Conformal uniqueness results in anisotropic electrical impedance imaging
Conformal uniqueness results in anisotropic electrical impedance imaging
复制标题
共形的独特性导致各向异性电阻抗成像
DOI：
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发表时间：
1997
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通讯作者：
W. Lionheart
中科院分区：
文献类型：
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作者：
W. Lionheart
在两种不同的假设下，给出了各向异性电导率反边值问题（或各向异性电阻抗成像重建问题）的几何形式，并证明了其唯一性.这些结果中的第一个依赖于由边界测量确定的电导率，直到边界上的一个单形固定点，这已经由Lee和Uhlmann在三维和更高维度上的分析电导率以及西尔维斯特在接近常数的电导率中证明。然后利用G-结构的装置证明了黎曼流形上固定边界上所有点的共形映射必定是恒等式。第二种方法，证明了结果的分段解析范畴，是一个简单的扩展工作的科恩和Vogelius的各向同性问题。
The anisotropic conductivity inverse boundary value problem (or reconstruction problem for anisotropic electrical impedance tomography) is presented in a geometric formulation and a uniqueness result is proved, under two different hypotheses, for the case where the conductivity is known up to a multiplicative scalar field. The first of these results relies on the conductivity being determined by boundary measurements up to a diffeomorphism fixing points on the boundary, which has been shown for analytic conductivities in three and higher dimensions by Lee and Uhlmann and for conductivities close to constant by Sylvester. The apparatus of G-structures is then used to show that a conformal mapping of a Riemannian manifold which fixes all points on the boundary must be the identity. A second approach, which proves the result in the piecewise analytic category, is a straightforward extension of the work of Kohn and Vogelius on the isotropic problem.