Application of Skeletonization-Based Method in Solving Inverse Scattering Problems

In electromagnetic inverse scattering problems, Scattered field commonly needs to be measured by a large number of receiving antennas to provide enough scattered information for image reconstruction, which may increase the cost of the experimental system and require a long testing time. In this paper, a skeletonization-based method was proposed to reduce the number of actual receiving antennas involved in an inverse scattering system. The skeleton points were obtained by performing a strong-rank-revealing QR factorization of Green’s function matrix. By measuring the scattered field only at the skeleton points, the number of receiving antennas could be effectively reduced, while the scattered field data at other receiving points could be accurately restored from the skeleton points. The numerical results show that, compared with the frequency domain zero-padding (FDZP) method, the skeletonization-based method was more accurate for antennas distributed in an elliptical shape (such as thorax imaging). In addition, the inverse scattering method using the skeletonization-based method was able to reduce the number of measurements while maintaining an image quality comparable to that of the actual full measurement system. The proposed method can serve as a guidance for building an experimental system for inverse scattering problems, especially for cases when the antennas are elliptically distributed.