Reconstructing Dispersive Scatterers with Minimal Frequency Data

Reconstructing the permittivity of dispersive scatterers from the measurements of scattered electromagnetic fields is a challenging problem due to the nonlinearity of the associated optimization problem. Traditionally, this has been addressed by collecting scattered field data at multiple frequencies and using lower frequency reconstructions as a priori information for higher frequency reconstructions. By modeling the object dispersion as a Debye medium, we propose an inversion technique that recovers the object permittivity with a minimum number of frequencies. We compare the performance of this method with our recently developed deep learning based technique (Sanghvi. et al., IEEE Trans. Comp. Imag., 2019) and show that given a properly trained neural network, single frequency reconstructions can be very competitive with multifrequency techniques that do not use neural networks. We quantify this performance via extensive numerical examples and comment on the hardware implications of both approaches.