The linearity of the scattering phenomenon with respect to primary sources allows to recombine a posteriori the available experiments and build, in a synthetic fashion, new 'virtual' experiments. Starting from this circumstance, an iterative procedure is proposed as an effective approach to tackle nonlinear inverse scattering problems. In this procedure, the virtual experiments, the Green's function, and the corresponding physical inspired field approximations are updated at each iteration. The structure and the complexity of the approach are comparable with those of the widely adopted distorted Born iterative method, but its performances are remarkably better, thanks to extended validity of the exploited field approximation. The overall approach also takes advantage of a compressive sensing inspired regularization scheme to promote sparsity in the search of piecewise constant dielectric profiles and further improve the accuracy of the imaging results. Examples with numerical and experimental data are given to assess the method.