The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace's equation. Our inclusions can be interior forces with compact support or obstacles with a fixed, given boundary condition. Our data consists of a single measurement of (say) voltage/current or temperature/heat flux on the external boundary. In the last part of the talk it will be shown how to extend this to the Helmholtz equation and far field measurements of the wave.

We propose an algorithm that under certain assumptions allows for the determination of the support set by solving a simpler "equivalent point source" problem.