Sparse-Aperture Qualitative Inverse Scattering using a Phase-Delay-Based Frequency Variation Constraint

The Linear Sampling Method (LSM) is a qualitative inverse scattering technique for reconstructing target support. The LSM has various beneficial qualities, including low computational expense and robustness to model error. However, it has a well-known limitation in that it requires dense, multiview, multistatic data. In this paper, we introduce a technique to improve multifrequency LSM imaging in sparse aperture scenarios by incorporating a priori knowledge of propagation-based phase delay into the LSM inversion. We apply the proposed technique to simulated data, and show that the phase-delay-based constraint leads to higher image fidelity in the form of significantly fewer imaging artifacts as compared to the conventional multifrequency LSM implementation, at the expense of a modest blurring of the imaged target boundaries in some cases due to imperfections in the phase assumptions for resonant target features.