A broadband soil dielectric spectra retrieval approach (1 MHz to 2 GHz) has been implemented for a layered half space. The inversion kernel consists of a two port transmission line forward model in the frequency domain and a constitutive material equation based of a power law soil mixture rule (Complex Refractive Index Model - CRIM) considering (i) the volume fractions of the soil phases, (ii) dielectric relaxation of the aqueous pore solution, (iii) electrical losses and (iv) low frequency dispersion due to the interactions between the pore solution and solid particles. The spatially distributed reconstruction of broadband dielectric spectra is achieved with a global optimization approach based on a Shuffled Complex Evolution (SCE) algorithm using the full set of the scattering parameter. The possibilities and limitations of the inverse parameter estimation were numerically analyzed.