| The inverse problem of reconstructing the support of an embedded scatterer within a non uniform background with a single probing incident wave of a single frequency can be thought of as an inverse source problem for the Helmholtz equation. Specifically, far away from the source we know the value, i.e. amplitude and phase, of a scattered wave generated by the interaction of a single fixed-frequency incident wave and a scattering inhomogeneity situated in a known background, e.g. the human brain. The inverse source problem is to then determine the size, shape and location of the inhomogeneity from the far field measurements of the scattered wave. We present results which establish the existence of convex lower bounds---called the convex scattering support---of the convex hull of the support of the scattering inhomogeneity. Additionally, we provide a viable reconstruction algorithm which can compute the convex scattering support from discrete measurements taken on the sphere at infinity. |
