American Institute of Mathematical Sciences

2011, 2011(Special): 844-853. doi: 10.3934/proc.2011.2011.844

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

 1 Department of Mathematics, Technical University of Denmark 2 Department of Mathematics, Colorado State University, Fort Collins, CO 80523,, United States

Received  August 2010 Revised  February 2011 Published  October 2011

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.
Citation: Kim Knudsen, Jennifer L. Mueller. The born approximation and Calderón's method for reconstruction of conductivities in 3-D. Conference Publications, 2011, 2011 (Special) : 844-853. doi: 10.3934/proc.2011.2011.844
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