电磁层析成像图像重建中的修正Landweber迭代算法
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摘要
电磁层析成像技术中图像重建算法的准确与快速是其在工业现场中得以应用的关键。Landweber迭代算法是电磁层析成像图像重建中应用最广泛的迭代算法,但其需要多次迭代,收敛速度慢。该文提出一种修正的Landweber迭代图像重建算法,该算法通过在构建的电磁层析成像逆问题目标泛函中添加正则化项,并采用自适应权重系数的方法,提高了收敛速度,并且改善了重建图像的质量。利用有限元法,在Maxwell中进行电磁层析成像正问题的求解,获得了图像重建所需的灵敏度矩阵。仿真和数值实验结果表明,修正的Landweber迭代算法在收敛速度和重建图像质量两方面均优于Landweber迭代算法。
The imaging speed and accuracy of image reconstruction algorithms in electromagnetic tomography are the keys to its application in industries. Landweber iteration algorithm is the most widely used iteration algorithm for image reconstruction of electromagnetic tomography, but it needs many iterations and has slow speed of convergence. A modified Landweber iteration algorithm was proposed through appending an additional regularization term into the constructed objective functional of the inverse problem of electromagnetic tomography and adopting adaptive weight coefficient method, which improves the speed of convergence and the quality of reconstructed image efficiently. Sensitivity matrix was obtained by using finite element method(FEM),which was conducted in Maxwell for the simulation of the forward problem of electromagnetic tomography. Both the simulation and numerical experiments results show that modified Landweber iteration algorithm is superior to Landweber iteration algorithm in the speed of convergence and quality of reconstructed image.
The imaging speed and accuracy of image reconstruction algorithms in electromagnetic tomography are the keys to its application in industries. Landweber iteration algorithm is the most widely used iteration algorithm for image reconstruction of electromagnetic tomography, but it needs many iterations and has slow speed of convergence. A modified Landweber iteration algorithm was proposed through appending an additional regularization term into the constructed objective functional of the inverse problem of electromagnetic tomography and adopting adaptive weight coefficient method, which improves the speed of convergence and the quality of reconstructed image efficiently. Sensitivity matrix was obtained by using finite element method(FEM),which was conducted in Maxwell for the simulation of the forward problem of electromagnetic tomography. Both the simulation and numerical experiments results show that modified Landweber iteration algorithm is superior to Landweber iteration algorithm in the speed of convergence and quality of reconstructed image.
引文
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[21]徐凯,陈广,尹武良,等.基于场量提取法的电磁层析成像系统的灵敏度推算[J].传感技术学报,2011,24(4):543-547.Xu Kai,Chen Guang,Yin Wuliang,et al.Sensitivity derivation and calculation of electromagnetic tomography(EMT)sensor based on field value extraction[J].Chinese Journal of Sensors and Actuators,2011,24(4):543-547(in Chinese).
[22]Yan Hua,Wang Yifan,Zhou Yinggang,et al.3D ECTreconstruction by an improved Landweber iteration algorithm[J].Flow Measurement and Instrumentation,2014,37:92-98.
[2]Griffiths H.Magnetic induction tomography[J].Measurement Science and Technology,2001,12(8):1126-1131.
[3]Yin Wuliang,Peyton A J.A planar EMT system for the detection of faults on thin metallic plates[J].Measurement Science and Technology,2006,17(8):2130-2135.
[4]Yin Wuliang,Chen Guang,Chen Lijing,et al.The design of a digital magnetic induction tomography(MIT)system for metallic object imaging based on half cycle demodulation[J].IEEE Sensors Journal,2011,11(10):2233-2240.
[5]Merwa R,Hollaus K,BiróO,et al.Detection of brain oedema using magnetic induction tomography:a feasibility study of the likely sensitivity and detectability[J].Physiological Measurement,2004,25(1):347-354.
[6]Ma Xiandong,Peyton A J,Higson S R,et al.Development of multiple frequency electromagnetic induction systems for steel flow visualization[J].Measurement Science and Technology,2008,19(9):094008.
[7]Liu Ze,Li Wen,Xue Fangqi,et al.Electromagnetic tomography rail defect inspection[J].IEEE Transactions on Magnetics,2015,51(10):6201907.
