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arXiv · 1202.1785

A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D

S. J. Hamilton·C. N. L. Herrera·J. L. Mueller·A. Von Herrmann
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Abstract

A direct reconstruction algorithm for complex conductivities in $W^{2,\infty}(\Omega)$, where $\Omega$ is a bounded, simply connected Lipschitz domain in $\mathbb{R}^2$, is presented. The framework is based on the uniqueness proof by Francini [Inverse Problems 20 2000], but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.

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S. J. Hamilton, C. N. L. Herrera, J. L. Mueller, A. Von Herrmann. 2012-02-08. A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D. https://doi.org/10.1088/0266-5611%2F28%2F9%2F095005

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