基于线性化的直接重建用于电阻抗断层成像的三角Zernike分解
Linearization-based direct reconstruction for EIT using triangular Zernike decompositions
AI总结：
本文提出了一种基于三角Zernike分解的线性化直接重建算法，用于电阻抗断层成像的数值测试与分析。
摘要：
本工作实现了并数值测试了[Garde & Hyvönen, SIAM J. Math. Anal., 2024]中提出的直接重建算法，用于二维线性化电阻抗断层成像。尽管该算法最初是为线性化设置设计的，我们通过数值测试展示了当输入数据为相应电流-电压边界算子的变化时，该算法的功能性。数值研究中考虑了理想连续模型和实际完整电极模型的测量，所研究的域为单位圆或凸多边形。特别关注于正则化该算法及其与截断线性化正向映射的奇异值分解以及源自所用Zernike多项式基函数性质的显式三角结构之间的联系。
英文摘要：
This work implements and numerically tests the direct reconstruction algorithm introduced in [Garde & Hyvönen, SIAM J. Math. Anal., 2024] for two-dimensional linearized electrical impedance tomography. Although the algorithm was originally designed for a linearized setting, we numerically demonstrate its functionality when the input data is the corresponding change in the current-to-voltage boundary operator. Both idealized continuum model and practical complete electrode model measurements are considered in the numerical studies, with the examined domain being either the unit disk or a convex polygon. Special attention is paid to regularizing the algorithm and its connections to the singular value decomposition of a truncated linearized forward map, as well as to the explicit triangular structures originating from the properties of the employed Zernike polynomial basis for the conductivity.
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