The use of the linear sampling method for obtaining super-resolution effects in Born approximation

A two-step reconstruction scheme is introduced to solve fixed frequency inverse scattering problems in Born approximation conditions. The aim of the approach is to achieve super-resolution effects by constraining the inversion method to exploit some a priori knowledge on the scatterer. Therefore, the first step is to apply the linear sampling method to the far-field data in order to obtain an estimate of the support of the inhomogeneity. The second step is to apply the projected Landweber method to the linearized scattering equation in order to obtain super-resolution effects via out-of-band extrapolation. The effectiveness of the approach, which has a rather wide applicability power, is tested in the case of a two-dimensional problem for some scatterers of simple geometry.