基于聚类的电学层析成像算法及应用
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摘要
近年来发展起来的电学层析成像技术(Electrical Tomography，简称ET)在两相流/多相流流动参数分布状况的测量方面取得了一定的进展，已经成为解决两相流参数检测的有效手段，具有很大的潜力和广阔的工业应用前景。
电学层析成像技术ET (Electrical Tomography,简称ET)是目前最为广泛研究的一种过程层析成像技术，它具有系统成本低、成像速度快、适用范围广、非侵入式等优点，在PT中很有优势。因而，电学层析成像技术成为研究的热点。
然而，尽管ET技术取得了较大的进展，但是图像重建的精度和速度却一直是没有获得很大的进展。为了获得更佳的图像质量和更快的成像速度，许多研究者进行了不懈的努力，提出了多种图像重建算法，如反投影法、Landweber的迭代法等，但是这些算法各有不同的适用场合与局限性。
针对目前断层成像重建图像算法存在的成像精度较低和速度较慢的问题，基于模糊聚类算法，我们提出了一种具有原创性的新型图像重建算法。与现有的成像算法不同的是，我们把不同的传感器所获取的信息有序地映射到一个向量的空间进行聚类分析。同时，通过特征分组加权，充分考虑特征之间度量值的不均衡性，更好地描述了数据中不同特征作用的差异。实验证明，我们提出的算法能够充分地利用已有信息，获得更好的图像重建效果。进一步地，我们提出的算法实现简单，计算复杂度低，能够实时、动态地更新计算结果，为图像重建技术提供一个全新的手段。
最后，又从数据融合的角度做了ERT和ECT图像融合的初步研究。
我们应用Comsol公司开发的Comsol软件在电磁方面强大的数据仿真功能，对我们所需要的实验数据用其仿真得到。一方面可以完全得到理想中的数据，另一方面，对于我们的新算法来说，完全应用理想化下的数据有利于对算法效果的验证以及算法的发展。
With the rapid development in recent several ten years, Electrical Tomography(Electrical Tomography, ET) techniques have been successfully used in two-phaseflow/multiphase flow parameter measurement, and ET techniques have great potentialand could be widely used in industry.
Electrical Tomography (Electrical Tomography, ET) is one of the techniques ofPT, which is widely researched. It has advantages of low-cost, high-speed, robust andnon-intrusive, et. al. Thus, ET technology has become a hot research.
However, despite the ET technology has made great progress, the accuracy andspeed of image reconstruction have not been achieved more progress. In order toobtain better image quality and faster imaging speed, many researchers have madegreat efforts on image reconstruction algorithm, such as LBP and Land Weber est. But,the applications of these algorithms have different situations and limitations.
To overcome the problems of speed and precision of the existing algorithms, wecreatively present a method of image reconstruction algorithm based on fuzzyclustering. Different from the existing algorithms, we map the information fromdifferent sensors into a vector space for clustering analysis., Then, all attributes ofeach vector are not equally important in clustering process，and alternatively theeffects of some attributes are enlarged while the other is reduced. Consequently, ouralgorithm can fully utilize the existing information to obtain the better reconstructedimages. Consequently, our algorithm is easily realized, lower time complexity, andupdated in a real-time and automatic manner. Thus our algorithm contributes a newway to the image reconstruction techniques.
Finally, we did the simple image fusion of ERT and ECT from the perspectiveof data fusion.
In addition, we apply Comsol’s great simulation on electromagnetic data, to getour experimental data. It can get completely satisfactory data, on the other hand, toour new algorithm; the ideal data can be favorable to our algorithm verification andthe development of algorithms.
电学层析成像技术ET (Electrical Tomography,简称ET)是目前最为广泛研究的一种过程层析成像技术，它具有系统成本低、成像速度快、适用范围广、非侵入式等优点，在PT中很有优势。因而，电学层析成像技术成为研究的热点。
然而，尽管ET技术取得了较大的进展，但是图像重建的精度和速度却一直是没有获得很大的进展。为了获得更佳的图像质量和更快的成像速度，许多研究者进行了不懈的努力，提出了多种图像重建算法，如反投影法、Landweber的迭代法等，但是这些算法各有不同的适用场合与局限性。
针对目前断层成像重建图像算法存在的成像精度较低和速度较慢的问题，基于模糊聚类算法，我们提出了一种具有原创性的新型图像重建算法。与现有的成像算法不同的是，我们把不同的传感器所获取的信息有序地映射到一个向量的空间进行聚类分析。同时，通过特征分组加权，充分考虑特征之间度量值的不均衡性，更好地描述了数据中不同特征作用的差异。实验证明，我们提出的算法能够充分地利用已有信息，获得更好的图像重建效果。进一步地，我们提出的算法实现简单，计算复杂度低，能够实时、动态地更新计算结果，为图像重建技术提供一个全新的手段。
最后，又从数据融合的角度做了ERT和ECT图像融合的初步研究。
我们应用Comsol公司开发的Comsol软件在电磁方面强大的数据仿真功能，对我们所需要的实验数据用其仿真得到。一方面可以完全得到理想中的数据，另一方面，对于我们的新算法来说，完全应用理想化下的数据有利于对算法效果的验证以及算法的发展。
With the rapid development in recent several ten years, Electrical Tomography(Electrical Tomography, ET) techniques have been successfully used in two-phaseflow/multiphase flow parameter measurement, and ET techniques have great potentialand could be widely used in industry.
