平面内不规则电导率的重建
Reconstruction of less regular conductivities in the plane
摘要：
研究了如何从物体边界上的静电测量数据重建物体各向同性电导率分布$γ$的电导率反问题。本文给出了由$\partial \Om.$上的Dirichlet到Neumann映射在平面域$Ω$上精确重建电导率$γ\in C^{1+ε}(\ol \Om)$的算法，从而改进了以往的重建结果.所使用的方法依赖于一个众所周知的一阶系统，其中的$\ol\partial$ -方法的逆散射理论可以应用。
英文摘要：
We study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution $γ$ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction algorithm for the conductivity $γ\in C^{1+ε}(\ol \Om)$ in the plane domain $Ω$ from the associated Dirichlet to Neumann map on $\partial \Om.$ Hence we improve earlier reconstruction results. The method used relies on a well-known reduction to a first order system, for which the $\ol\partial$-method of inverse scattering theory can be applied.
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