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

Kim Knudsen; Jennifer L. Mueller

doi:10.3934/proc.2011.2011.844

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

Kim Knudsen
, Jennifer L. Mueller

Colorado State University

Research output: Contribution to journal › Journal article › Research › peer-review

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.

Original language	English
Journal	Discrete and Continuous Dynamical Systems. Series A
Volume	2011
Issue number	Special
Pages (from-to)	844-853
ISSN	1078-0947
DOIs	https://doi.org/10.3934/proc.2011.2011.844
Publication status	Published - 2011

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http://www.aimsciences.org/journals/displayArticles.jsp?paperID=7068

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title = "The born approximation and Calder{\'o}n's method for reconstruction of conductivities in 3-D",

abstract = "Two algorithms for the direct reconstruction of conductivities in a bounded domain in [\textbackslash{}mathbb\{R\}\textasciicircum{}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. ",

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AB - 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.

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DO - 10.3934/proc.2011.2011.844

M3 - Journal article

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SP - 844

EP - 853

JO - Discrete and Continuous Dynamical Systems. Series A

JF - Discrete and Continuous Dynamical Systems. Series A

IS - Special

ER -

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

Abstract

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