Engineering School, Kinneret College on the Sea of Galilee, Israel.
IEEE Trans Biomed Eng. 2010 May;57(5):1227-33. doi: 10.1109/TBME.2009.2038168. Epub 2010 Feb 5.
Image reconstruction in electrical impedance tomography is, generally, an ill-posed nonlinear inverse problem. Regularization methods are widely used to ensure a stable solution. Herein, we present a case study, which uses a novel electrical impedance tomography method for reconstruction of layered biological tissues with piecewise continuous plane-stratified profiles. The algorithm implements the recently proposed reconstruction scheme for piecewise constant conductivity profiles, utilizing Legendre expansion in conjunction with improved Prony method. It is shown that the proposed algorithm is capable of successfully reconstructing piecewise continuous conductivity profiles with moderate slop. This reconstruction procedure, which calculates both the locations and the conductivities, repetitively provides inhomogeneous depth discretization, i.e., the depths grid is not equispaced. Incorporation of this specific inhomogeneous grid in the widely used mean least square reconstruction procedure results in a stable and accurate reconstruction, whereas, the commonly selected equispaced depth grid leads to unstable reconstruction. This observation establishes the main result of our investigation, highlighting the impact of physical phenomenon (the image series expansion) on electrical impedance tomography, leading to a physically motivated stabilization of the inverse problem, i.e., an inhomogeneous depth discretization renders an inherent regularization of the mean least square algorithm. The effectiveness and the significance of inhomogeneous discretization in electrical impedance tomography reconstruction procedure is further demonstrated and verified via numerical simulations.
电阻抗断层成像中的图像重建通常是一个不适定的非线性反问题。正则化方法被广泛用于确保稳定的解。本文提出了一种新的电阻抗断层成像方法，用于重建具有分段连续平面分层轮廓的分层生物组织。该算法实现了最近提出的用于分段常导率轮廓的重建方案，利用勒让德展开结合改进的普朗尼方法。结果表明，所提出的算法能够成功重建具有中等斜率的分段连续电导率轮廓。该重建过程可以同时计算位置和电导率，重复提供非均匀深度离散化，即深度网格不是等距的。在广泛使用的平均最小二乘重建过程中，将这种特殊的非均匀网格纳入其中会导致稳定而准确的重建，而通常选择的等距深度网格会导致不稳定的重建。这一观察结果确立了我们研究的主要结果，强调了物理现象（图像级数展开）对电阻抗断层成像的影响，导致逆问题的物理驱动稳定化，即非均匀深度离散化使得平均最小二乘算法固有正则化。通过数值模拟进一步证明和验证了电阻抗断层成像重建过程中不均匀离散化的有效性和重要性。
