对称性分析在单目标电阻抗成像中的应用

The Application of Symmetry Analysis in Electrical Impedance Tomography with Single Target

摘要: 为了改进现有的电阻抗成像算法，同时体现物理学的应用价值，本文利用对称性分析方法研究了单目标电阻抗成像问题。采用Comsol multiphysics 4.3a设计了薄圆盘实验系统，共有16个电极，以直径的端点为固定电流的输入和输出点，分析了7组关于输入输出电流方向对称点之间的电势差，讨论了单目标小圆圆心的位矢和半径与7组对称点电势差的关系。根据对称性分析可以很快确定小圆圆心位矢的区域在哪个π/8圆心角，这对静态电阻抗成像算法的初值选取具有重要意义；目标小圆圆心位矢、半径对7组对称点电势差的影响有较大差异，根据这些差异可以消除一部分关于小圆圆心位矢和半径的不确定性，对提高成像质量和成像速度有重要的参考价值；此外，对称性分析的方法对于只需要定性判断“有无成像目标”具有决定性的意义。

Abstract: In order to improve the present algorithm of electrical impedance tomography and develop the application value of physics, the symmetry analysis is used to study the electrical impedance to-mography with single target. Comsol multiphysics 4.3a is used to design a thin disc experimental system with 16 electrodes, the current is in- and out-put from the endpoints of one diameter, 7 potential differences of symmetry points that correspond to the current diameter are analyzed and their relation with the vector position and radius of the target small circle’s center are also discussed. Using symmetry analysis can determine the vector position of the small circle’s center and its radius in which π/8 central angle, this is very important for the initial value choosing of static electrical impedance tomography algorithm; the vector position of target circle’s center and its radius have different effect to the 7 potential difference and these different effect can be used to remove some uncertainty about to determine the vector position of target circle’s center and its radius, this point has important reference value for improving the imaging quality and velocity; and the symmetry analysis is decisive for those only need judge “yes or no” cases.