The Factorization Method for Electrical Impedance Tomography in the Half-Space

We consider the inverse problem of electrical impedance tomography in a conducting half space, given electrostatic measurements on its boundary, i.e., a hyperplane. We first provide a rigorous weak analysis of the corresponding forward problem, and then develop a numerical algorithm to solve an associated inverse problem. This inverse problem consists in the reconstruction of certain inclusions within the half space, which have a different conductivity than the background. To solve the inverse problem we employ the so-called factorization method of Kirsch, which so far has only been considered for the impedance tomography problem in bounded domains. Our analysis of the forward problem makes use of a Liouville type argument which says that a harmonic function in the entire two dimensional plane must be a constant if some weighted L2 norm of this function is bounded. Key words. Electrical impedance tomography, half space problem, factorization method. AMS subject classifications. 65N21, ...

• Type: Journal
• Year: 2008
• Where: SIAMAM
• Authors: Martin Hanke, Birgit Schappel
• Keywords: Electrical Impedance Tomography, Impedance Tomography, Inverse Problem, SIAMAM 2008