphase Flows, 2004, 632～635
[13]许燕斌,基于USB技术的电阻层析成像系统通讯方法的研究:[硕士学位论文],天津:天津大学,2003
[14]王保良,乐嘉华,黄志尧,多相流参数检测电容层析成像技术研究,石油化工自动化,1998,2(4):4～6
[15]申世安,是度芳,李春芳等,修改的联合代数迭代法及其再图像重建中的应用,量子电子学报,2001,18(6):481～484
[16]董峰,电阻层析成像技术在两相流测量中的应用:[博士学位论文],天津:天津大学,2002
[17]邵嘉庆,徐苓安,电阻层析成象系统的研究,自动化与仪表,1999,14(2):1～3
[18]Barber D C, Brown B H, Applied potential tomography, Journal Physics E: Science Instrument 1984, 17(9): 723～733
[19]Sastry, C.S., Das, P.C., A convolution back projection algorithm for local tomography, Australian & New Zealand Industrial and Applied Mathematics Journal, 2005, 46: 341～360
[20]Robert Guardo, Christian Boulary, Bruno Murray, et al., An Experimental Study in Electrical Impedance Tomography Using Backprojection Reconstruction, IEEE Transactions on Biomedical Engineering, 1991, 38(7):617~627
[21]马艺馨,电阻层析成像技术及其在气/液两相泡状流检测种的应用:[博士学位论文],天津:天津大学,1999
[22]Muller, N., Magaia, L., Herbst, B.M., Singular value decomposition, eigenfaces, and 3D reconstructions, SIAM Review, 2004, 46(3):518-545
[23]李睿凡,郭学彬,瞿安连,基于奇值分解的三维光学切片显微图像恢复算法研究,光学精密工程,2001,9 (3):212～215
[24]姜瑞忠,姚彦平,苗盛等,核磁共振T2谱奇异值分解反演改进算法,石油学报,2005,26(6):57～59
[25]王化祥,王超,陈磊,基于Landweber迭代的图像重建算法,信号处理, 2000,16(4): 354～356
[26]李英,黄志尧,等,两相流参数测量ERT图像重建算法的研究,浙江大学学报(工学版),2003,37(4): 382～385
[27]Wang Chao, Wang Huaxiang, Modified Landweber algorithm for solving the inverse problem in EIT, Chinese Journal of Electronics, 2005, 14 (1): 96～98
[28]Yang Gang, Wang Yu-Tao, Shao Fu-Qun, et al, Preconditioning Landweber iterative method for ECT image reconstruction, Dongbei Daxue Xuebao/Journal of Northeastern University, 2006, 27(9): 953～956
[29]王化祥,朱学明,张立峰,用于电容层析成像技术的共轭梯度算法,天津大学学报,2005,38(1):1～4
[30]李铮,李长军,邵新慧,在最优准则下的共轭梯度重建算法,东北大学学报(自然科学版),2003,24(12):1134～1136
[31]俞鸿波,赵荣椿,王兵等,单幅图像三维表面重建中的共轭梯度算法,计算机工程与应用, 2003,35:24～26
[32]Wang Hua-Xiang, Zhu Xue-Ming, Zhang Li-Feng, Conjugate gradient algorithm for electrical capacitance tomography, Tianjin Daxue Xuebao, 2005,38(1):1～4
[33]付峰,王志敏,董秀珍等,电阻抗断层成像中Newton-Raphson重构算法的计算机模拟研究,第四军医大学学报,1996,17(1): 55～58
[34]杜岩,柳重堪,程吉宽,电阻抗成像的加权Newton-Raphson算法,北京航空航天大学学报,1998,24(12):161～164
[35]Ji Hoon Kim, Bong Yeol Chol, Kyung Youn Kim, Novel iterative image reconstruction algorithm for electrical capacitance tomography: directional algebraic reconstruction technique, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2006, E89-A(6):1578～1584
[36]Melvin, C., Thulasiraman, P., Gordon, R., Parallel algebraic reconstruction technique for computed tomography, Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA'2003), 23-26 June 2003. 532～536.
