A Hybrid Segmentation and D-Bar Method for Electrical Impedance Tomography
A Hybrid Segmentation and D-Bar Method for Electrical Impedance Tomography
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DOI：
10.1137/15m1025992
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发表时间：
2015-06
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影响因子：
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通讯作者：
S. Hamilton;J. M. Reyes;S. Siltanen;Xiaoqun Zhang
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文献类型：
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作者：
S. Hamilton;J. M. Reyes;S. Siltanen;Xiaoqun Zhang
电阻抗层析成像（EIT）的正则化d柱法为直接求解全非线性反演问题提供了一种严格的数学方法，即不需要迭代。它是基于（非线性）频域的低通滤波。然而，由此产生的d条重建本质上是平滑的，导致边缘区分的丧失。本文提出了一种将d条法与全变分正则化的保边特性相结合的新方法。该方法还包括一种以D-bar法的关键函数（CGO解）为指导的数据驱动对比度调整技术。新的电视增强d条方法产生更清晰的边缘和改进的对比度重建。这是通过使用电视诱导边缘来增加非线性频域散射数据的截断半径，从而增加低通滤波器的半径来实现的。在数值模拟的含噪EIT数据和实测数据上对算法进行了验证。
The regularized D-bar method for electrical impedance tomography (EIT) provides a rigorous mathematical approach for solving the full nonlinear inverse problem directly, i.e., without iterations. It is based on a low-pass filtering in the (nonlinear) frequency domain. However, the resulting D-bar reconstructions are inherently smoothed, leading to a loss of edge distinction. In this paper, a novel method that combines a D-bar approach with the edge-preserving nature of total variation (TV) regularization is presented. The method also includes a data-driven contrast adjustment technique guided by the key functions (CGO solutions) of the D-bar method. The new TV-enhanced D-bar method produces reconstructions with sharper edges and improved contrast. This is achieved by using the TV-induced edges to increase the truncation radius of the scattering data in the nonlinear frequency domain, thereby increasing the radius of the low-pass filter. The algorithm is tested on numerically simulated noisy EIT data and d...