通过考虑线圈中的趋肤效应和邻近效应求解 MIT 逆问题
Solving the MIT Inverse Problem by Considering Skin and Proximity Effects in Coils
AI总结：
针对 MIT 低电导率重建中线圈趋肤与邻近效应被忽略的问题，本文改进正演模型并结合自适应正则化 Gauss-Newton 算法，在二维 8 线圈系统中验证其对绝对电导率重建的关键作用。
摘要：
本文提出了一种改进技术，通过考虑线圈中的趋肤效应和邻近效应来求解磁感应断层成像（MIT）中的逆问题。MIT 是一种非接触、无创且低成本的成像方式，用于获取物体内部的电导率分布。由于测量信号本身较弱，且重建问题具有高度非线性和不适定性，因此利用 MIT 重建低电导率分布需要更精确的技术。以往的 MIT 逆问题研究在正演方法中忽略了线圈内部的趋肤效应和邻近效应。本文中，改进技术将这些效应纳入正演方法。此外，该技术采用正则化 Gauss-Newton 算法重建电导率分布。正则化参数通过一种自适应方法获得，该方法使用两个输入参数：一个系数和一个初始电导率分布。新的 Jacobian 矩阵基于标准技术计算。为了在具有低电导率区域的潜在医学和工业应用中比较早期正演方法与改进正演方法，本文对一个二维 8 线圈 MIT 系统进行建模，并对合成模型体模执行图像重建。结果表明，使用改进的正演方法对于重建绝对电导率值至关重要。
英文摘要：
This paper presents an improved technique for solving the inverse problem in magnetic induction tomography (MIT) by considering skin and proximity effects in coils. MIT is a non-contact, noninvasive, and low-cost imaging modality for obtaining the distribution of conductivity inside an object. Reconstruction of low conductivity distribution by MIT requires more accurate techniques since measured signals are inherently weak and the reconstruction problem is highly nonlinear and ill-posed. Previous MIT inverse problem studies have ignored skin and proximity effects inside coils in the forward method. In this article, the improved technique incorporates these effects in the forward method. Furthermore, it employs the regularized Gauss-Newton algorithm to reconstruct the conductivity distribution. The regularization parameter is obtained by an adaptive method using the two input parameters: a coefficient and an initial conductivity distribution. The new Jacobian matrix is computed based on a standard technique. To compare the early and improved forward methods in possible medical and industrial applications with low conductivity regions, a 2D 8-coil MIT system is modeled, and image reconstruction is performed for synthetic phantoms. Results show that it is crucial to use the improved forward method for the reconstruction of the absolute conductivity values.
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