Determination of the convex hull of radiating or scattering systems: a new, simple and effective approach

This paper presents a novel, effective, simple and computationally inexpensive approach to detect, from electromagnetic or acoustic data at a fixed frequency, the convex hull of a set of radiators (scatterers or sources) whose dimension is comparable with the wavelength. The method, presented here for 2D geometry, is based on a new concept of the point source spectral content of the reduced field. Without any restriction on the shape of the observation domain, the searching algorithm evaluates the convex hull as the intersection of the minimum cones, with vertex on the observation domain, containing the radiators. The numerical analysis proves the effectiveness of the approach in the case of sources and perfectly conducting scatterers and shows its robustness against noise.