8 July 1994 Two-step linear inversion approach for the reconstruction of two-dimensional distributions of electrical conductivity
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Abstract
We introduce a novel approach to the inversion of 2D distributions of electrical conductivity illuminated by line sources. The algorithm stems from the newly developed extended Born approximation, 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 band. Similar comparisons indicate that the new approximation is nearly as computationally efficient as the first-order Born approximation. We show that the mathematical structure governing 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 elaborate on this procedure and compare it against a more conventional iterative approach applied to a limited-angle tomography experiment. Preliminary numerical tests show excellent performance of the two-step linear inversion process.
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Carlos Torres-Verdin, Carlos Torres-Verdin, Tarek M. Habashy, Tarek M. Habashy, } "Two-step linear inversion approach for the reconstruction of two-dimensional distributions of electrical conductivity", Proc. SPIE 2241, Inverse Optics III, (8 July 1994); doi: 10.1117/12.179747; https://doi.org/10.1117/12.179747
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