Electrical Tomography (Electrical Tomography, ET) is one of the techniques ofPT, which is widely researched. It has advantages of low-cost, high-speed, robust andnon-intrusive, et. al. Thus, ET technology has become a hot research.
However, despite the ET technology has made great progress, the accuracy andspeed of image reconstruction have not been achieved more progress. In order toobtain better image quality and faster imaging speed, many researchers have madegreat efforts on image reconstruction algorithm, such as LBP and Land Weber est. But,the applications of these algorithms have different situations and limitations.
To overcome the problems of speed and precision of the existing algorithms, wecreatively present a method of image reconstruction algorithm based on fuzzyclustering. Different from the existing algorithms, we map the information fromdifferent sensors into a vector space for clustering analysis., Then, all attributes ofeach vector are not equally important in clustering process，and alternatively theeffects of some attributes are enlarged while the other is reduced. Consequently, ouralgorithm can fully utilize the existing information to obtain the better reconstructedimages. Consequently, our algorithm is easily realized, lower time complexity, andupdated in a real-time and automatic manner. Thus our algorithm contributes a newway to the image reconstruction techniques.
Finally, we did the simple image fusion of ERT and ECT from the perspectiveof data fusion.
In addition, we apply Comsol’s great simulation on electromagnetic data, to getour experimental data. It can get completely satisfactory data, on the other hand, toour new algorithm; the ideal data can be favorable to our algorithm verification andthe development of algorithms.
引文
[1]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.
[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]王保良,电容层析成像技术及其在两相流检测中的应用研究:(硕士学位论文)杭州浙江大学,1998
[4]徐立军，徐苓安，超声层析成像监测气液两相流体分布，大津大学学报，1995,28(2):129-135
[5] Yan Y.Mass flow measurement of bulk solids in pneumatic pipelines,Meas.Sci.Technol,1996,7:1687-1706
[6]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.
[7]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.
[8]何敏，EMT逆问题仿真研究：（硕士学位论文），天津：天津大学，2001.
[9]徐苓安,电容层析成像技术在生产过程中的应用,东北大学学报,2000,21(1):1-5
[10]李开泰，有限元方法及应用，西安：西安交通大学出版社，1992
[11]曾余庚，电磁场有限单元法，北京，科学出版社，1982
[12]倪光正，钱秀英，电磁场数值计算，北京：高等教育出版社，1996
[13] xie C G，Mass flow measurement of solids in a gravity drop conveyor usingcapacitance transducers,1988,Ph .D Thesis, University of Manchester
[14] Huang S M, Tomographic imaging of two-component flow using capacitancesensors, 1989 ,J.Phys.E:Sci.Instrum.221 73-177
[15] Xie C G et al, 8-electrode capacitance system for two-component flowidentification part l: tomographic flow imaging,19 89,IE EP roceedings136(4)17 3- 18 3
[16] Isaksen ,A review of reconstruction techniques for capacitancetomography ,1996,Meas.Sci.Technol.7 325-337
[17] Tikhonov A N and Arsenin V Y, Solutions of ill-posed problems,1977,( Washington ,DC: Winston)America
[18] Kaipio J P et al, Statistic inversion in Monte Carlo sampling methods in electricalimpedance tomography,2000,Inverse Problems 16 1487-1522
[19] Vauhkonen M, Electrical impedance tomography and prior information.1997,Ph.D Thesis, Kuopio University, Kuopio, Finland
[20] Wang M, Inverse solutions for electrical impedance tomography based onconjugate gradients methods,2002.Meas.Sci.Technol.131 01-117
[21] Isaksen and Nordtvedt J E, A new reconstruction algorithm for processtomography, 1993, Meas.Sci.Technol.41464-1475
[22] Vauhkonen M et al , Tikhonov regularization and prior in formation in electricalimpedance tomography,1998,IEEE Transactions on Medical Imaging 17(2)285-293
[22] Lionheart W R B, Conformal uniqueness results in anistropic electricalimpedance image, 1997, Inverse Problems 13,125-134
