电容层析成像系统的算法研究
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摘要
电容层析成像技术具有非侵入、响应速度快、结构简单、成本低、安全性能好等优点，是一种非常有发展潜力的PT技术，可适用于两相流检测的很多应用领域。
目前在ECT系统中较常用的两种图像重建算法是线性反投影(LBP)算法和迭代算法。LBP算法重建速度快，适合在线实时成像，但重建图像的精度不高；迭代算法属于多步算法，可反复修正成像结果得到较高精度，缺点是速度较慢。由于ECT技术在线实时成像的精度较低，还不能满足工业生产的要求，限制了ECT技术的推广应用。
ECT图像重建精度不高的主要原因是ECT敏感场的“软场”问题以及投影数据有限。本文从两个方面着手研究改善ECT技术重建图像的质量，一是增加投影数据，获得较多的介质分布信息，二是图像重建算法。
增加ECT系统的测量极板数目，可以增加投影数据量。考虑到增加极板数须减少极板宽度，进而会加大测量电路的检测难度，本文采用神经网络实现投影数据的增加，由8极板投影数据通过一个预先训练好的神经网络获得16极板的投影数据。神经网络训练采用的是贝叶斯正则化和Levenberg-Marquardt法相结合的训练算法，可以提高网络的泛化能力并且收敛速度很快。仿真结果表明，这种方法可以提高重建图像的精度。
本文提出一种基于灵敏度矩阵奇异值分解的图像重建算法，用奇异值分解方法求ECT灵敏度矩阵的逆，可以获得较好的近似，并可以通过去除较小的奇异值增加重建的稳定性。该算法重建图像所用的时间与LBP算法相当，而重建图像的质量与迭代算法相近，是一种精度较高的实时重建算法。
Electrical capacitance tomography (ECT) technique has the advantage of being non-intrusive, fast in response, simple in structure, low in cost and good in security, so it is one technique which has great developing potential in industrial application. ECT technique can be applied in many areas of two-phase flow detection.
At present, linear back-projection (LBP) algorithm and iterative algorithm are the most common used algorithms. LBP algorithm has the advantage of fast speed in image reconstruction. This algorithm is fit for real-time image reconstruction, but its reconstruction quality is not accurate. Iterative algorithm is a multi-step algorithm; the reconstruction image will be amended repeatedly to acquire more accurate result. But more time consuming is its disadvantage. The quality of real-time image reconstructed by ECT system does not satisfy production needs, which limits ECT application in practical industry.
There are two main reasons that cause ECT reconstruction images not accurate: the soft field characteristic of ECT sensor sensitivity, and the very small projection data. Two aspects to improve ECT image reconstruction quality are investigated in this paper. One is increasing the number of projection data to obtain more information of medium distribution; the other is researching rapid and accurate image reconstruction algorithm.
Using more measurement electrodes in ECT system can obtain more projection data. However, when electrode number is increased, the electrode width must be lessened. This will bring detection difficulty of measured circuit. In this paper, artificial neural network technique is applied to acquire more projection data. 16-electrode ECT system's projection data is acquired when the 28 measurements of an 8-electrode ECT sensor are fed into a pre-trained neural network. Levenberg-Marquardt algorithm and Bayesian regularization are used in network training and the network can convergence rapidly and generalize well. The simulation results show this algorithm can improve image reconstruction quality.
In this paper, an image reconstruction algorithm based on singular value decomposition (SVD) of sensitivity matrix is proposed; the inverse of ECT sensitivity matrix is calculated use SVD method. This method can obtain a more accurate approximation of sensitivity inverse, and
the smaller singular value can be neglected to improve stability of the reconstruction result. The time consumed in reconstruction is similar to that of LBP algorithm. The image result is more accurate than that of LBP algorithm and similar to that of iterative algorithm. So this new method is a real-time and more accurate reconstruction algorithm.