[37]Datta A. N., Bandyopadhyay B., An improved SIRT-style reconstruction algorithm for microwave tomography, IEEE Transactions on Biomedical Engineering, 1985, BME-32(9):719～723
[38]Balanis,C. A., Hill, H. W. , Freeland, K.A., Improved SIRT correction factors and redistribution in geotomography, 1983 International Geoscience and Remote Sensing Symposium (IGARSS '83), 31 Aug.-2 Sept. 1983. FP.2.2/1～4
[39]肖斌,刘石,阎润生等,基于MOR的两相流电容层析成像图像重建,电子测量技术,2002,5:3～4
[40]Zhao Jinchuang, Lu Jianbo, Fu Wenli, et al., Research on 3-D image reconstruction of electrical capacitance tomography and its application to discrete phase volume measurement of two-phase flow, Chinese Journal of Scientific Instrument, 2005, 26(2):202～205
[41]Sun K. Yoo, Ge Wang, Fred Collison, et al., Three-Dimensional Localization of Cochlear Implant Electrodes Using Epipolar Stereophotogrammetry, IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, 2004, 51(5):838~846
[42]P.A.T. Pinheiro, W.W. Lon, F.J. Dickin. Three-dimensional reconstruction algorithm for electrical resistance tomography, IEEE Proceedings science measurement and technology, 1998, 145(3): 85～93
[43]P. Metherall, D.C. Barber, R.H. Smallwood et al., Three-dimensional electrical impedance tomography, Letters to Nature, 1996, 380(11):509～512
[44]P.A.T. Pinheiro, W.W. Loh, F.J. Dickin, Three-dimensional reconstruction algorithm for electrical resistance tomography, IEEE Proceedings science measurement and technology, 1998, 145(3):85～93
[45]安源,任世超,电阻抗断层功能成像技术的发展,第四军医大学学报,2001,22(1):90～92
[46]许会,电容层析成像在气固两相流浓度测量中的应用技术研究:[博士学位论文],沈阳:东北大学,1999
[47]刘福平,边界元素法中含距离倒数二次方曲面积分的计算方法,胜利油田职工大学学报,2000,14(4):43～46
[48]Yang zhenjun, Application of scaled boundary finite element method in static and dynamic fracture problems, Acta Mechanica Sinica/Lixue Xuebao, 2006, 22(3):243～256
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[53]赵进创,傅文利,胡强等,电容层析成像系统重建图像质量评价方法探讨,广西大学学报,2003,28(1):61～64
[54]肖建,C++ Builder 6编程基础,北京:清华大学出版社,2002.1～8
[55]向世明,Open GL编程与实例,北京:电子工业出版社,1999.1～7
[2]董峰,崔晓会,电阻层析成像技术的发展,仪器仪表学报,2003,24(2):23～27
[3]吴小平,汪彤彤,电阻率三维反演方法研究进展,地球物理学进展,2002,17(1):156～162
[4]任超世,生物电阻抗测量技术,中国医疗器械信息,2004,10(1):21～25
[5]Dickin F., Wang M., Electrical Resistance Tomography for Process Application, Measurement Science &Technology, 1996, 7(3):247～260
[6]Wang M, Dickin D J, Williams R A, Electrical resistance tomography of metal walled vessels and pipelines, 1994, 30(10):771～773
[7]Xu L A, Jiang Z C, Performance Analysis of the UMIST MK1b Electrical Impedance Tomography System, ECAPT’94, 1994. 114～119
[8]Cillierts J.J., Xie W. ,Neethling S.J., et al. , Electrical resistance tomography using a bi-directional current pulse technique, Measurement Science and Technology, 2001, l2(8) : 997～1001
[9]Primrose K, Qiu C, Performance and Application Studies of an Electrical Resistance Tomography System, 1st World Congress on Industrial Process Tomography, 1999, 133～139
[10]Y Ma, N Holliday, Y Dai et al., A High Performance Online Data Processing EIT System, 3rd World Congress on Industrial Process Tomography, Banff, Canada, 2003. 27～32
[11] Deng X, Dong F, Xu L J, et al., The design of a dual-plane ERT system for cross correlation measurement of bubbly gas/liquid pipe flow, Measurement Science and Technology 2001, 12(8):1024～1031
[12] Wang Wenhui, Dong Feng Xie Lipeng, The Study of ERT System Performance Improvement, The 4th International Symposium on Measurement Technique for Multiphase Flows, 2004, 632～635
[13]许燕斌,基于USB技术的电阻层析成像系统通讯方法的研究:[硕士学位论文],天津:天津大学,2003
[14]王保良,乐嘉华,黄志尧,多相流参数检测电容层析成像技术研究,石油化工自动化,1998,2(4):4～6
[15]申世安,是度芳,李春芳等,修改的联合代数迭代法及其再图像重建中的应用,量子电子学报,2001,18(6):481～484
[16]董峰,电阻层析成像技术在两相流测量中的应用:[博士学位论文],天津:天津大学,2002
[17]邵嘉庆,徐苓安,电阻层析成象系统的研究,自动化与仪表,1999,14(2):1～3
