Paper's Title:

Stability of the D-Bar Reconstruction Method for Complex Conductivities

Author(s):

¹S. El Kontar, ¹T. El Arwadi, ¹H. Chrayteh, ²J.-M. Sac-Épée

¹Department of Mathematics and Computer Science,
Faculty of Science, Beirut Arab University,
P.O. Box: 11-5020, Beirut,
Lebanon.

E-mail: srs915@student.bau.edu.lb

²Institut Élie Cartan de Lorraine,
Université de Lorraine - Metz,
France.

Abstract:

In 2000, Francini solved the inverse conductivity problem for twice-differentiable conductivities and permittivities. This solution was considered to be the first approach using D-bar methods with complex conductivities. In 2012, based on Francini's work, Hamilton introduced a reconstruction method of the conductivity distribution with complex values. The method consists of six steps. A voltage potential is applied on the boundary. Solving a D-Bar equation gives the complex conductivity. In this paper, the stability of the D-Bar equation is studied via two approximations, t^exp and t^B, for the scattering transform. The study is based on rewriting the reconstruction method in terms of continuous operators. The conductivity is considered to be non smooth.

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