A Direct D-bar Reconstruction Algorithm for Recovering a Complex Conductivity in 2D

Authors

Sarah J. Hamilton, Marquette UniversityFollow
C. N. L. Herrera, University of Sao Paulo, Brazil
J. L. Mueller, Colorado State University
A. Von Herrmann, DePauw University

Document Type

Article

Language

eng

Format of Original

24 p.

Publication Date

2012

Publisher

IOP Publishing

Source Publication

Inverse Problems

Source ISSN

0266-5611

Abstract

A direct reconstruction algorithm for complex conductivities in W^{2, ∞}(Ω), where Ω is a bounded, simply connected Lipschitz domain in R² , is presented. The framework is based on the uniqueness proof by Francini (2000 Inverse Problems 6 107–19), but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.

Comments

Accepted version. Inverse Problems, Vol. 28, No. 9 (2012). DOI. © IOP Publishing. Used with permission.

Sarah Hamilton was affiliated with Colorado State University at the time of publication.

Recommended Citation

Hamilton, Sarah J.; Herrera, C. N. L.; Mueller, J. L.; and Von Herrmann, A., "A Direct D-bar Reconstruction Algorithm for Recovering a Complex Conductivity in 2D" (2012). Mathematics, Statistics and Computer Science Faculty Research and Publications. 468.
https://epublications.marquette.edu/mscs_fac/468