Rank analysis of the anisotropic inverse conductivity problem

Abascal, Juan Felipe P. J. and Lionheart, William R.B. (2004) Rank analysis of the anisotropic inverse conductivity problem. In: International Conference on Electrical Bioimpedance and Electrical Impedance Tomography, 20-24 June 2004, Gdansk, Poland..

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Abstract

Anisotropic conductivity arises in bio-medical EIT, for example in muscle tissue, however the anisotropic inverse conductivity problem can be solved uniquely only up to a diffeomorphism which fixes all points on the boundary. Although a scalar conductivity can be reconstructed from current and voltage measurements, extra information must be provided to uniquely recover the full symmetric tensor field in the anisotropic case. Rank analysis of the sensitivity matrix reveals that fixing the mesh a-priori selects one of the infinity of possible diffeomorphisms, but may lead to a wrong solution. Hence one should not attempt solving the problem for a fixed mesh, and we suggest a procedure to resolve the ambiguity by imposing some constraints which restore uniqueness of the solution.

Item Type:	Conference or Workshop Item (Paper)
Uncontrolled Keywords:	Electrical impedance tomography, anisotropy, Singular value decomposition
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 35 Partial differential equations MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis MSC 2010, the AMS's Mathematics Subject Classification > 78 Optics, electromagnetic theory
Depositing User:	Prof WRB Lionheart
Date Deposited:	15 Apr 2008
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1079

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