|
|
|
| Improved Tikhonov Regularization Method for Image Reconstruction |
| WEN Li-mei,ZHOU Miao-miao,LI Ming,MA Min |
| College of Electronic Information and Automation, Civil Aviation University of China,Tianjin 300300, China |
|
|
|
|
Abstract Tikhonov regularization method can resolve the ill-posedness of the inverse problem and balance the stability and accuracy of the solution in electrical capacitance tomography image reconstruction. However, its effectiveness can be seriously affected by the gross error of measurement data. Improved Tikhonov regularization method combines 2-norm and robust estimation, substitute a slower-growing Cauchy function for the quadratic sum in the least square method to further improve the robustness and adaptability of least square estimation. The effectiveness of the developed method is verified by COMSOL and MATLAB software. Reconstruction results demonstrate that the improved Tikhonov regularization method can effectively reduce influence of the gross error and improve image reconstruction accuracy and spatial resolution.
|
|
Received: 13 March 2017
Published: 05 September 2018
|
|
|
|
|
|
［1］Wilcox M, Ransom D, Henry M, et al. Engine Distress Detection in Gas Turbines with Electrostatic Sensors ［C］//ASME Turbo Expo 2010: Power for Land, Sea, and Air. Glasgow, UK:International Gas Turbine Institute, 2010:39-51.
［2］陆耿, 彭黎辉, 姚丹亚, 等. 电容层析成像系统的实用化设计［J］. 计量学报, 2004,25(3):241-243.
［3］李耀华. 静电感应技术在航空发动机气路状态监测上的应用研究［D］. 南京:南京航空航天大学,2011.
［4］Fisher C E. Gas path debris monitoring-a 21st century PHM tool ［J］. IEEE Aerospace Conference Proceedings, 2000, 6(4):441-448.
［5］李利品, 党瑞荣, 黄燕群. 层析成像技术在多相流中的研究动态［J］. 地球物理学进展, 2012, 27(2):651-659.
［6］张立峰,王化祥. 一种修正的电阻层析成像Landweber迭代算法［J］. 计量学报, 2016,37(3): 271-274.
［7］马敏, 高振幅, 王化祥. 基于BP神经网络的ECT图像重建算法［J］. 计量学报, 2013, 34(6):524-528.
［8］马敏, 王化祥, 张炜宇. 数字化电容层析成像系统［J］. 计量学报, 2007, 28(3):253-256.
［9］张立峰, 刘晶, 田沛. 一种电容层析成像系统电极组合激励测量方法［J］. 计量学报, 2017, 38(4): 469-472.
［10］马敏, 王伯波, 闫超奇, 等. 基于旋转电极的电容层析成像技术图像融合算法［J］. 计量学报, 2018, 39(1): 43-46.
［11］Liu J Z, Liu L, Zhang W B, et al. A novel combined regularization algorithm of total variation and Tikhonov regularization for open electrical impedance tomography ［J］. Physiological Measurement, 2013,34(7):823-838.
［12］雷兢. 多相流的电容层析成像图像重建研究［D］. 北京:中国科学院工程物理研究所, 2008.
［13］Hebert T,Leahy R . A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors［J］. IEEE Transactions on Medical Imaging, 1989,8(2):194-202.
［14］Powrie H E G, Fisher C E. Engine health monitoring: Towards total prognostics ［J］. IEEE Aerospace Conference Proceedings,1999,3(7):11-20.
［15］Powrie H E G, Fisher C E. Monitoring of foreign objects into the intake of a gas turbine aero-engine［C］// International Conference on Condition Monitoring Proceedings. Swansea, UK, 1999, 175-190.
［16］马敏, 张彩霞, 姬晶晶, 等. 改进的共轭梯度算法的图像重建算法［J］. 计量学报, 2013, 34(1):27-30. |
|
|
|
2018, Vol. 39 