[18]Barber D C, Brown B H, Applied potential tomography, Journal Physics E: Science Instrument 1984, 17(9): 723～733
[19]Sastry, C.S., Das, P.C., A convolution back projection algorithm for local tomography, Australian & New Zealand Industrial and Applied Mathematics Journal, 2005, 46: 341～360
[20]Robert Guardo, Christian Boulary, Bruno Murray, et al., An Experimental Study in Electrical Impedance Tomography Using Backprojection Reconstruction, IEEE Transactions on Biomedical Engineering, 1991, 38(7):617~627
[21]马艺馨,电阻层析成像技术及其在气/液两相泡状流检测种的应用:[博士学位论文],天津:天津大学,1999
[22]Muller, N., Magaia, L., Herbst, B.M., Singular value decomposition, eigenfaces, and 3D reconstructions, SIAM Review, 2004, 46(3):518-545
[23]李睿凡,郭学彬,瞿安连,基于奇值分解的三维光学切片显微图像恢复算法研究,光学精密工程,2001,9 (3):212～215
[24]姜瑞忠,姚彦平,苗盛等,核磁共振T2谱奇异值分解反演改进算法,石油学报,2005,26(6):57～59
[25]王化祥,王超,陈磊,基于Landweber迭代的图像重建算法,信号处理, 2000,16(4): 354～356
[26]李英,黄志尧,等,两相流参数测量ERT图像重建算法的研究,浙江大学学报(工学版),2003,37(4): 382～385
[27]Wang Chao, Wang Huaxiang, Modified Landweber algorithm for solving the inverse problem in EIT, Chinese Journal of Electronics, 2005, 14 (1): 96～98
[28]Yang Gang, Wang Yu-Tao, Shao Fu-Qun, et al, Preconditioning Landweber iterative method for ECT image reconstruction, Dongbei Daxue Xuebao/Journal of Northeastern University, 2006, 27(9): 953～956
[29]王化祥,朱学明,张立峰,用于电容层析成像技术的共轭梯度算法,天津大学学报,2005,38(1):1～4
[30]李铮,李长军,邵新慧,在最优准则下的共轭梯度重建算法,东北大学学报(自然科学版),2003,24(12):1134～1136
[31]俞鸿波,赵荣椿,王兵等,单幅图像三维表面重建中的共轭梯度算法,计算机工程与应用, 2003,35:24～26
[32]Wang Hua-Xiang, Zhu Xue-Ming, Zhang Li-Feng, Conjugate gradient algorithm for electrical capacitance tomography, Tianjin Daxue Xuebao, 2005,38(1):1～4
[33]付峰,王志敏,董秀珍等,电阻抗断层成像中Newton-Raphson重构算法的计算机模拟研究,第四军医大学学报,1996,17(1): 55～58
[34]杜岩,柳重堪,程吉宽,电阻抗成像的加权Newton-Raphson算法,北京航空航天大学学报,1998,24(12):161～164
[35]Ji Hoon Kim, Bong Yeol Chol, Kyung Youn Kim, Novel iterative image reconstruction algorithm for electrical capacitance tomography: directional algebraic reconstruction technique, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2006, E89-A(6):1578～1584
[36]Melvin, C., Thulasiraman, P., Gordon, R., Parallel algebraic reconstruction technique for computed tomography, Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA'2003), 23-26 June 2003. 532～536.
[37]Datta A. N., Bandyopadhyay B., An improved SIRT-style reconstruction algorithm for microwave tomography, IEEE Transactions on Biomedical Engineering, 1985, BME-32(9):719～723
[38]Balanis,C. A., Hill, H. W. , Freeland, K.A., Improved SIRT correction factors and redistribution in geotomography, 1983 International Geoscience and Remote Sensing Symposium (IGARSS '83), 31 Aug.-2 Sept. 1983. FP.2.2/1～4
[39]肖斌,刘石,阎润生等,基于MOR的两相流电容层析成像图像重建,电子测量技术,2002,5:3～4
[40]Zhao Jinchuang, Lu Jianbo, Fu Wenli, et al., Research on 3-D image reconstruction of electrical capacitance tomography and its application to discrete phase volume measurement of two-phase flow, Chinese Journal of Scientific Instrument, 2005, 26(2):202～205
[41]Sun K. Yoo, Ge Wang, Fred Collison, et al., Three-Dimensional Localization of Cochlear Implant Electrodes Using Epipolar Stereophotogrammetry, IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, 2004, 51(5):838~846
[42]P.A.T. Pinheiro, W.W. Lon, F.J. Dickin. Three-dimensional reconstruction algorithm for electrical resistance tomography, IEEE Proceedings science measurement and technology, 1998, 145(3): 85～93
[43]P. Metherall, D.C. Barber, R.H. Smallwood et al., Three-dimensional electrical impedance tomography, Letters to Nature, 1996, 380(11):509～512
[44]P.A.T. Pinheiro, W.W. Loh, F.J. Dickin, Three-dimensional reconstruction algorithm for electrical resistance tomography, IEEE Proceedings science measurement and technology, 1998, 145(3):85～93
[45]安源,任世超,电阻抗断层功能成像技术的发展,第四军医大学学报,2001,22(1):90～92
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