目前在ECT系统中较常用的两种图像重建算法是线性反投影(LBP)算法和迭代算法。LBP算法重建速度快，适合在线实时成像，但重建图像的精度不高；迭代算法属于多步算法，可反复修正成像结果得到较高精度，缺点是速度较慢。由于ECT技术在线实时成像的精度较低，还不能满足工业生产的要求，限制了ECT技术的推广应用。
ECT图像重建精度不高的主要原因是ECT敏感场的“软场”问题以及投影数据有限。本文从两个方面着手研究改善ECT技术重建图像的质量，一是增加投影数据，获得较多的介质分布信息，二是图像重建算法。
增加ECT系统的测量极板数目，可以增加投影数据量。考虑到增加极板数须减少极板宽度，进而会加大测量电路的检测难度，本文采用神经网络实现投影数据的增加，由8极板投影数据通过一个预先训练好的神经网络获得16极板的投影数据。神经网络训练采用的是贝叶斯正则化和Levenberg-Marquardt法相结合的训练算法，可以提高网络的泛化能力并且收敛速度很快。仿真结果表明，这种方法可以提高重建图像的精度。
本文提出一种基于灵敏度矩阵奇异值分解的图像重建算法，用奇异值分解方法求ECT灵敏度矩阵的逆，可以获得较好的近似，并可以通过去除较小的奇异值增加重建的稳定性。该算法重建图像所用的时间与LBP算法相当，而重建图像的质量与迭代算法相近，是一种精度较高的实时重建算法。
Electrical capacitance tomography (ECT) technique has the advantage of being non-intrusive, fast in response, simple in structure, low in cost and good in security, so it is one technique which has great developing potential in industrial application. ECT technique can be applied in many areas of two-phase flow detection.
At present, linear back-projection (LBP) algorithm and iterative algorithm are the most common used algorithms. LBP algorithm has the advantage of fast speed in image reconstruction. This algorithm is fit for real-time image reconstruction, but its reconstruction quality is not accurate. Iterative algorithm is a multi-step algorithm; the reconstruction image will be amended repeatedly to acquire more accurate result. But more time consuming is its disadvantage. The quality of real-time image reconstructed by ECT system does not satisfy production needs, which limits ECT application in practical industry.
There are two main reasons that cause ECT reconstruction images not accurate: the soft field characteristic of ECT sensor sensitivity, and the very small projection data. Two aspects to improve ECT image reconstruction quality are investigated in this paper. One is increasing the number of projection data to obtain more information of medium distribution; the other is researching rapid and accurate image reconstruction algorithm.
Using more measurement electrodes in ECT system can obtain more projection data. However, when electrode number is increased, the electrode width must be lessened. This will bring detection difficulty of measured circuit. In this paper, artificial neural network technique is applied to acquire more projection data. 16-electrode ECT system's projection data is acquired when the 28 measurements of an 8-electrode ECT sensor are fed into a pre-trained neural network. Levenberg-Marquardt algorithm and Bayesian regularization are used in network training and the network can convergence rapidly and generalize well. The simulation results show this algorithm can improve image reconstruction quality.
In this paper, an image reconstruction algorithm based on singular value decomposition (SVD) of sensitivity matrix is proposed; the inverse of ECT sensitivity matrix is calculated use SVD method. This method can obtain a more accurate approximation of sensitivity inverse, and
the smaller singular value can be neglected to improve stability of the reconstruction result. The time consumed in reconstruction is similar to that of LBP algorithm. The image result is more accurate than that of LBP algorithm and similar to that of iterative algorithm. So this new method is a real-time and more accurate reconstruction algorithm.
引文
[1] 颜华，王师．电容层析成像技术及应用．工业仪表与自动化装置，1999(3)：22～25
[2] 李海青，黄志尧．特种检测技术及应用．杭州：浙江大学出版社，2000．
[3] 董峰，邓湘，徐立军，等．过程层析成像技术综述．仪器仪表用户．2001，8(1)：6～11
[4] Xie C G, Huang S M, Hoyle B S, et al. Electrical capacitance tomography for flow reconstruction imaging system model for development of image reconstruction algorithms and design of primary sensors. IEE Proceedings-G, February 1992, 139(1): 89～98
[5] 王兴，颜华．电容层析成像技术及发展现状．沈阳工业大学学报．2001，23(6)：497～500
[6] 袁曾任．人工神经元网络及其应用．北京：清华大学出版社，1999．
[7] Hagan M T，Demuth H B，Beale M H．神经网络设计．北京：机械工业出版社，2002．
[8] Castleman K R．数字图像处理．北京：电子工业出版社，2002．
[9] 颜华．电容层析成象技术及在高炉块状区物料可视化监测中应用的基础研究：学位论文．沈阳：东北大学，1999．
[10] Loser T, Wajman R, Mewes D. New reconstruction algorithm for electrical capacitance tomography. 2nd World Congress on Industrial Process Tomography, Hannover, Germany, 29th-31st August 2001:20～28
[11] Foresee F D, Hagan M T. Gauss-Newton approximation to Bayesian learning. Proceedings of the 1997 International Joint Conference on Neural Networks. 1997.
