用于完整电极模型电阻抗断层成像的自适应Nesterov动量方法
Adaptive Nesterov Momentum Method for Electrical Impedance Tomography with the Complete Electrode Model
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中文总结 AI 辅助
该研究将自适应Nesterov动量方法应用于完整电极模型电阻抗断层成像，结合三类强凸惩罚项及伴随方程，在KIT4水箱数据上验证了其对实测数据的实际适用性。
中文摘要 AI 辅助
我们将自适应Nesterov动量（ANM）方法[30]应用于完整电极模型（CEM）下的电阻抗断层成像（EIT）问题。正问题在考虑有限电极尺寸、接触阻抗、绝缘间隙及无平均电压规范的变分CEM框架中构建；所得非线性逆问题采用统一的对偶转原始框架处理，结合三类强凸结构惩罚项：L2型惩罚项、促进与校准均匀背景稀疏偏差的L1型惩罚项，以及支持具有尖锐界面的近似分段常数电导率的TV型惩罚项，其中TV类采用平滑TV和Huber-TV两种形式实现。数据拟合残差梯度通过CEM伴随方程计算，并经Sobolev平滑稳定化处理。在对无物体测量得到的背景电导率和接触阻抗校准后，该方法在公开可用的KIT4水箱测量数据上进行评估，实验包含单目标、多目标、混合电导率及几何挑战性的体模配置。L2型惩罚项通常产生平滑但弥散的重建结果，L1型惩罚项得到更干净的背景但偶尔出现几何失真，平滑TV和Huber-TV惩罚项则提供更具空间一致性的定位，且在多数测试配置中表现出相似的重建行为。这些结果证明了自适应Nesterov框架对实测CEM-EIT数据的实际适用性。
英文摘要
We apply the adaptive Nesterov momentum (ANM) method [30] to electrical impedance tomography under the complete electrode model. The forward problem is formulated in the variational CEM setting, accounting for finite electrode size, contact impedance, insulating gaps, and the mean-free voltage gauge. The resulting nonlinear inverse problem is treated within a unified dual-to-primal framework using three classes of strongly convex structural penalties: an L2-type penalty, an L1-type penalty promoting sparse deviations from a calibrated homogeneous background, and a TV-type penalty favoring approximately piecewise-constant conductivities with sharp interfaces. The TV class is implemented using both smoothed TV and Huber-TV formulations. The data- misfit gradient is computed through CEM adjoint equations and stabilized by Sobolev smoothing. The method is evaluated on the publicly available KIT4 tank measurement data after calibration of the background conductivity and contact impedance from no-object measurements. The experiments include single, multiple, mixed-conductivity, and geometrically challenging phantom configurations. The L2-type penalty generally produces smooth but diffuse reconstructions, whereas the L1-type penalty yields cleaner backgrounds with occasional geometric distortion. The smoothed TV and Huber-TV penalties provide more spatially coherent localization and exhibit similar reconstruction behavior across most tested configurations. These results demonstrate the practical applicability of the adaptive Nesterov framework to measured CEM-EIT data.
