Special Session 57: Inverse problems in PDE and geometry
Contents
We consider the reconstruction problem in electrical impedance tomography for partial boundary data in 2D and 3D. That is from current and voltage measurements on part of the boundary to reconstruct inclusions with a conductivity different from the background. This is known to be a highly ill-posed problem.
We describe a numerical algorithm for the solution based on a regularised least squares formulation of the problem. This formulation is flexible and allows us to consider partial data and apply prior information in terms of estimates of the support of the inclusions. We show by numerical examples that this approach improves both the resolution and the contrast in the reconstruction.