This paper presents a parametric level set-based reconstruction method for nonstationary applications using electrical impedance tomography (EIT). Due to relatively low signal-to-noise ratios in EIT measurement systems and the diffusive nature of EIT, the reconstructed images often suffer from low spatial resolution. In addressing these challenges, we propose a computationally efficient shape-estimation approach where the conductivity distribution to be reconstructed is assumed to be piecewise constant, and the region boundaries are assumed to be nonstationary in the sense that the characteristics of region boundaries change during measurement time. The EIT inverse problem is formulated as a state estimation problem in which the system is modeled with a state equation and an observation equation. Given the temporal evolution model of the boundaries and observation model, the objective is to estimate a sequence of states for the nonstationary region boundaries. The implementation of the approach is based on the finite-element method and a parametric representation of the region boundaries using level set functions. The performance of the proposed approach is evaluated with the simulated examples of thorax imaging, using noisy synthetic data and experimental data from a laboratory setting. In addition, robustness studies of the approach with respect to the modeling errors caused by inaccurately known boundary shape, non-homogeneous background and varying conductivity values of the targets are carried out and it is found that the proposed approach tolerates such kind of modeling errors, leading to good reconstructions in nonstationary situations.

中文翻译：

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使用基于参数水平集的扩展卡尔曼滤波器方法进行电阻抗断层扫描中的非平稳形状估计

本文提出了一种基于参数水平集的重建方法，用于使用电阻抗断层扫描 (EIT) 的非平稳应用。由于 EIT 测量系统中相对较低的信噪比和 EIT 的扩散性质，重建的图像通常会受到低空间分辨率的影响。为了解决这些挑战，我们提出了一种计算效率高的形状估计方法，其中假设要重建的电导率分布是分段常数，并且假设区域边界是非平稳的，因为区域边界的特征在测量时间内会发生变化. EIT 逆问题被表述为状态估计问题，其中系统用状态方程和观测方程建模。给定边界和观察模型的时间演化模型，目标是估计非平稳区域边界的状态序列。该方法的实现基于有限元方法和使用水平集函数的区域边界的参数表示。使用来自实验室环境的嘈杂合成数据和实验数据，通过胸部成像的模拟示例评估所提出方法的性能。此外，针对由不准确已知边界形状、非均匀背景和目标的不同电导率值引起的建模误差，对该方法进行了稳健性研究，发现所提出的方法可以容忍此类建模误差，