A microwave imaging process, and a system controlled by an associated software product, illuminate a target with microwaves from a transmitting antenna. Receiving antennas receive microwaves scattered by the target, and form microwave data. The illumination and receiving repeat over multiple transmitting antennas and multiple microwave frequencies. The microwave data is processed to form permittivity and conductivity images by selecting a background dispersion model for permittivity and conductivity. Permittivity and conductivity dispersion coefficients are determined, and permittivity and conductivity distributions are calculated, for each of the microwave frequencies. Forward solutions at multiple frequencies are determined from property distributions, and a dispersion coefficient based Jacobian matrix is determined. Dispersion coefficient updates are determined using the microwave data, and the dispersion coefficients are updated. Permittivity and conductivity distributions are recalculated for each of the frequencies, and the forward solutions are determined at multiple frequencies from property distributions.