American Institute of Mathematical Sciences

Advanced
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

Kim Knudsen 1, and  Jennifer L. Mueller 2,

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.
Keywords: Reconstruction algorithm, Electrical Impedance Tomography, Inverse conductivity problem, Calderón problem.
Mathematics Subject Classification: 35R30, 65N21.
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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