[23] Borsic A, Regularization in electrical imaging reconstruction, 2002, Ph.D ThesisOxford Brookes University, England
[24] Kolehmainen V et al, A Bayesian approach and total variation priors in 3Delectrical impedance tomography,1998, Proceedings of the 20th AnnualInternational Conference of the IEEE Engineering in Medicine and BiologySociety 20(20)
[25]Kak A C, Slaney M，Principles of Computerized Tomographic Image[M]，NewYork: IEEE Press, 1988
[26]Calder A J，Duncan R，Young A W，et a1．Caricaturing facial expressions [J]．Cognition，2000，76(2)：105～146
[27]Fasel B，Luettin J．Automatic facial expression analysis：A survey[J]．PatternRecognition，2003，36(1)：259～275
[28]Kobayashi H，Hara F．The recognition of basic facial expressions by neuraln28twork[A]．In：Proceedings of IEEE International Joint Conference on NeuralNetworks，Seattle，1991．460-466
[29]Ralescu A，1wamoto H．Recognition of and reasoning about facial expressionsusing fuzzy logic[A]．In：Proceedings of the 2nd IEEE International Workshop onRobot and Human Communication．Wako，1993．259-264
[30]Huang C L，Huang Y M．Facial expression recognition using model-basedfeature extraction and action parameters classification [J] Visual Communicationand Image Representation，1997，8(3)：278-290
[31]Gao Y S，Maylor K H Leung，et a1．Facial expression recognition fromline-base caricatures[J]．IEEE Transactions on Systems，M an，andCybernetics-Part A：Systems and Humans，2003，33(3)：407-412
[32]Johnson CA, Sofer A，A Data-Parallel Algorithm for Tomographic ImageReconstruction[A]，Proceedings of the 7th Symposium on the Frontiers ofMassively Parallel Computation, IEEE Computer Society Press, 1999, P1265
[33]D W Shattuck,J Rapela etc，Internet2-based 3D PET Image Reconstruction Usinga PC Cluster[J], Phys Med Biol, 2002,47:2785
[34]Kak A C, Slaney M，Principles of Computerized Tomographic Image[M] NewYork: IEEE Press, 1988
[35]ISAKSEN 0，DICO A S，HAMMER E A．A capacitance—based tomographysystem for interface measurement in separation vessels[J]．Measurement Scienceand Technology，1994，5(1O)：1262-1271．
[36]ZHU K，MADHUSUDANA R S，WANG C H，et a1．Electrical ca．pacitancetomography measurements on vertical an d inclined pneumatic conveying ofgranular solids[J]．Chemical Engineering Science，2003，58(18)：4225-4245．
[37]KOTRE c J．A sensitivity coefficient method for the reconstruction of electricalimpedance tornogrmrm [J]．Clinical Physics and Phrao~giea]Mtllsurtm~t，1989，10(3)：275-281．
[38]张洧淳，彭黎辉，姚丹亚，等。采用改进的主元分析算法测量两相流相浓度[J]。清华大学学报：自然科学版，2003，43(3)：400-401，403。
[39]吴新杰，王师，王凤翔。基于粗糙集理论两相流流型辨识方法研究[J]。仪器仪表学报，2003，24(3)：221-225。
[40]刘石，潘忠刚，燕贵章，等。应用电容层析成象和差压对比法对流化床内固体颗粒浓度分布的测量研究[J]。工程热物理学报，2000，21(6)：759-763。
[41]刘石，王海刚，姜凡，等。循环流化床固体分布的层析成象测量[J]。工程热物理学报，2001，22(5)：645-648。
[42]黄志尧，冀海峰，王保良，等。电容层析成像技术在线测量气固流化床空隙率的研究[J]。高校化学工程学报，2002，16(5)：490-495。
[43]王雷，冀海峰，黄志尧，等。基于ECT传感器和模式识别的气液两相流空隙率测量新方法研究[J]。仪器仪表学报，2005，26(6)：57-561。
[44]Xie C G and Huang S M et al, Electrical capacitance tomography for flowimaging: system model for development of image reconstruction algorithmsand design of primary sensors, 1992, IEE Proceedings-G 139(1):89-98
[45]Chen Q et al, Electrical field interaction and an enhanced reconstructionalgorithm in capacitance process tomography, 1994, Proc.1 ECAPT Conf.(Manchester) pp205-212
[46]Chen Q, Imaging reconstruction algorithm in capacitance based processtomography, 1993, Ph, D Dissertation, University of Leeds, England
[47]Liu S et al, Optimization of an iterative image reconstruction algorithm forelectrical capacitance tomography, 1999, Meas. Sci. Techol. 10 L37-L39
[48]邓乃杨等，无约束最优化计算方法[M], 1982,北京：科学出版社
[49]Hanke M, Conjugate gradient tye methods for ill posed problems, 1995, Scientific& Technical, Longman, Essex
[50]颜华.电容层析成像技术及在高炉块状区物料可视化监测中应用的基石韶研究东北大学博士学位论文.沈阳:东北大学，1999.
