Two-Dimensional Microwave Imaging Based on Hybrid Scatterer Representation and Differential Evolution

A hybrid method for solving two-dimensional inverse scattering problems is proposed. The method utilizes differential evolution as a global optimizer and is based on two alternative representations of the unknown scatterer. Initially, the scatterer properties are represented by means of truncated cosine Fourier series expansion that involves limited number of unknown expansion coefficients. Then, the reconstructed profile obtained is used as an initial estimate and the differential evolution is further applied to a scatterer representation based on pulse function expansion. In this representation, the scatterer region is subdivided by a fine grid and the scatterer properties are considered constant within each cell. When the truncated cosine Fourier expansion representation is adopted, the dimension of the solution space can be reduced and the instabilities caused by the ill-posedness of the problem are suppressed. In the second step of the hybrid method, where the pulse functions representation is considered, the scatterer reconstruction is finer and more accurate due to its quite accurate initial estimate. Numerical results show that the hybrid method results in lower reconstruction error compared to above-mentioned representations. Also, the hybrid method outperforms the other two representations, even in the presence of noisy field measurements.