Estimation of the support of a radiating/scattering object by means of supporting cones

This paper presents a novel and computationally inexpensive approach to estimate, in the case of a three-dimensional (3D) geometry, the support of a set of sources and/or scatterers from radiated and/or scattered (single frequency and single view) field data on a given observation plane. The approach is based on the concept of the point source spectral content of the reduced field, and represents a significant and nontrivial extension of the method to detect the convex hull of a radiating/scattering system introduced by some of the authors in the 2D geometry. The volume estimated by the proposed technique, obtained as the intersection of the complement sets of supporting cones, contains the support of the object and is not larger than the convex hull of the object under test and can also be non-convex and non-connected. The numerical analysis proves the effectiveness of the approach for objects made up of a set of sources or a set of perfectly conducting scatterers, whose sizes are comparable to the wavelength and shows its robustness against noise. It further confirms the capability of the technique to describe the non-convexity and the non-connectedness of the support of the object under test.