A direct reconstruction algorithm for complex conductivities in W2,∞ (Ω), where Ω is a bounded, simply connected Lipschitz domain in ℝ2, is presented. The framework is based on the uniqueness proof by Francini [Inverse Problems 20 2000], but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.

中文翻译：

---

用于恢复二维复杂电导率的直接 D-bar 重建算法

提出了一种用于 W2,∞ (Ω) 中复杂电导率的直接重建算法，其中 Ω 是 ℝ2 中的有界、简单连接的 Lipschitz 域。该框架基于 Francini [Inverse Problems 20 2000] 的唯一性证明，但该工作中不存在将 Dirichlet-to-Neumann 与散射变换和指数增长解相关的方程，而是从此处导出的。该算法构成了第一个用于重建二维电导率和介电常数的 D-bar 方法。包括在器官边界处具有不连续性的数值模拟胸部体模的重建。