Electrical impedance tomography for piecewise constant domains using boundary element shape-based inverse solutions
Electrical impedance tomography for piecewise constant domains using boundary element shape-based inverse solutions
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DOI：
10.1109/tmi.2006.887367
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发表时间：
2007-05-01
影响因子：
10.6
通讯作者：
Brooks, Dana H.
中科院分区：
文献类型：
--
作者：
Babaeizadeh, Saeed;Brooks, Dana H.
基于形状的解决方案最近受到关注，某些不适定的反问题。它们的优点包括隐式施加相关的约束和减少未知数的数量，特别是重要的非线性不适定问题。我们将基于形状的方法应用于电流注入电阻抗断层成像（EIT）重建。我们采用边界元法（BEM）为基础的解决方案EIT。我们介绍了两种形状模型，一个基于修改的B样条，另一个基于球谐函数，形状的边界元建模。这些方法使我们能够参数化的几何形状的电导率不均匀性的内部的体积。我们假设分段常数不均匀性的一般形状是已知的，但它们的电导率和它们的确切位置和形状是未知的。我们还假设内部电导率分布是分段恒定的，这意味着每个区域具有恒定的电导率。我们提出并测试了三种不同的正则化技术，用于任何形状模型。我们的方法的性能示出通过模拟在数字躯干模型和幻影实验时，有一个单一的内部对象。我们观察到，在噪声环境中，无论是模拟噪声还是真实的噪声源的实验研究中，我们都得到了合理的重建。由于现代EIT仪器中预期的信噪比（SNR）高于本研究中使用的信噪比，因此这些重建方法在实践中可能是有用的。
Shape-based solutions have recently received attention for certain ill-posed inverse problems. Their advantages include implicit imposition of relevant constraints and reduction in the number of unknowns, especially important for nonlinear ill-posed problems. We apply the shape-based approach to current-injection electrical impedance tomography (EIT) reconstructions. We employ a boundary element method (BEM) based solution for EIT. We introduce two shape models, one based on modified B-splines, and the other based on spherical harmonics, for BEM modeling of shapes. These methods allow us to parameterize the geometry of conductivity inhomogeneities in the interior of the volume. We assume the general shape of piecewise constant inhomogeneities is known but their conductivities and their exact location and shape is not. We also assume the internal conductivity profile is piecewise constant, meaning that each region has a constant conductivity. We propose and test three different regularization techniques to be used with either of the shape models. The performance of our methods is illustrated via both simulations in a digital torso model and phantom experiments when there is a single internal object. We observe that in the noisy environment, either simulated noise or real sources of noise in the experimental study, we get reasonable reconstructions. Since the signal-to-noise ratio (SNR) expected in modern EIT instruments is higher than that used in this study, these reconstruction methods may prove useful in practice.