Primal and dual problems in electrical impedance imaging
Date
2005ISBN
07803956899780780395688
Source
Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDCECC '05Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDCECC '05
Volume
2005Pages
38683873Google Scholar check
Keyword(s):
Metadata
Show full item recordAbstract
Illposed inverse boundary value problems are usually approached as problems of inference under a given set of boundary observations. The parameters and data are modelled as random variables so that to encompass the uncertainty of their actual values. This uncertainty is expressed in probability distributions of the variables which are subsequently conjuncted to form the basis of the regularized inverse problem. In this work, we consider the linearized inverse conductivity problem, also known as electrical impedance imaging problem, where a finite set of noise infused boundary voltage measurements is used to reconstruct the conductivity distribution in the interior of simply connected domains. We derive the primal and dual problems in the generalized Tikhonov formulation, and cast the linearized inverse problem as a quadratic optimization problem with an inequality ℓ2 norm constraint. We show that Tikhonov regularization can be implemented in the context of primaldual interior point methods to yield optimal images and regularization parameters with respect to the choice of prior information equations and the noise level in the data. The approach can be extended in nonlinear trustregion regularization using algorithms based on consecutive linearization steps. © 2005 IEEE.
Collections
Cite as
Related items
Showing items related by title, author, creator and subject.

Article
The singular function boundary integral method for 3D Laplacian problems with a boundary straight edge singularity
Christodoulou, Evgenia; Elliotis, Miltiades C.; Xenophontos, Christos A.; Georgiou, Georgios C. (2012)Threedimensional Laplace problems with a boundary straightedge singularity caused by two intersecting flat planes are considered. The solution in the neighbourhood of the straight edge can be expressed as an asymptotic ...

Article
The numerical solution of threedimensional Signorini problems with the method of fundamental solutions
Poullikkas, A.; Karageorghis, Andreas; Georgiou, Georgios C. (2001)The method of fundamental solutions (MFS) is formulated for threedimensional Signorini boundaryvalue problems. The method is tested on a threedimensional electropainting problem related to the coating of vehicle roofs. ...

Article
The method of fundamental solutions for axisymmetric potential problems
Karageorghis, Andreas; Fairweather, G. (1999)In this paper, we investigate the application of the Method of Fundamental Solutions (MFS) to two classes of axisymmetric potential problems. In the first, the boundary conditions as well as the domain of the problem, are ...