This work considers the optimization of electrode positions in head imaging by electrical impedance tomography. The study is motivated by maximizing the sensitivity of electrode measurements to conductivity changes when monitoring the condition of a stroke patient, which justifies adopting a linearized version of the complete electrode model as the forward model. The algorithm is based on finding a (locally) A-optimal measurement configuration via gradient descent with respect to the electrode positions. The efficient computation of the needed derivatives of the complete electrode model is one of the focal points. Two algorithms are introduced and numerically tested on a three-layer head model. The first one assumes a region of interest and a Gaussian prior for the conductivity in the brain, and it can be run offline, i.e., prior to taking any measurements. The second algorithm first computes a reconstruction of the conductivity anomaly caused by the stroke with an initial electrode configuration by combining lagged diffusivity iteration with sequential linearizations, which can be interpreted to produce an approximate Gaussian probability density for the conductivity perturbation. It then resorts to the first algorithm to find new, more informative positions for the available electrodes with the constructed density as the prior.

翻译：本文探讨了电阻抗层析成像中头部成像电极位置的优化问题。研究旨在最大化电极测量对脑卒中患者状态监测过程中电导率变化的灵敏度，因此采用完整电极模型的线性化版本作为正演模型。该算法基于通过电极位置的梯度下降法寻找（局部）A-最优测量配置，其中完整电极模型所需导数的有效计算是研究重点之一。本文提出两种算法，并在三层头部模型上进行了数值测试。第一种算法假设关注区域及脑内电导率服从高斯先验分布，可离线运行（即在获取任何测量数据前执行）。第二种算法首先通过组合滞后扩散迭代与序贯线性化方法，利用初始电极配置重建脑卒中导致的电导率异常，该方法可解释为生成电导率扰动的近似高斯概率密度函数。随后，该算法以该密度函数作为先验分布，采用第一种算法为可用电极寻找信息量更丰富的新位置。