Babaeizadeh Saeed, Brooks Dana H
Advanced Algorithm Research Center, Philips Medical Systems, Thousand Oaks, CA 91320, USA.
IEEE Trans Med Imaging. 2007 May;26(5):637-47. doi: 10.1109/TMI.2006.887367.
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.
基于形状的解决方案最近在某些不适定逆问题上受到关注。它们的优点包括隐式施加相关约束以及减少未知数的数量，这对于非线性不适定问题尤为重要。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。我们采用基于边界元法（BEM）的EIT解决方案。我们引入两种形状模型，一种基于修正的B样条，另一种基于球谐函数，用于形状的BEM建模。这些方法使我们能够对体积内部电导率不均匀性的几何形状进行参数化。我们假设分段常数不均匀性的一般形状是已知的，但它们的电导率以及它们的确切位置和形状未知。我们还假设内部电导率分布是分段常数的，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，可与任何一种形状模型一起使用。当存在单个内部物体时，通过在数字躯干模型中的模拟和体模实验说明了我们方法的性能。我们观察到，在有噪声的环境中，无论是模拟噪声还是实验研究中的实际噪声源，我们都能得到合理的重建结果。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，这些重建方法在实际中可能会证明是有用的。