[12] David J C, MacKay. Bayesian Interpolation. Neural Computation. 1992, 4(3): 415～447
[13] Ge S M, Yang W Q. Filtering in image reconstruction for electrical capacitance tomography. 2nd World Congress on Industrial Process Tomography, Hannover, Germany, 29th-31st August 2001. 41～47
[14] Yan H, Liu L J, Xu H, et al. Image reconstruction in electrical capacitance tomography using multiple linear regression and regularization. Measurement Science and Technology, 2001, 12(5): 575～581
[15] Yang W Q, Spink D M, York T A, et al. An image-reconstruction algorithm based on Landweber's iteration method for electrical-capacitance tomography. Meas. Sci. Technol., 1999(10): 1065～1069
[16] 赵进创．电容层析成像技术及在两相流可视化监测中的应用研究：学位论文．沈阳：东北大学，2001．
[17] Liu S, Fu L, Yang W Q. Optimization of an iterative image reconstruction algorithm for electrical capacitance tomography. Meas. Sci. Technol., 1999(10): L37～L39
[18] 傅鹂，刘石，杨五强．两相流测量中电容层析成像图像重建的广义逆最小模解与线性反投影和迭代法的比较．仪器仪表学报．2001，22(1)：74～84
[19] 蔡芹，马宁，苏祥芳，等．电容层析成像的BP网络重建．武汉大学学报(自然科学版)．1997，43(1)：107～112
[20] 史志才，刘兴斌，乔卓尔，等．12电极电容层析成像系统灵敏场分布的确定．测井技术．2000，24(4)：253～257
[21] 吴新杰，王师．径向基神经网络在层析成像中的应用．仪表技术与传感器．2000(3)：35～37
[22] 肖化，何惠玲，胡广莉，等．基于多层神经网络的电容层析成像研究．电路与系统学报．1998，3(2)：82～86
[23] 王国荣．矩阵与算子广义逆．北京：科学出版社，1994．
[24] Cann H M, Yang W Q, Polydorides N P, Information Retrieval by Electrical Capacitance Tomography: Evaluation of an Iterative Algorithra and the Importance of
Boundary Conditions. 1st World Congress on Industrial Process Tomography, Buxton, Great Manchester, April 14-17, 1999:206～210
[25] 严杰，郭红星，常鸿森，等．一种新的基于敏感场变换的电容层析成像算法．电路与系统学报．1999，4(2)：80～85
[26] 闻新，周露，王丹力，等．MATLAB神经网络应用设计．北京：科学出版社．2000．
[27] Demuth H, Beale M. Neural Network Toolbox. Matlab User's Guide. The Math Works
[28] 王化祥，杨五强．电容过程成像技术的进展．仪器仪表学报．2000，21(1)：4～11
[29] 史志才．电容层析成像图像重建的不适定性及其改进．计算机工程与应用．2002，38(15)：25～26
[30] 严杰，郭红星，常鸿森，等．敏感场在电容层析成像中的分析与处理．电子学报．1999，27(2)：103～105
[31] 颜华，邵富群，王师，等．电容层析成像传感器软场性能分析．东北大学学报．1999，20(5)：457～460
[32] 许会．电容层析成象在气固两相流浓度测量中的应用技术研究：学位论文．沈阳：东北大学，1999．
[33] 边肇祺．模式识别．北京：清华大学出版社．2000．
[34] 盛骤，谢式干，潘承毅．概率论与数理统计．北京：高等教育出版社．1989．
[35] Process Tomography Ltd.. Application Note AN4 An Iterative Method for Improving ECT Images. Process Tomography Ltd.. 1999.
