Accurate reconstruction of the radiation of sparse sources from a small set of near-field measurements by means of a smooth-weighted norm for cluster-sparsity problems

The aim of this contribution is to present an approach that allows to improve the quality of the reconstruction of the far-field from a small number of measured samples by means of sparse recovery using a relatively coarse grid for source positions (with sample spacing of the order of λ/8) compared to the grid usually required. In particular, the iterative method proposed employs a smooth-weighted constrained minimization, that guarantees a better probability of correct estimate of the sparse sources and an improved quality in the reconstruction, with a similar computational effort respect to the standard ℓ1 re-weighted minimization approach.