The linear sampling method (LSM) is a qualitative inverse scattering technique for reconstructing the shape of a target. It has several beneficial qualities, including the avoidance of nonlinear optimization and simplified scattering approximations. However, it often struggles when sensors can only be placed on one side of the target. In this paper, we investigate two alternative LSM formulations for overcoming the limited-aspect challenge. The first, the phase-delay frequency variation LSM (PDFV-LSM), incorporates coherent processing across frequency to improve discrimination in the range direction. The second, the phase-encoded LSM (PE-LSM), enhances the PDFV-LSM approach with a receive-beamforming operation to decrease the complexity of the inverse problem. We apply both techniques to simulated data from three-dimensional targets and three-dimensional limited-aspect arrays. We generate three-dimensional reconstructions and compare them to reconstructions from both the conventional LSM and conventional backprojection-based processing. The results demonstrate superior reconstruction fidelity for either the PDFV-LSM, the PE-LSM, or both, across a wide variety of imaging scenarios due to finer range resolution. They also demonstrate trade-offs between the two enhanced LSM techniques, with the PE-LSM achieving better range resolution and robustness to noise and the PDFV-LSM achieving better lateral resolution.
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