[36] 韩力群．人工神经网络理论、设计及应用．北京：化学工业出版社．2002．
[37] 史志才，黄志尧，王保良，等．电容层析成像系统图像重建稳定性的研究．浙江大学学报．2001，35(2)：220～224
[38] 常鸿森，保宗悌．电容层析成像原理及其在工业中的应用．物理．1997，26(9)：552～556
[39] 苏邦良，张以恒，彭黎辉，等．同步迭代图像重建技术在电容层析成像系统中的应用．清华大学学报．2000，40(9)：90～92
[40] 夏靖波，魏颖，陆增喜，等．基于最大熵电容成象图象重建算法的研究．控制与决策．2000，15(4)：431～434
[41] Liu S, Fu L, Yang W Q. Comparison of Three Image Reconstruction Algorithms for Electrical Capacitance Tomography. 2nd World Congress on Industrial Process Tomography. Hannover, Germany, 29th-31st August 2001: 29～34
[42] 徐立军，徐苓安．超声层析成像监测气／液两相流体分布．天津大学学报．1995，28(2)：129～135
[43] 马艺馨，徐苓安，姜常珍，等．电阻层析成像技术的研究．仪器仪表学报．2001，22(2)：195～213
[44] 吕宗伟，熊汉亮，徐苓安．电磁层析成像技术的研究．自动化与仪表．1999，14(3)：1～5
[45] 何敏，刘泽，董峰，等．电磁层析成像技术图像重建的仿真研究．天津大学学报．2001，34(4)：435～438
[46] 王兴．电容层析成像投影数据采集系统的研究：学位论文．沈阳：沈阳工业大学，2002．
[2] 李海青，黄志尧．特种检测技术及应用．杭州：浙江大学出版社，2000．
[3] 董峰，邓湘，徐立军，等．过程层析成像技术综述．仪器仪表用户．2001，8(1)：6～11
[4] Xie C G, Huang S M, Hoyle B S, et al. Electrical capacitance tomography for flow reconstruction imaging system model for development of image reconstruction algorithms and design of primary sensors. IEE Proceedings-G, February 1992, 139(1): 89～98
[5] 王兴，颜华．电容层析成像技术及发展现状．沈阳工业大学学报．2001，23(6)：497～500
[6] 袁曾任．人工神经元网络及其应用．北京：清华大学出版社，1999．
[7] Hagan M T，Demuth H B，Beale M H．神经网络设计．北京：机械工业出版社，2002．
[8] Castleman K R．数字图像处理．北京：电子工业出版社，2002．
[9] 颜华．电容层析成象技术及在高炉块状区物料可视化监测中应用的基础研究：学位论文．沈阳：东北大学，1999．
[10] Loser T, Wajman R, Mewes D. New reconstruction algorithm for electrical capacitance tomography. 2nd World Congress on Industrial Process Tomography, Hannover, Germany, 29th-31st August 2001:20～28
[11] Foresee F D, Hagan M T. Gauss-Newton approximation to Bayesian learning. Proceedings of the 1997 International Joint Conference on Neural Networks. 1997.
