Region Iteration Method Based on Gauss–Newton Optimization for Highly Nonlinear Inverse Scattering Problems

To successfully reconstruct the strong scatterers with high contrast in electromagnetic inverse scattering problems (ISPs), this letter proposes a region iteration method (RIM) based on the computational scheme of optimizing a discrete loss. By reducing the number of unknowns to decrease the nonlinearity of ISPs, the optimization in the RIM method does not easily fall into a local minimum. In the inversion process, RIM uses the GaussNewton optimization technique to minimize loss function and obtains the initial permittivity distribution of the scatterer. Then, with the idea of region iteration, the iterative results are divided into two regions according to a pre-set threshold. In the first region, the results larger than the threshold are taken as the known values for the next iterative inversion. Therefore, in the subsequent iterative process, only the results smaller than the threshold need to be reconstructed in the second region, which greatly reduces the nonlinearity of ISPs. Thus, the inversion quality can be improved iteratively. The inversion results, including numerical and experimental examples, show that the proposed method has good accuracy and efficiency and it is applicable to scatterers with high contrast.