All density profile reconstruction techniques for both O-mode and X-mode are based on the assumption that the cut-off frequency profile is monotonic. However, there are many sources of perturbations to the plasma that generate hollow areas in the cut-off frequency profile, breaking the aforementioned assumption. This causes a significant immediate reconstruction error that is not rapidly damped. Inside these hollow areas, the probing microwaves exhibit no specular reflections, so they are referred to as blind areas. It is demonstrated that even though no reflections occur inside the blind areas, the higher probing frequencies that propagate through these areas carry information about them that can be used to estimate their properties. The information used is the perturbation signature imprinted in the time-of-flight signal. In addition to the reconstruction algorithm not handling well non-monotonic profiles, the reconstruction algorithm is based on the WKB approximation of the reflectometer signal, which ignores all full-wave features that are present in experimental signals. The corresponding full-wave features are investigated here with the use of full-wave simulations in 1D, with a special attention paid to the perturbed frequency band. The simulated signals of excess time-of-flight, coming from sine shaped perturbations, are used to build a database of perturbation signatures on 5 dimensions of parameters. The database is then used in a synthetic example to invert the perturbation signature and determine its size. The same procedure is also demonstrated in experimental reflectometry data corresponding to a magnetic island during a Tore Supra discharge. The new adapted reconstruction scheme, when compared to the standard reconstruction algorithm, improved the description of the density profile inside the blind area and along 10 cm after. This technique is pioneer in describing the density profile in blind areas to the reflectometer. Further research will focus on applying the method to additional experimental cases and ways to improve the perturbation signature extraction and the assumptions on the perturbation shape.