[51]美国德州仪器公司，CMOS集成电路特性手册，上海无线电十九厂翻译组译，北京天华出版社，1976.
[52]董峰，赵国勋，徐荃安.应用电阻层析成像技术测定两相流中气含率的研究.东北大学学报，2000,21(S.1):169-172
[53]张宝芬，焦清，黄松明.电容式两相流浓度传感器的仿真和优化，清华大学学报，1992,32(1):25-31
[54]王静，基于聚类的图像重建算法及应用，天津大学硕士论文：天津大学，2009
[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]王保良,电容层析成像技术及其在两相流检测中的应用研究:(硕士学位论文)杭州浙江大学,1998
[4]徐立军，徐苓安，超声层析成像监测气液两相流体分布，大津大学学报，1995,28(2):129-135
[5] Yan Y.Mass flow measurement of bulk solids in pneumatic pipelines,Meas.Sci.Technol,1996,7:1687-1706
[6]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.
[7]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.
[8]何敏，EMT逆问题仿真研究：（硕士学位论文），天津：天津大学，2001.
[9]徐苓安,电容层析成像技术在生产过程中的应用,东北大学学报,2000,21(1):1-5
[10]李开泰，有限元方法及应用，西安：西安交通大学出版社，1992
[11]曾余庚，电磁场有限单元法，北京，科学出版社，1982
[12]倪光正，钱秀英，电磁场数值计算，北京：高等教育出版社，1996
[13] xie C G，Mass flow measurement of solids in a gravity drop conveyor usingcapacitance transducers,1988,Ph .D Thesis, University of Manchester
[14] Huang S M, Tomographic imaging of two-component flow using capacitancesensors, 1989 ,J.Phys.E:Sci.Instrum.221 73-177
[15] Xie C G et al, 8-electrode capacitance system for two-component flowidentification part l: tomographic flow imaging,19 89,IE EP roceedings136(4)17 3- 18 3
[16] Isaksen ,A review of reconstruction techniques for capacitancetomography ,1996,Meas.Sci.Technol.7 325-337
[17] Tikhonov A N and Arsenin V Y, Solutions of ill-posed problems,1977,( Washington ,DC: Winston)America
[18] Kaipio J P et al, Statistic inversion in Monte Carlo sampling methods in electricalimpedance tomography,2000,Inverse Problems 16 1487-1522
[19] Vauhkonen M, Electrical impedance tomography and prior information.1997,Ph.D Thesis, Kuopio University, Kuopio, Finland
[20] Wang M, Inverse solutions for electrical impedance tomography based onconjugate gradients methods,2002.Meas.Sci.Technol.131 01-117
[21] Isaksen and Nordtvedt J E, A new reconstruction algorithm for processtomography, 1993, Meas.Sci.Technol.41464-1475
[22] Vauhkonen M et al , Tikhonov regularization and prior in formation in electricalimpedance tomography,1998,IEEE Transactions on Medical Imaging 17(2)285-293
[22] Lionheart W R B, Conformal uniqueness results in anistropic electricalimpedance image, 1997, Inverse Problems 13,125-134
[23] Borsic A, Regularization in electrical imaging reconstruction, 2002, Ph.D ThesisOxford Brookes University, England
[24] Kolehmainen V et al, A Bayesian approach and total variation priors in 3Delectrical impedance tomography,1998, Proceedings of the 20th AnnualInternational Conference of the IEEE Engineering in Medicine and BiologySociety 20(20)
[25]Kak A C, Slaney M，Principles of Computerized Tomographic Image[M]，NewYork: IEEE Press, 1988
[26]Calder A J，Duncan R，Young A W，et a1．Caricaturing facial expressions [J]．Cognition，2000，76(2)：105～146
[27]Fasel B，Luettin J．Automatic facial expression analysis：A survey[J]．PatternRecognition，2003，36(1)：259～275
[28]Kobayashi H，Hara F．The recognition of basic facial expressions by neuraln28twork[A]．In：Proceedings of IEEE International Joint Conference on NeuralNetworks，Seattle，1991．460-466
