Back-projection source reconstruction in the presence of point scatterers

Inverse source and inverse scattering problems can benefit from multipath due to a scattering environment. At the same time, multipath can be source of artefacts in the reconstructions. In this paper the aim is to understand when and how multipath manifests its positive or negative effects. To this end, a simple scenario is considered. First of all, the problem is cast within a 2D scalar setting where multipath is assumed due to known 'extra' point-like scatterers. In order to make the study easier, the inverse source problem is dealt with. This allows us to handle a modelling operator with fewer terms than inverse scattering and hence it makes the study less tedious. A back-projection inversion method based on the adjoint of the radiation operator is exploited. This allows us to easily compute the model resolution kernels, i.e. the point spread function, whose dominant contributions are determined by phase stationary arguments. The role played by the point scatterers and how they contribute to an improvement of the achievable resolution is highlighted.