电阻抗层析成像系统"软场"非线性特性 --基于统计的方法

基于图方法与均匀设计方法，分析了电阻抗层析成像系统中的非线性特性．定义了非线性度。研究了圆域内两子区域的参数变化。采用正态图及半正态图方法分析了5因子2水平的情形，采用8因子6水平进行均匀设计，“最坏”情形的非线性度为-93．265％，并采用基于灵敏度矩阵的双共轭梯度法进行图像重建．结果表明，由于灵敏度矩阵法将各区域的电导率变化与测量电压变化存在的非线性关系线性化，忽略了EIT系统中由于“软场”性质引起的耦合效应，导致图像质量降低及迭代次数不确定；由于不同子区域间的耦合效应，尽管控制迭代次数可实现部分补偿，但基于灵敏度定理的迭代重建算法仍有其局限性，难于重建精确图像．

Nonlinearity of "Soft" Field in Electrical Impedance Tomography System --Based on Statistical Methods

The nonlinearity in the electrical impedance tomography (EIT) system has been studied based on the graph method and the uniform design method. The nonlinearity degree is defined to analyze the case of two subareas with changed parameters in the circular area. The case of five factors at two levels is analyzed using normal and half-normal plots. The uniform design with eight factors at six levels is applied and the nonlinearity degree of the worst case is -93. 265%. Images are reconstructed based on the bi-conjugate gradients method with the sensitivity matrix. The results show that, since the sensitivity matrix linearizes the nonlinear relationship between the change of electrical potential on the measuring electrodes and the change of the electrical conductivity in a subarea, and the coupling effect caused by the property of soft field in the EIT system is neglected, the image quality is low and the iteration time is uncertain. As the coupling effect exists between different subareas in the EIT system, though it can be partially compensated by limiting the iteration times, the iterative algorithms based on sensitivity matrix have their intrinsic limitations, and do not pertain to exact image reconstruction.