用于优化电阻抗断层成像协议的灵敏度分析
Sensitivity Analysis for Optimizing Electrical Impedance Tomography Protocols
AI总结：
本文提出用于电阻抗断层成像的灵敏度分析及协议优化方法，通过缩减模型空间维度并筛选高灵敏度正交向量，大幅提升反演速度与抗噪能力。
摘要：
电阻抗断层成像（Electrical impedance tomography, EIT）是一种无创成像方法，该方法根据预设的协议集在导电介质边界进行电学测量（得到数据），再通过反演绘制内部电导率分布图（即模型）。本文提出了一种灵敏度分析方法，以及相应的反演与协议优化方法，该方法推广了断层成像反演的准则，以最小化模型空间维度并最大化数据重要性。\n灵敏度向量被定义为线性化正问题中雅可比矩阵的行向量，用于将目标电导率特征从模型空间映射到数据空间；这些向量在模型空间中的体积外积被称为灵敏度平行多面体体积，可作为数据协议优化的品质因数。可基于先验信息定义能将模型空间精确约束到感兴趣特征的正交基函数。通过增加接触点数量来扩大可能测量值的数量Dmax，并将模型空间缩减为仅描述感兴趣特征的最少基函数数量M0，可识别出张成该模型空间、长度最大且正交性最强的M0 << Dmax个灵敏度向量。模型空间维度的降低将反演速度提升了数个数量级，且增强后的灵敏度可承受比标准协议高1000倍的噪声水平。
英文摘要：
Electrical impedance tomography (EIT) is a noninvasive imaging method whereby electrical measurements on the boundary of a conductive medium (the data) are taken according to a prescribed protocol set and inverted to map the internal conductivity (the model). This paper introduces a sensitivity analysis method and corresponding inversion and protocol optimization that generalizes the criteria for tomographic inversion to minimize the model-space dimensionality and maximize data importance. Sensitivity vectors, defined as rows of the Jacobian matrix in the linearized forward problem, are used to map targeted conductivity features from model-space to data-space, and a volumetric outer-product of these vectors in model-space called the sensitivity parallelotope volume provides a figure-of-merit for data protocol optimization. Orthonormal basis functions that accurately constrain the model-space to features of interest can be defined from a priori information. By increasing the contact number to expand the number of possible measurements Dmax, and by reducing the model-space to a minimal number M0 of basis functions that describe only the features of interest, the M0 << Dmax sensitivity vectors of greatest length and maximal orthogonality that span this model-space can be identified. The reduction in model-space dimensionality accelerates the inversion by several orders of magnitude, and the enhanced sensitivity can tolerate noise levels up to 1,000 times larger than standard protocols.
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