电阻抗断层成像中电极位置的优化
Optimizing electrode positions in electrical impedance tomography
摘要：
这项工作考虑基于关于电导率的可用先验信息在贝叶斯范式内找到电极的最佳位置;目的是放置电极，使得（离散化）电导率的后验密度，即，给定测量值的电导率的条件密度尽可能局部化。为了使这种方法在计算上可行，阻抗断层成像的完整电极前向模型围绕电导率的先验期望线性化，允许（近似）后验协方差阵的明确表示。两种方法被认为是：最小化的痕迹或后验协方差的行列式。所介绍的优化算法是最速下降型的，所需的梯度是根据完整电极模型的适当Fréchet导数计算的。通过二维数值实验证明了该方法的功能。
英文摘要：
This work considers finding optimal positions for the electrodes within the Bayesian paradigm based on available prior information on the conductivity; the aim is to place the electrodes so that the posterior density of the (discretized) conductivity, i.e., the conditional density of the conductivity given the measurements, is as localized as possible. To make such an approach computationally feasible, the complete electrode forward model of impedance tomography is linearized around the prior expectation of the conductivity, allowing explicit representation for the (approximate) posterior covariance matrix. Two approaches are considered: minimizing the trace or the determinant of the posterior covariance. The introduced optimization algorithm is of the steepest descent type, with the needed gradients computed based on appropriate Fréchet derivatives of the complete electrode model. The functionality of the methodology is demonstrated via two-dimensional numerical experiments.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
