Premium
Uniqueness, Shape, and Dimension in EIT
Author(s) -
LIONHEART WILLIAM R. B.
Publication year - 1999
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1999.tb09495.x
Subject(s) - uniqueness , electrical impedance tomography , resistor , dimension (graph theory) , boundary (topology) , mathematical analysis , planar , mathematics , domain (mathematical analysis) , boundary value problem , inverse problem , electrical impedance , physics , computer science , pure mathematics , computer graphics (images) , quantum mechanics , voltage
A bstract : We briefly review the known mathematical results on uniqueness of solution in electrical impedance tomography (EIT). Generally, a real or complex conductivity is determined uniquely by complete boundary data. Uniqueness results are also known for planar resistor networks. However, it is common to make gross errors in the forward modeling of the electrical fields and this may result in no consistent solution. In particular, a two‐dimensional model is often used when data are collected from a three‐dimensional domain. The boundary shape is often inaccurately known, and commonly modeled by a circle. No model conductivity consistent with measured data exists when the dimension or the boundary shape is wrong.