A regularized solution for the inverse conductivity problem using mollifiers

Abstract

In this article, we present a reconstruction method for the inverse conductivity problem suitable for smooth conductivity distributions. The inverse problem is reformulated in terms of a pair of coupled integral equations, one of which is of the first kind which we regularize using mollifier methods. An interesting feature of this method is that the kernel of this integral equation is not given, but can be modified for the choice of mollifier. We are able to obtain conductivity reconstructions rapidly and without relying on accurate a priori information.

Keywords:

• inverse conductivity problem
• electrical impedance tomography
• integral equation methods
• mollifiers
• nonlinear inverse problems
• ill-posed problems

AMS Subject Classifications::

• 31B10
• 45Q05
• 45B05
• 47A52