[12] David J C, MacKay. Bayesian Interpolation. Neural Computation. 1992, 4(3): 415～447
[13] Ge S M, Yang W Q. Filtering in image reconstruction for electrical capacitance tomography. 2nd World Congress on Industrial Process Tomography, Hannover, Germany, 29th-31st August 2001. 41～47
[14] Yan H, Liu L J, Xu H, et al. Image reconstruction in electrical capacitance tomography using multiple linear regression and regularization. Measurement Science and Technology, 2001, 12(5): 575～581
[15] Yang W Q, Spink D M, York T A, et al. An image-reconstruction algorithm based on Landweber's iteration method for electrical-capacitance tomography. Meas. Sci. Technol., 1999(10): 1065～1069
[16] 赵进创．电容层析成像技术及在两相流可视化监测中的应用研究：学位论文．沈阳：东北大学，2001．
[17] Liu S, Fu L, Yang W Q. Optimization of an iterative image reconstruction algorithm for electrical capacitance tomography. Meas. Sci. Technol., 1999(10): L37～L39
[18] 傅鹂，刘石，杨五强．两相流测量中电容层析成像图像重建的广义逆最小模解与线性反投影和迭代法的比较．仪器仪表学报．2001，22(1)：74～84
[19] 蔡芹，马宁，苏祥芳，等．电容层析成像的BP网络重建．武汉大学学报(自然科学版)．1997，43(1)：107～112
[20] 史志才，刘兴斌，乔卓尔，等．12电极电容层析成像系统灵敏场分布的确定．测井技术．2000，24(4)：253～257
[21] 吴新杰，王师．径向基神经网络在层析成像中的应用．仪表技术与传感器．2000(3)：35～37
[22] 肖化，何惠玲，胡广莉，等．基于多层神经网络的电容层析成像研究．电路与系统学报．1998，3(2)：82～86
[23] 王国荣．矩阵与算子广义逆．北京：科学出版社，1994．
[24] Cann H M, Yang W Q, Polydorides N P, Information Retrieval by Electrical Capacitance Tomography: Evaluation of an Iterative Algorithra and the Importance of
Boundary Conditions. 1st World Congress on Industrial Process Tomography, Buxton, Great Manchester, April 14-17, 1999:206～210
[25] 严杰，郭红星，常鸿森，等．一种新的基于敏感场变换的电容层析成像算法．电路与系统学报．1999，4(2)：80～85
[26] 闻新，周露，王丹力，等．MATLAB神经网络应用设计．北京：科学出版社．2000．
[27] Demuth H, Beale M. Neural Network Toolbox. Matlab User's Guide. The Math Works
[28] 王化祥，杨五强．电容过程成像技术的进展．仪器仪表学报．2000，21(1)：4～11
[29] 史志才．电容层析成像图像重建的不适定性及其改进．计算机工程与应用．2002，38(15)：25～26
[30] 严杰，郭红星，常鸿森，等．敏感场在电容层析成像中的分析与处理．电子学报．1999，27(2)：103～105
[31] 颜华，邵富群，王师，等．电容层析成像传感器软场性能分析．东北大学学报．1999，20(5)：457～460
[32] 许会．电容层析成象在气固两相流浓度测量中的应用技术研究：学位论文．沈阳：东北大学，1999．
[33] 边肇祺．模式识别．北京：清华大学出版社．2000．
[34] 盛骤，谢式干，潘承毅．概率论与数理统计．北京：高等教育出版社．1989．
[35] Process Tomography Ltd.. Application Note AN4 An Iterative Method for Improving ECT Images. Process Tomography Ltd.. 1999.
[36] 韩力群．人工神经网络理论、设计及应用．北京：化学工业出版社．2002．
[37] 史志才，黄志尧，王保良，等．电容层析成像系统图像重建稳定性的研究．浙江大学学报．2001，35(2)：220～224
[38] 常鸿森，保宗悌．电容层析成像原理及其在工业中的应用．物理．1997，26(9)：552～556
[39] 苏邦良，张以恒，彭黎辉，等．同步迭代图像重建技术在电容层析成像系统中的应用．清华大学学报．2000，40(9)：90～92
[40] 夏靖波，魏颖，陆增喜，等．基于最大熵电容成象图象重建算法的研究．控制与决策．2000，15(4)：431～434
[41] Liu S, Fu L, Yang W Q. Comparison of Three Image Reconstruction Algorithms for Electrical Capacitance Tomography. 2nd World Congress on Industrial Process Tomography. Hannover, Germany, 29th-31st August 2001: 29～34
[42] 徐立军，徐苓安．超声层析成像监测气／液两相流体分布．天津大学学报．1995，28(2)：129～135
[43] 马艺馨，徐苓安，姜常珍，等．电阻层析成像技术的研究．仪器仪表学报．2001，22(2)：195～213
[44] 吕宗伟，熊汉亮，徐苓安．电磁层析成像技术的研究．自动化与仪表．1999，14(3)：1～5
[45] 何敏，刘泽，董峰，等．电磁层析成像技术图像重建的仿真研究．天津大学学报．2001，34(4)：435～438
[46] 王兴．电容层析成像投影数据采集系统的研究：学位论文．沈阳：沈阳工业大学，2002．
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