Approximating idealized boundary data of electric impedance tomography by electrode measurements
Approximating idealized boundary data of electric impedance tomography by electrode measurements
复制标题
通过电极测量近似电阻抗断层扫描的理想化边界数据
DOI：
10.1142/s0218202509003759
复制
发表时间：
2009
影响因子：
3.5
通讯作者：
Nuutti Hyvönen
中科院分区：
文献类型：
--
作者：
Nuutti Hyvönen
在电阻抗层析成像中，人们试图从电流和电压的边界测量中恢复物体内部的空间导纳分布。在理论考虑中，通常假设可用的数据是无限维诺伊曼-狄利克雷映射，即假设可以使用任何边界电流并在物体边界上的任何地方测量相应的电势。然而，在实践中，数据由一个有限维算子组成，将电极电流映射到相应的电极电位。此外，测量结果还受到电极-物体界面处接触阻抗的影响。在本文中，我们证明了一个合适的非正交投影算子的引入，使得在平方可积函数的有界线性算子的拓扑中，通过其电极对偶来近似neumann - dirichlet映射成为可能，其差异线性地依赖于相邻电极中心之间的距离。特别是，在不假设电极覆盖所有目标边界的情况下证明了收敛性。理论结果得到了二维数值实验的补充。
In electric impedance tomography, one tries to recover the spatial admittance distribution inside a body from boundary measurements of current and voltage. In theoretical considerations, it is usually assumed that the available data is the infinite-dimensional Neumann-to-Dirichlet map, i.e. one assumes to be able to use any boundary current and measure the corresponding potential everywhere on the object boundary. However, in practice, the data consists of a finite-dimensional operator mapping the electrode currents onto the corresponding electrode potentials. What is more, the measurements are affected by the contact impedance at the electrode-object interfaces. In this paper, we show that the introduction of a suitable nonorthogonal projection operator makes it possible to approximate the Neumann-to-Dirichlet map by its electrode counterpart in the topology of bounded linear operators on square integrable functions, with the discrepancy depending linearly on the distance between centers of adjacent electrodes. In particular, convergence is proved without assuming that the electrodes cover all of the object boundary. The theoretical results are complemented by two-dimensional numerical experiments.