The reconstruction of sources and inclusions by rational approximation
Seminar Room 2, Newton Institute Gatehouse
AbstractThe 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 elliptic case. In particular we consider steady-state electrostatic or thermal imaging and giving boundary value problems for Laplace's equation or the case of inverse scattering and near/far field data for the Helmholtz equation. Our inclusions can be interior forces with compact support or obstacles with a fixed, given boundray condition although we shall concentrate on the former situation. We propose a series of algorithms that under certain assumptions allows for the determination of the support set by solving a simpler ``equivalent point source'' problem.
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