一种改进牛顿-拉夫逊ERT绝对图像重建算法
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摘要
为了提高电阻层析成像重建图像分辨率,提出一种改进牛顿-拉夫逊绝对图像重建算法.在算法迭代过程中,采取灵敏度矩阵自动更新的策略,同时结合图像重建结果自动选取阈值,并根据阈值修正电阻率.仿真实验结果表明:相比单纯采用灵敏度矩阵自动更新策略的改进牛顿-拉夫逊算法,在无噪声干扰下,新算法图像相对误差平均降低了35.620%,在1%幅度噪声干扰下,新算法图像相对误差平均降低了31.962%,在实现绝对图像重建的同时,有效提高了图像重建质量.
A modified Newton-Raphson absolute image reconstruction algorithm was proposed to improve the space resolution of the reconstructed image in electrical resistance tomography(ERT). In the iteration process,the sensitivity matrix was updated automatically;meanwhile,the resistivity was corrected according to a threshold determined by referring to the reconstruction result. Simulation experimental results demonstrate that compared to the modified Newton-Raphson method with sensitivity matrix updating,the proposed method reduces the relative image error by 35.620% in the noise-free case. With the existence of 1% noise,the proposed method reduces the relative image error by 31.962%. The proposed method enhances the imaging quality effectively while realizing absolute image reconstruction.
A modified Newton-Raphson absolute image reconstruction algorithm was proposed to improve the space resolution of the reconstructed image in electrical resistance tomography(ERT). In the iteration process,the sensitivity matrix was updated automatically;meanwhile,the resistivity was corrected according to a threshold determined by referring to the reconstruction result. Simulation experimental results demonstrate that compared to the modified Newton-Raphson method with sensitivity matrix updating,the proposed method reduces the relative image error by 35.620% in the noise-free case. With the existence of 1% noise,the proposed method reduces the relative image error by 31.962%. The proposed method enhances the imaging quality effectively while realizing absolute image reconstruction.
引文
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[16]Dong Feng,Xu Yanbin.Application of electrical resistance tomography in two-phase flow measurement[J].Journal of Engineering Thermophysics,2006,27(5):791-794.
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[18]肖理庆,王化祥,韩成春.一种新型拓扑结构的电阻层析成像有限元模型[J].中国电机工程学报,2011,31(20):100-106.Xiao Liqing,Wang Huaxiang,Han Chengchun.A new topology structure finite element model of electrical resistance tomography system[J].Proceedings of the CSEE,2011,31(20):100-106(in Chinese).
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[20]陈晓艳,张静.采用阈值修正法改善电阻抗图像质量[J].中国生物医学工程学报,2011,30(4):481-486.Chen Xiaoyan,Zhang Jing.Using threshold correction method to improve the image quality of EIT[J].Chinese Journal of Biomedical Engineering,2011,30(4):481-486(in Chinese).
[21]董峰,赵佳,许燕斌,等.用于电阻层析成像的快速自适应硬阈值算法[J].天津大学学报:自然科学与工程技术版,2015,48(4):305-310.Dong Feng,Zhao Jia,Xu Yanbin,et al.A fast adaptive iterative hard threshold algorithm for electrical resistance tomography[J].Journal of Tianjin University:Science and Technology,2015,48(4):305-310(in Chinese).
[22]肖理庆,王化祥,徐晓菊.改进牛顿-拉夫逊电阻层析成像图像重建算法[J].中国电机工程学报,2012,32(8):91-97.Xiao Liqing,Wang Huaxiang,Xu Xiaoju.Improved Newton-Raphson algorithm for electrical resistance tomography image reconstruction[J].Proceedings of the CSEE,2012,32(8):91-97(in Chinese).
[2]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).
[3]Yin W,Peyton A J.A planar EMT system for the detection of faults on thin metallic plates[J].Measurement Science&Technology,2006,17(8):2130-2135.
[4]尹武良,王奔,王化祥.电磁层析成像中基于半周期采样的数字解调方法[J].天津大学学报,2011,44(12):1118-1123.Yin Wuliang,Wang Ben,Wang Huaxiang.Digital demodulation based on half-period sampling in electromagnetic tomography[J].Journal of Tianjin University,2011,44(12):1118-1123(in Chinese).
[5]王超,张军青,徐传进.基于FPGA的EMT系统设计[J].天津大学学报,2011,44(2):95-100.Wang Chao,Zhang Junqing,Xu Chuanjin.Design of an electromagnetic tomography(EMT)system based on FPGA[J].Journal of Tianjin University,2011,44(2):95-100(in Chinese).
[6]Chen Qi,Liu Shi.Flame imaging in meso-scale porous media burner using electrical capacitance tomography[J].Chinese Journal of Chemical Engineering,2012,20(2):329-336.
[7]陈江涛,刘石.融合电容层析成像先验信息的集合卡尔曼滤波统计估计[J].化学工程,2012,40(4):36-39.Chen Jiangtao,Liu Shi.Statistical estimation of ensemble Kalman filter fusion based on priori information approach in electrical capacitance tomography[J].Chemical Engineering,2012,40(4):36-39(in Chinese).
