Microwave imaging method developed in Lebesgue spaces for inspecting dielectric targets

As it is well known, the realization of imaging systems working at microwave frequencies requires the effective solution of the electromagnetic inverse scattering problem [1]. The research in this area is ever expanding and new procedures are continuously reported. Beside qualitative methods, in which approximations are used, tomography usually requires the use of exact approaches, i.e., aimed at solving the equations of the inverse scattering problem without approximations different from those related to the numerical procedure adopted to discretize them. In the past years, several different methods have been applied. Gauss-Newton methods seem very effective in this framework