论文标题
2D和3D域中EIT最佳控制问题的离散和收敛性
Discretization and Convergence of the EIT Optimal Control Problem in 2D and 3D Domains
论文作者
论文摘要
我们根据给定电极电流的$ M $电极上的边界电压测量$ M $电极的测量，考虑了恢复体内电导率和电势的逆电阻抗层析成像（EIT）问题。在最佳控制框架中提出了变异公式，在该框架中，电导率和边界电压是控制参数，而成本函数是从给定电流模式和从测量值的边界电极电压发出的边界电极电流的范围下降。 EIT最佳控制问题使用有限差异的方法完全离散。引入了新的Sobolev-Hilbert空间，并在2维和3维域中的功能和控制方面证明了有限维最佳控制问题对EIT系数最佳控制问题的收敛性。
We consider Inverse Electrical Impedance Tomography (EIT) problem on recovering electrical conductivity and potential in the body based on the measurement of the boundary voltages on the $m$ electrodes for a given electrode current. The variational formulation is pursued in the optimal control framework, where electrical conductivity and boundary voltages are control parameters, and the cost functional is the norm declinations of the boundary electrode current from the given current pattern and boundary electrode voltages from the measurements. EIT optimal control problem is fully discretized using the method of finite differences. New Sobolev-Hilbert space is introduced, and the convergence of the sequence of finite-dimensional optimal control problems to EIT coefficient optimal control problem is proved both with respect to functional and control in 2- and 3-dimensional domains.
