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

Pages: 844 - 853, Issue Special, September 2011

 Abstract        Full Text (379.7K)              

Kim Knudsen - Department of Mathematics, Technical University of Denmark, Denmark (email)
Jennifer L. Mueller - Department of Mathematics, Colorado State University, Fort Collins, CO 80523,, United States (email)

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

Received: August 2010;      Revised: February 2011;      Published: October 2011.