[29]Ralescu A，1wamoto H．Recognition of and reasoning about facial expressionsusing fuzzy logic[A]．In：Proceedings of the 2nd IEEE International Workshop onRobot and Human Communication．Wako，1993．259-264
[30]Huang C L，Huang Y M．Facial expression recognition using model-basedfeature extraction and action parameters classification [J] Visual Communicationand Image Representation，1997，8(3)：278-290
[31]Gao Y S，Maylor K H Leung，et a1．Facial expression recognition fromline-base caricatures[J]．IEEE Transactions on Systems，M an，andCybernetics-Part A：Systems and Humans，2003，33(3)：407-412
[32]Johnson CA, Sofer A，A Data-Parallel Algorithm for Tomographic ImageReconstruction[A]，Proceedings of the 7th Symposium on the Frontiers ofMassively Parallel Computation, IEEE Computer Society Press, 1999, P1265
[33]D W Shattuck,J Rapela etc，Internet2-based 3D PET Image Reconstruction Usinga PC Cluster[J], Phys Med Biol, 2002,47:2785
[34]Kak A C, Slaney M，Principles of Computerized Tomographic Image[M] NewYork: IEEE Press, 1988
[35]ISAKSEN 0，DICO A S，HAMMER E A．A capacitance—based tomographysystem for interface measurement in separation vessels[J]．Measurement Scienceand Technology，1994，5(1O)：1262-1271．
[36]ZHU K，MADHUSUDANA R S，WANG C H，et a1．Electrical ca．pacitancetomography measurements on vertical an d inclined pneumatic conveying ofgranular solids[J]．Chemical Engineering Science，2003，58(18)：4225-4245．
[37]KOTRE c J．A sensitivity coefficient method for the reconstruction of electricalimpedance tornogrmrm [J]．Clinical Physics and Phrao~giea]Mtllsurtm~t，1989，10(3)：275-281．
[38]张洧淳，彭黎辉，姚丹亚，等。采用改进的主元分析算法测量两相流相浓度[J]。清华大学学报：自然科学版，2003，43(3)：400-401，403。
[39]吴新杰，王师，王凤翔。基于粗糙集理论两相流流型辨识方法研究[J]。仪器仪表学报，2003，24(3)：221-225。
[40]刘石，潘忠刚，燕贵章，等。应用电容层析成象和差压对比法对流化床内固体颗粒浓度分布的测量研究[J]。工程热物理学报，2000，21(6)：759-763。
[41]刘石，王海刚，姜凡，等。循环流化床固体分布的层析成象测量[J]。工程热物理学报，2001，22(5)：645-648。
[42]黄志尧，冀海峰，王保良，等。电容层析成像技术在线测量气固流化床空隙率的研究[J]。高校化学工程学报，2002，16(5)：490-495。
[43]王雷，冀海峰，黄志尧，等。基于ECT传感器和模式识别的气液两相流空隙率测量新方法研究[J]。仪器仪表学报，2005，26(6)：57-561。
[44]Xie C G and Huang S M et al, Electrical capacitance tomography for flowimaging: system model for development of image reconstruction algorithmsand design of primary sensors, 1992, IEE Proceedings-G 139(1):89-98
[45]Chen Q et al, Electrical field interaction and an enhanced reconstructionalgorithm in capacitance process tomography, 1994, Proc.1 ECAPT Conf.(Manchester) pp205-212
[46]Chen Q, Imaging reconstruction algorithm in capacitance based processtomography, 1993, Ph, D Dissertation, University of Leeds, England
[47]Liu S et al, Optimization of an iterative image reconstruction algorithm forelectrical capacitance tomography, 1999, Meas. Sci. Techol. 10 L37-L39
[48]邓乃杨等，无约束最优化计算方法[M], 1982,北京：科学出版社
[49]Hanke M, Conjugate gradient tye methods for ill posed problems, 1995, Scientific& Technical, Longman, Essex
[50]颜华.电容层析成像技术及在高炉块状区物料可视化监测中应用的基石韶研究东北大学博士学位论文.沈阳:东北大学，1999.
[51]美国德州仪器公司，CMOS集成电路特性手册，上海无线电十九厂翻译组译，北京天华出版社，1976.
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