[8]赵玉磊,郭宝龙,闫允一.电容层析成像技术的研究进展与分析[J].仪器仪表学报,2012,33(8):1909-1920.Zhao Yulei,Guo Baolong,Yan Yunyi.Latest develpoment and analysis of electrical capacitance tomography technology[J].Chinese Journal of Scientific Instrument,2012,33(8):1909-1920(in Chinese).
[9]郭志恒,律德才,邵富群.基于差分灵敏度模型的电容层析成像图像重建方法[J].中国电机工程学报,2012,32(23):75-82.Guo Zhiheng,LüDecai,Shao Fuqun.Image reconstruction method for electrical capacitance tomography based on the difference sensitivity model[J].Proceedings of the CSEE,2012,32(23):75-82(in Chinese).
[10]Xue Qian,Wang Huaxiang,Cui Ziqiang,et al.Electrical capacitance tomography using an accelerated proximal gradient algorithm[J].Review of Scientific Instruments,2012,83(4):1-7.
[11]陈德运,高明,李伟,等.新型ECT数据采集系统设计与实现[J].电机与控制学报,2013,17(5):87-92.Chen Deyun,Gao Ming,Li Wei,et al.Design and implementation of data acquisition system for the electrical capacitance tomography[J].Electric Machines and Control,2013,17(5):87-92(in Chinese).
[12]王化祥,黄文瑞,范文茹.三维电阻抗成像的测量模式[J].天津大学学报,2012,45(8):729-734.Wang Huaxiang,Huang Wenrui,Fan Wenru.Measurement pattern for 3D electrical impedance tomography[J].Journal of Tianjin University,2012,45(8):729-734(in Chinese).
[13]范文茹,王化祥,郝魁红.基于两步迭代TV正则化的电阻抗图像重建算法[J].仪器仪表学报,2012,33(3):625-630.Fan Wenru,Wang Huaxiang,Hao Kuihong.Two-step iterative TV regularization algorithm for image reconstruction of electrical impedance tomography[J].Chinese Journal of Scientific Instrument,2012,33(3):625-630(in Chinese).
[14]范文茹.医学电阻抗成像算法研究[D].天津:天津大学电气与自动化工程学院,2008.Fan Wenru.Research on Image Reconstruction Algorithm Based on Medical Electrical Impedance Tomography[D].Tianjin:School of Electrical Engineering and Automation,Tianjin University,2008(in Chinese).
[15]张玲玲,王化祥,范文茹.基于1范数的电阻层析成像图像重建算法[J].天津大学学报,2011,44(9):786-790.Zhang Lingling,Wang Huaxiang,Fan Wenru.Image reconstruction algorithm based on 1-norm for electrical resistance tomography[J].Journal of Tianjin University,2011,44(9):786-790(in Chinese).
[16]Dong Feng,Xu Yanbin.Application of electrical resistance tomography in two-phase flow measurement[J].Journal of Engineering Thermophysics,2006,27(5):791-794.
[17]李守晓,王化祥,范文茹,等.基于三维模型的改进正则化ERT成像算法[J].天津大学学报,2012,45(3):215-220.Li Shouxiao,Wang Huaxiang,Fan Wenru,et al.Improved regularization reconstruction algorithm based on3D model for ERT system[J].Journal of Tianjin University,2012,45(3):215-220(in Chinese).
[18]肖理庆,王化祥,韩成春.一种新型拓扑结构的电阻层析成像有限元模型[J].中国电机工程学报,2011,31(20):100-106.Xiao Liqing,Wang Huaxiang,Han Chengchun.A new topology structure finite element model of electrical resistance tomography system[J].Proceedings of the CSEE,2011,31(20):100-106(in Chinese).
[19]Daily W,Ramirez A.Electrical resistance tomography[J].Society of Exploration Geophysicists,2004,23(5):438-442.
[20]陈晓艳,张静.采用阈值修正法改善电阻抗图像质量[J].中国生物医学工程学报,2011,30(4):481-486.Chen Xiaoyan,Zhang Jing.Using threshold correction method to improve the image quality of EIT[J].Chinese Journal of Biomedical Engineering,2011,30(4):481-486(in Chinese).
[21]董峰,赵佳,许燕斌,等.用于电阻层析成像的快速自适应硬阈值算法[J].天津大学学报:自然科学与工程技术版,2015,48(4):305-310.Dong Feng,Zhao Jia,Xu Yanbin,et al.A fast adaptive iterative hard threshold algorithm for electrical resistance tomography[J].Journal of Tianjin University:Science and Technology,2015,48(4):305-310(in Chinese).
[22]肖理庆,王化祥,徐晓菊.改进牛顿-拉夫逊电阻层析成像图像重建算法[J].中国电机工程学报,2012,32(8):91-97.Xiao Liqing,Wang Huaxiang,Xu Xiaoju.Improved Newton-Raphson algorithm for electrical resistance tomography image reconstruction[J].Proceedings of the CSEE,2012,32(8):91-97(in Chinese).