电阻抗断层成像中电导率、边界形状和接触阻抗的同时重建
Simultaneous reconstruction of conductivity, boundary shape and contact impedances in electrical impedance tomography
摘要：
电阻抗断层成像（EIT）的目的是基于身体边界处的电流和电压测量来重建物理身体的内部电导率。在许多医学应用中，无法获得域边界的确切形状和接触阻抗。这是有问题的，因为即使是计算域的边界形状或接触阻抗值中的小误差也会在重建图像中产生大的伪影，这导致相关信息的丢失。提出了一种从EIT数据同时重建电导率、接触阻抗和边界形状的方法。该方法包括三个步骤：首先，未知的接触阻抗和各向异性电导率再现测量EIT数据在一个模型域计算。其次，使用等温坐标，构造变形，使电导率各向同性。最后一步使用保形变形使真实和重建的已知几何特性（如电极长度）的误差最小化。该方法的可行性说明与实验EIT数据，具有强大的和准确的重建的电导率和边界形状。
英文摘要：
The objective of electrical impedance tomography (EIT) is to reconstruct the internal conductivity of a physical body based on current and voltage measurements at the boundary of the body. In many medical applications the exact shape of the domain boundary and contact impedances are not available. This is problematic as even small errors in the boundary shape of the computation domain or in the contact impedance values can produce large artifacts in the reconstructed images which results in a loss of relevant information. A method is proposed that simultaneously reconstructs the conductivity, the contact impedances and the boundary shape from EIT data. The approach consists of three steps: first, the unknown contact impedances and an anisotropic conductivity reproducing the measured EIT data in a model domain are computed. Second, using isothermal coordinates, a deformation is constructed that makes the conductivity isotropic. The final step minimizes the error of true and reconstructed known geometric properties (like the electrode lengths) using conformal deformations. The feasibility of the method is illustrated with experimental EIT data, with robust and accurate reconstructions of both conductivity and boundary shape.
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