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The born approximation and Calderón's method for reconstruction of conductivities in 3-D

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  • Two algorithms for the direct reconstruction of conductivities in a bounded domain in $\mathbb{R}^3$ from surface measurements of the solutions to the conductivity equation are presented. The algorithms are based on complex geometrical optics solutions and a nonlinear scattering transform. We test the algorithms on three numerically simulated examples, including an example with a complex coefficient. The spatial resolution and amplitude of the examples are well-reconstructed.
    Mathematics Subject Classification: 35R30, 65N21.

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