论文标题
通过二维电阻抗扫描中的电极数据模仿相对连续测量
Mimicking relative continuum measurements by electrode data in two-dimensional electrical impedance tomography
论文作者
论文摘要
本文介绍了一种建设性方法，用于根据源自点电极模型或完整电极模型的数据近似二维电阻断层扫描中的相对连续测量。相应的近似误差的上限明确取决于所使用的电极的数量（和大小）以及模仿的连续电流的规则性。特别是，如果输入电流和对象边界是无限光滑的，则与点电极模型相关的差异比电极数量的任何负功率快于零。结果首先是通过三角插值和正交规则证明了单位磁盘的，随后将它们扩展到更通用的域，借助整形型映射。
This paper introduces a constructive method for approximating relative continuum measurements in two-dimensional electrical impedance tomography based on data originating from either the point electrode model or the complete electrode model. The upper bounds for the corresponding approximation errors explicitly depend on the number (and size) of the employed electrodes as well as on the regularity of the continuum current that is mimicked. In particular, if the input current and the object boundary are infinitely smooth, the discrepancy associated with the point electrode model converges to zero faster than any negative power of the number of electrodes. The results are first proven for the unit disk via trigonometric interpolation and quadrature rules, and they are subsequently extended to more general domains with the help of conformal mappings.
