This letter introduces variable changes constraint for relative permittivity and conductivity reconstructions in the framework of full waveform inversion, by an iterative Gauss-Newton algorithm with a standard Tikhonov regularization. These variable changes bound the values of permittivity and conductivity during the reconstruction. The robustness of this algorithm is tested against the Fresnel Institute dataset. Its main advantages stem from the knowledge of the medium's parameters, including uncertainties, and the controlled free-space configuration. The results are analyzed qualitatively and quantitatively using reconstruction indicators. The reconstructions are clearly improved by these variable changes, and more specifically, a better identification of the different objects and their small details with a high level of accuracy is achieved.