二维复电导率重建的直接D-bar重构算法
A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D
AI总结：
提出一种基于Francini唯一性证明的D-bar直接重构算法，用于从Dirichlet-to-Neumann数据重建二维有界Lipschitz域中的复电导率，并包含数值模拟的胸部体模重建结果。
摘要：
提出了一种针对$W^{2,\infty}(Ω)$中复电导率的直接重建算法，其中$Ω$是$\mathbb{R}^2$中有界、单连通的Lipschitz域。该框架基于Francini [Inverse Problems 20 2000]的唯一性证明，但该工作中未给出Dirichlet-to-Neumann映射与散射变换及指数增长解之间的关系，本文推导了这些关系。该算法构成了二维电导率和介电常数重建的首个D-bar方法。文中还包含了对器官边界处存在不连续性的数值模拟胸部体模的重建结果。
英文摘要：
A direct reconstruction algorithm for complex conductivities in $W^{2,\infty}(Ω)$, where $Ω$ is a bounded, simply connected Lipschitz domain in $\mathbb{R}^2$, 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
