Estimates on resolution and stabilization for the linearized inverse conductivity problem

Abstract

The inverse conductivity problem is that of recovering a spatially varying conductivity in the interior of some bounded region by means of steady-state measurements taken at the boundary. The author focuses on characterizing information content for the linearized inverse conductivity problem in terms of the 'distinguishability' of conductivities. Assuming a fixed tolerance for measurement errors, information content is bounded in terms of two simple estimates on linearized map. An upper bound is obtained which gives a description of the resolution limit inherent in the linearized problem. A lower bound on the linearized map is given which describes a stabilizing set.