北京生物医学工程

离散化误差对二维EIT影响的初步定量研究

Preliminary quantitative study on influence of FEM discretization error on EIT forward and inverse problem

作者：吴克坚付峰赵清波刘锐岗陶峰徐清华杨继庆董秀珍

单位：                      第四军医大学生物医学工程学院数理教研室(西安710032)        

关键词：电阻抗断层成像；图像重建；有限元法；模型误差

分类号：

出版年·卷·期（页码）：2013·32·3（221-225）

摘要：

目的结合具体重建算法，定量讨论有限元离散化误差对正逆问题的影响。方法利用软件NETGEN产生7个不同剖分规模的圆域模型，以其中最密剖分模型为参考，讨论其他模型的边界电压误差，然后提出重建图像质量函数D、结构相似度SSIM和误差总和TE三种重建图像评价指标，对无噪声和含有不同信噪比噪声两种情况的NOSER算法重建图像进行了比较。结果在无噪声和噪声信噪比不太小 (>35dB) 的仿真实验中，剖分愈密成像质量愈高。当剖分规模达到一定程度时，图像质量提高幅度有限。结论有限元离散化误差对于EIT问题至关重要，对于NOSER这种线性近似的非迭代算法，圆域模型选择中等剖分规模(如2000～3000个单元)即可达到很高的精度。

Objective The influence of FEM discretization error on EIT forward and inverse problem was quantitatively studied with specific algorithms. Methods Circular models of 7 different meshing scales were generated by using NETGEN. The boundary voltage errors of other meshes were studied by using the mesh with the highest resolution as the reference. Three reconstruction evaluation indexes were proposed to compare the NOSER reconstruction images with and without noises of different SNR：reconstruction quality function D，structural similarity image measurement (SSIM) and total error (TE). Results In simulations where there was no noise or noise of SNR bigger than 35dB，the more the number of elements and nodes was，the finer the reconstruction images were. When the meshing scale reached a certain degree，the improvement of the reconstruction was limited. Conclusions The FEM discretization error is crucial to EIT. For non-iterative algorithms with linear approximation such as NOSER，moderate meshing scale (2000-3000 elements) of circular model satisfies the accuracy requirement.

参考文献：

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