We discuss inverse problems for the Helmholtz equation at fixed energy, specifically the inverse source problem and the inverse scattering problem from a medium or an obstacle. We introduce the convex scattering support of a far field, a set which will be a subset of the convex hull of the support of any source which can produce it. We give several theorems which explain how to compute the convex scattering support and how to relate it to the actual support of a source, medium, or obstacle.
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Kusiak et al. (2003) studied this question.
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