Abstract: The standard density profile reconstruction techniques are based on the WKB approximation of the probing wave’s phase, making them unable to properly reconstruct blind areas in the cut-off frequency profile. The reconstruction suffers a significant immediate error that is not rapidly damped. It is demonstrated that even though no reflections occur inside the hollow region causing the blind area, the higher probing frequencies that propagate through it carry information that can be used to estimate its properties. The usually ignored full-wave effects were investigated with the use of full-wave simulations in 1D, with special attention paid to the frequency band where they are dominant. A database of perturbation signals was simulated on five-dimensions of parameters and an application of the database inversion was demonstrated for a magnetic island in a Tore Supra discharge. The new adapted reconstruction scheme improved the description of the density profile inside the hollow region and also along 10 cm after it.