On the regularization of the inverse conductivity problem with discontinuous conductivities

Pages: 397 - 409, Volume 2, Issue 3, August 2008

doi:10.3934/ipi.2008.2.397       Abstract        References        Full Text (201.8K)       Related Articles

Luca Rondi - Dipartimento di Matematica e Informatica, Università degli Studi di Trieste, via Valerio, 12/1, 34127 Trieste, Italy (email)

Abstract: We consider the regularization of the inverse conductivity problem with discontinuous conductivities, like for example the so-called inclusion problem. We theoretically validate the use of some of the most widely adopted regularization operators, like for instance total variation and the Mumford-Shah functional, by proving a convergence result for the solutions to the regularized minimum problems.

Keywords:  Electrical impedance tomography, inclusion, regularization, $BV$ functions, $\Gamma$-convergence.
Mathematics Subject Classification:  Primary: 35R30; Secondary: 47J06, 49J45.

Received: May 2008;      Revised: June 2008;      Published: July 2008.

 References