A two-step linear inversion of two-dimensional electrical conductivity

We introduce a novel approach to the inversion of two-dimensional distributions of electrical conductivity illuminated by line sources. The algorithm stems from the newly developed extended Born approximation (see J. Geophys. Res., vol.98, no.B2, p.1759, 1993), which sums in a simple analytical expr...

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Bibliographic Details
Published inIEEE transactions on antennas and propagation Vol. 43; no. 4; pp. 405 - 415
Main Authors Torres-Verdin, C., Habashy, T.M.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.04.1995
Institute of Electrical and Electronics Engineers
Subjects
Applied sciences
Approximation algorithms
Approximation methods
Conductivity
Diffraction, scattering, reflection
Electromagnetic fields
Electromagnetic scattering
Exact sciences and technology
Finite difference methods
Frequency
Integral equations
Iterative methods
Radiocommunications
Radiowave propagation
Telecommunications
Telecommunications and information theory
Tomography
Two dimensional model
Electrical conductivity
Simulation
Multiple scattering
Born approximation
Wave scattering
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Summary:We introduce a novel approach to the inversion of two-dimensional distributions of electrical conductivity illuminated by line sources. The algorithm stems from the newly developed extended Born approximation (see J. Geophys. Res., vol.98, no.B2, p.1759, 1993), which sums in a simple analytical expression an infinitude of terms contained in the Neumann series expansion of the electric field resulting from multiple scattering. Comparisons of numerical performance against a finite-difference code show that the extended Born approximation remains accurate up to conductivity contrasts of 1:1000 with respect to a homogeneous background, even with large-size scatterers and for a wide frequency range. Moreover, the new approximation is nearly as computationally efficient as the first-order Born approximation. Most importantly, we show that the mathematical form of the extended Born approximation allows one to express the nonlinear inversion of electromagnetic fields scattered by a line source as the sequential solution of two Fredholm integral equations. We compare this procedure against a more conventional iterative approach applied to a limited-angle tomography experiment. Our numerical tests show superior CPU time performance of the two-step linear inversion process.< >
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0018-926X
1558-2221
DOI:10.1109/8.376039