Tikhonov regularization based on second order derivative matrix  for electrical capacitance tomography image reconstruction

JIANG Peng; PENG Lihui; XIAO Deyun

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Tikhonov regularization based on second order derivative matrix for electrical capacitance tomography image reconstruction

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- Tikhonov regularization based on second order derivative matrix for electrical capacitance tomography image reconstruction
- CIESC Journal Issue 2, Pages: 405-409(2008)
- 作者机构：
  
  清华大学自动化系
- 作者简介：
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- Online First：05 February 2008，
  
  Published：05 February 2008
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JIANG Peng, PENG Lihui, XIAO Deyun. Tikhonov regularization based on second order derivative matrix for electrical capacitance tomography image reconstruction[J]. CIESC Journal, 2008, (2): 405-409.
DOI：

JIANG Peng, PENG Lihui, XIAO Deyun. Tikhonov regularization based on second order derivative matrix for electrical capacitance tomography image reconstruction[J]. CIESC Journal, 2008, (2): 405-409. DOI：

摘要

Tikhonov正则化方法是解决病态逆问题的常用方法，正则化项的引入能改善问题的病态性。利用Laplace算子对正则化项中所包含的图像信息进行锐化处理，可提高电容成像图像重建的质量。仿真结果表明，相对于标准形式的Tikhonov正则化方法，采用正则算子为二阶导数算子的正则化方法图像重建结果边缘及轮廓清晰，对于各种设定流型均具有良好的适应能力，且图像重建结果对初始设定解不敏感，图像重建结果质量更高。

Abstract

Tikhonov regularization method is widely used in certain inverse problems.A regularization term is introduced to lessen the ill-posedness in inverse problems.In order to improve the quality of image reconstruction for electrical capacitance tomography

a second order derivative operator is introduced to sharpen the reconstructed images.Simulation results show that

in comparison with standard Tikhonov regularization method

the method with the second order derivative operator for regularization provides reconstruction results with clearer contours.In addition

the method is adaptive to all test models and not sensitive to the initial solutions.

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