Study on the inverse problem of electrical impedance tomography based on self-diagnosis regularization_Journal of Biomedical Engineering

Authors：

 LI Xing ¹ , YANG Fan ¹ , YU Xiao ¹ , TIAN Hao ² , HU Jiayuan ³ , QIAN Zhouhai ²

1. State Key Laboratory of Power Transmission Equipment & System Security and New Technology, School of Electrical Engineering, Chongqing University, Chongqing 400044, P.R.China;
2. Hangzhou Yi Neng Electric Technology Co., Ltd., Hangzhou 310014, P.R.China;
3. Electric Power Science Research Institute of Zhejiang Electric Power Corporation, Hangzhou 310007, P.R.China;

Corresponding author：

LI Xing, Email: lx918star@163.com

Keywords：

electrical impedance tomography; inverse problem; regularization; mean square error; anti-noise ability

DOI：

10.7507/1001-5515.201708024

Video：

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Abstract Full text Figures/Tables Video References Cited by

The inverse problem of electrical impedance tomography (EIT) is seriously ill-posed, which restricts the clinical application of EIT. Regularization is an important numerical method to improve the stability of the EIT inverse problem as well as the resolution of the imaging. This paper proposes a self-diagnosis regularization method based on Tikhonov regularization and diagonal weight regularization method (DWRM). Firstly, the ill-posedness of the inverse problem is analyzed by sensitivity. Then, the performance of the self-diagnosis regularization is analyzed through the singular value theory. Finally, some simulated experiments including simulations and flume experiment are carried out and verify that the self-diagnosis regularization has better image quality and anti-noise ability than those of traditional regularization methods. The self-diagnosis regularization method weakens the ill-posedness of inverse problem of EIT and can prompt the practical application of EIT.

Citation： LI Xing, YANG Fan, YU Xiao, TIAN Hao, HU Jiayuan, QIAN Zhouhai. Study on the inverse problem of electrical impedance tomography based on self-diagnosis regularization. Journal of Biomedical Engineering, 2018, 35(3): 460-467. doi: 10.7507/1001-5515.201708024 Copy

1.	Holder D S. Electrical impedance tomography of global cerebral ischaemia with cortical or scalp electrodes in the anaesthetized rat. Clin Phys Physiol Meas, 1992, 13(1): 87-98.
2.	Heikkinen L M, Kourunen J, Savolainen T, et al. Real time three-dimensional electrical impedance tomography applied in multiphase flow imaging. Measurement Science and Technology, 2006, 17(8): 2083-2087.
3.	熊秀芳, 杨光, 张炜, 等. 基于电阻抗成像的食品中异物检测仿真研究. 中国科技论文, 2016, 11(02): 224-230.
4.	李英, 冀海峰, 黄志尧, 等. 电阻层析成像系统软场特性研究. 仪器仪表学报, 2002, 23(z1): 208-209.
5.	Novati P, Russo M R. A GCV based Arnoldi-Tikhonov regularization method. Bit Numerical Mathematics, 2014, 54(2): 501-521.
6.	Lei Jing, Liu Shi, Li Zhihong, et al. An image reconstruction algorithm based on the extended Tikhonov regularization method for electrical capacitance tomography. Measurement, 2009, 42(3): 368-376.
7.	Gonzalez G, Kolehmainen V, Seppanen A. Isotropic and anisotropic total variation regularization in electrical impedance tomography. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74(3):564-576.
8.	Clay M T, Ferree T C. Weighted regularization in electrical impedance tomography with applications to acute cerebral stroke. IEEE Trans Med Imaging, 2002, 21(6): 629-637.
9.	Vauhkonen M, Vadász D, Karjalainen P A, et al. Tikhonov regularization and prior information in electrical impedance tomography. IEEE Trans Med Imaging, 1998, 17(2): 285-293.
10.	郭荣, 房怀庆, 裘剡, 等. 基于 Tikhonov 正则化及奇异值分解的载荷识别方法. 振动与冲击, 2014, 33(6): 53-58.
11.	夏登俊. 电阻网络电流分配的能量损耗最小原理. 数学的实践与认识, 2004, 34(1): 7-12.
12.	黄卡玛, 赵翔. 电磁场中的逆问题及应用. 北京: 科学出版社, 2005: 34-36.
13.	Su Guanqun, Zhou Xiaolong, Wang Lijia, et al. An inversion method of 2D NMR relaxation spectra in low fields based on LSQR and L-curve. J Magn Reson, 2016, 265: 146-152.
14.	卢波. 病态问题的奇异值分解算法与比较. 测绘信息与工程, 2011, 36(4): 19-22.
15.	褚江, 陈强, 杨曦晨. 全参考图像质量评价综述. 计算机应用研究, 2014, 31(01): 13-22.

1. Holder D S. Electrical impedance tomography of global cerebral ischaemia with cortical or scalp electrodes in the anaesthetized rat. Clin Phys Physiol Meas, 1992, 13(1): 87-98.
2. Heikkinen L M, Kourunen J, Savolainen T, et al. Real time three-dimensional electrical impedance tomography applied in multiphase flow imaging. Measurement Science and Technology, 2006, 17(8): 2083-2087.
3. 熊秀芳, 杨光, 张炜, 等. 基于电阻抗成像的食品中异物检测仿真研究. 中国科技论文, 2016, 11(02): 224-230.
4. 李英, 冀海峰, 黄志尧, 等. 电阻层析成像系统软场特性研究. 仪器仪表学报, 2002, 23(z1): 208-209.
5. Novati P, Russo M R. A GCV based Arnoldi-Tikhonov regularization method. Bit Numerical Mathematics, 2014, 54(2): 501-521.
6. Lei Jing, Liu Shi, Li Zhihong, et al. An image reconstruction algorithm based on the extended Tikhonov regularization method for electrical capacitance tomography. Measurement, 2009, 42(3): 368-376.
7. Gonzalez G, Kolehmainen V, Seppanen A. Isotropic and anisotropic total variation regularization in electrical impedance tomography. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74(3):564-576.
8. Clay M T, Ferree T C. Weighted regularization in electrical impedance tomography with applications to acute cerebral stroke. IEEE Trans Med Imaging, 2002, 21(6): 629-637.
9. Vauhkonen M, Vadász D, Karjalainen P A, et al. Tikhonov regularization and prior information in electrical impedance tomography. IEEE Trans Med Imaging, 1998, 17(2): 285-293.
10. 郭荣, 房怀庆, 裘剡, 等. 基于 Tikhonov 正则化及奇异值分解的载荷识别方法. 振动与冲击, 2014, 33(6): 53-58.
11. 夏登俊. 电阻网络电流分配的能量损耗最小原理. 数学的实践与认识, 2004, 34(1): 7-12.
12. 黄卡玛, 赵翔. 电磁场中的逆问题及应用. 北京: 科学出版社, 2005: 34-36.
13. Su Guanqun, Zhou Xiaolong, Wang Lijia, et al. An inversion method of 2D NMR relaxation spectra in low fields based on LSQR and L-curve. J Magn Reson, 2016, 265: 146-152.
14. 卢波. 病态问题的奇异值分解算法与比较. 测绘信息与工程, 2011, 36(4): 19-22.
15. 褚江, 陈强, 杨曦晨. 全参考图像质量评价综述. 计算机应用研究, 2014, 31(01): 13-22.

Journal of Biomedical Engineering

Study on the inverse problem of electrical impedance tomography based on self-diagnosis regularization

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