采用二阶导数阵作为正则化的电容成像图像重建算法

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。

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

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.