This work implements and numerically tests the direct reconstruction algorithm introduced in [Garde & Hyv\"onen, 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.

翻译：本研究实现并数值测试了Garde与Hyvönen（SIAM J. Math. Anal., 2024）提出的二维线性化电阻抗成像直接重建算法。尽管该算法最初针对线性化场景设计，但通过数值实验验证了其在输入数据为对应电流-电压边界算子变化量时的功能有效性。数值研究中同时考虑了理想连续模型与实用完整电极模型的测量方案，测试区域包括单位圆盘与凸多边形。算法正则化处理及其与截断线性化前向映射奇异值分解的关联是重点关注的课题，此外还深入探讨了基于电导率泽尔尼克多项式基函数特性产生的显式三角结构。