Electrical impedance tomography and Calderon's problem

被引：274

作者：

Uhlmann, G. ^{[1
]}

机构：

[1] Univ Washington, Dept Math, Seattle, WA 98195 USA

来源：

INVERSE PROBLEMS | 2009年 / 25卷 / 12期

关键词：

INVERSE CONDUCTIVITY PROBLEM; BOUNDARY-VALUE PROBLEM; GEOMETRICAL-OPTICS SOLUTIONS; COMPLEX SPHERICAL WAVES; GLOBAL UNIQUENESS; GROWING SOLUTIONS; RECENT PROGRESS; NEUMANN MAP; CAUCHY DATA; RECONSTRUCTION;

D O I：

10.1088/0266-5611/25/12/123011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We survey mathematical developments in the inverse method of electrical impedance tomography which consists in determining the electrical properties of a medium by making voltage and current measurements at the boundary of the medium. In the mathematical literature, this is also known as Calderon's problem from Calderon's pioneer contribution (Calder on 1980 Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro, 1980) p 65 (Soc. Brasil. Mat.)). We concentrate this review around the topic of complex geometrical optics solutions that have led to many advances in the field. In the last section, we review some counterexamples to Calder on's problems that have attracted a lot of interest because of connections with cloaking and invisibility.

引用

页数：39

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