This work introduces a method for preprocessing measurements of electrical impedance tomography to considerably reduce the effect uncertainties in the electrode contacts have on the reconstruction quality, without a need to explicitly estimate the contacts. The idea is to compute the Jacobian matrix of the forward map with respect to the contact strengths and project the electrode measurements and the forward map onto the orthogonal complement of the range of this Jacobian. Using the smoothened complete electrode model as the forward model, it is demonstrated that inverting the resulting projected equation with respect to only the internal conductivity of the examined body results in good quality reconstructions both when resorting to a single step linearization with a smoothness prior and when combining lagged diffusivity iteration with total variation regularization. The quality of the reconstructions is further improved if the range of the employed projection is also orthogonal to that of the Jacobian with respect to the electrode positions. These results hold even if the projections are formed at internal and contact conductivities that significantly differ from the true ones; it is numerically demonstrated that the orthogonal complement of the range of the contact Jacobian is almost independent of the conductivity parameters at which it is evaluated. In particular, our observations introduce a numerical technique for inferring whether a change in the electrode measurements is caused by a change in the internal conductivity or alterations in the electrode contacts, which has potential applications, e.g., in bedside monitoring of stroke patients. The ideas are tested both on simulated data and on real-world water tank measurements with adjustable contact resistances.

翻译：本研究提出一种电阻抗断层成像测量数据的预处理方法，该方法能显著降低电极接触不确定性对重建质量的影响，且无需显式估计接触参数。该方法的核心思想是计算前向映射关于接触强度的雅可比矩阵，并将电极测量数据与前向映射投影至该雅可比矩阵值域的正交补空间。以光滑化完整电极模型作为前向模型进行验证，结果表明：无论采用基于光滑先验的单步线性化方法，还是结合滞后扩散迭代与全变分正则化方法，仅针对被测物体内部电导率对投影后方程进行反演，均可获得高质量重建结果。若所采用的投影空间同时与电极位置雅可比矩阵的值域正交，重建质量可得到进一步提升。即使投影构建时所采用的内部电导率与接触电导率参数与真实值存在显著差异，上述结论依然成立；数值实验表明接触雅可比矩阵值域的正交补空间几乎独立于其计算时所采用的电导率参数。特别值得注意的是，本研究的观测结果提供了一种数值技术，可用于判断电极测量值的变化究竟源于内部电导率改变还是电极接触状态变化，该技术在临床床边监测（如中风患者监护）等领域具有潜在应用价值。本文通过模拟数据和可调接触电阻的真实水箱测量数据对相关理论进行了验证。