[8]Terzija N,Yin Wuliang,Gerbeth G,et al.Use of electromagnetic induction tomography for monitoring liquid metal/gas flow regimes on a model of an industrial steel caster[J].Measurement Science and Technology,2011,22(1):015501.
[9]付妍,董峰,谭超.电磁层析成像系统敏感场激励特性仿真研究[J].中国电机工程学报,2011,31(8):73-79.Fu Yan,Dong Feng,Tan Chao.Simulation of excitation characteristics in sensing field of electromagnetic tomography system[J].Proceedings of the CSEE,2011,31(8):73-79(in Chinese).
[10]付妍,董峰,谭超.被测物场空间分布对电磁测量系统相位检测的影响分析[J].中国电机工程学报,2014,34(20):3362-3368.Fu Yan,Dong Feng,Tan Chao.Effect of space distribution in phase detection on magnetic induction measurement system[J].Proceedings of the CSEE,2014,34(20):3362-3368(in Chinese).
[11]Yang Wuqiang,Peng Lihui.Image reconstruction algorithms for electrical capacitance tomography[J].Measurement Science and Technology,2003,14(1):R1-R13.
[12]彭黎辉,陆耿,杨五强.电容成像图像重建算法原理及评价[J].清华大学学报:自然科学版,2004,44(4):478-484.Peng Lihui,Lu Geng,Yang Wuqiang.Image reconstruction algorithms for electrical capacitance tomography:state of the art[J].Journal of Tsinghua University:Science&Technology,2004,44(4):478-484(in Chinese).
[13]Liu S,Fu L,Yang Wuqiang.Optimization of an iterative image reconstruction algorithm for electrical capacitance tomography[J].Measurement Science and Technology,1999,10(7):L37-L39.
[14]Yang Wuqiang,Spink D M,York T A,et al.An image-reconstruction algorithm based on Landweber’s iteration method for electrical-capacitance tomography[J].Measurement Science and Technology,1999,10(11):1065-1069.
[15]Liu Shi,Fu L,Yang Wuqiang,et al.Prior-online iteration for image reconstruction with electrical capacitance tomography[J].IEE Proceedings-Science,Measurement and Technology,2004,151(3):195-200.
[16]董向元,陈琪,李惊涛,等.基于快速投影LANDWEBER法的电容层析成像图像重建算法研究[J].中国电机工程学报,2005,25(14):89-92.
[17]Dong Xiangyuan,Chen Qi,Li Jingtao,et al.A fast projected-Landweber method for image reconstruction for ECT[J].Proceedings of the CSEE,2005,25(14):89-92(in Chinese).
[18]Liu Ze,Yang Guoyin,He Nan,et al.Landweber iterative algorithm based on regularization in electromagnetic tomography for multiphase flow measurement[J].Flow Measurement and Instrumentation,2012,27:53-58.
[19]Jang J D,Lee S H,Kim K Y,et al.Modified iterative Landweber method in electrical capacitance tomography[J]Measurement Science and Technology,2006,17(7):1909-1917.
[20]刘泽,薛芳其,杨国银,等.电磁层析成像灵敏度矩阵实验测试方法[J].仪器仪表学报,2013,34(9):1982-1988.Liu Ze,Xue Fangqi,Yang Guoyin,et al.Experimental measurement method of sensitivity matrix for electromagnetic tomography[J].Chinese Journal of Scientific Instrument,2013,34(9):1982-1988(in Chinese).
[21]徐凯,陈广,尹武良,等.基于场量提取法的电磁层析成像系统的灵敏度推算[J].传感技术学报,2011,24(4):543-547.Xu Kai,Chen Guang,Yin Wuliang,et al.Sensitivity derivation and calculation of electromagnetic tomography(EMT)sensor based on field value extraction[J].Chinese Journal of Sensors and Actuators,2011,24(4):543-547(in Chinese).
[22]Yan Hua,Wang Yifan,Zhou Yinggang,et al.3D ECTreconstruction by an improved Landweber iteration algorithm[J].Flow Measurement and Instrumentation,2014,37:92-98.