梯度引导电学成像自适应网格生成方法

电学层析成像是一种观测场域内电导率分布的无损检测技术。有限元法是求解电学层析成像问题的常用方法。其作为线性化的近似方法，剖分单元的大小会影响有限元法求解的精度。更密的尺寸可以提高重建图像的空间分辨率，但会增加计算成本，同时未知量个数的增加会加剧逆问题的欠定性。针对上述问题，提出一种基于图像梯度的自适应网格生成方法。根据初始重建图像的梯度，自适应地提高内含物区域的网格密度，降低其他区域的网格密度，并对场域边界进行精确拟合来优化被测场域的网格剖分。通过仿真与实验研究对比分析了所提方法与常用网格剖分方法。结果表明，所提方法的重建结果图像误差平均降低15%,相关系数平均提高7%,因此所提方法在不显著增加或减少网格数的情况下，可以有效提高内含物的重建精度和图像重建质量。

Gradient guided adaptive mesh generation for image reconstruction of electrical tomography

Electrical tomography is a kind of non-destructive testing technique to image the conductivity distribution within the observation domain. The finite element method is commonly used to solve the inverse problem. The size of the mesh elements can affect the accuracy of the approximation method. The finer size is usually utilized to improve the spatial resolution of the reconstructed image. However, the computational cost will be increased, which makes the inverse problem more underdetermined since the number of unknowns is increased. To address this issue, an adaptive mesh generation method based on the image gradient is proposed to optimize mesh generation to improve the reconstructed accuracy on the premise of not significantly increasing ill-condition. According to the gradient of the initial reconstructed image, the proposed method optimizes the subdivision of the observation field by adaptively improving the mesh density of the inclusion region and reducing the mesh density of other regions. The commonly used mesh generation methods are used to compare with the proposed method. Simulation and experiments show that the reconstructed image error is reduced by 15% on average and the correlation coefficient is increased by 7% on average. Results show that the proposed mesh generation method can improve the reconstruction accuracy of inclusions and the image reconstruction quality, and reduce the calculation error without increasing the number of grids.