All density profile reconstruction techniques for both O-mode and X-mode are based on the assumption that the cutoff frequency profile is monotonic. However, experimentally, there are many perturbations to the plasma that generate hollow areas in the cutoff frequency profile. They cause a significant immediate reconstruction error that is not rapidly damped. It is demonstrated that even though no reflections occur inside the hollow region, the higher probing frequencies that propagate through this area carry information about it that can be used to estimate its properties. In addition, the reconstruction algorithm is based on the WKB approximation of the phase, which ignores all full-wave features found in experimental signals. These 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 is simulated on 5 dimensions of parameters an application is 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.