Phase-Encoded Linear Sampling Method Imaging of Conducting Surfaces From Full and Limited Synthetic Apertures

The linear sampling method (LSM) is a qualitative inverse scattering technique that can create good-fidelity imagery at low computational expense. However, it is challenging to use in many practical scenarios due to its need for wide-angle multistatic-multiview data with dense spatial sampling. We present a new LSM formulation for imaging conducting targets from a more limited sensor distribution. The technique mitigates the challenge of limited multistatic diversity by disciplining the solution via a propagation-based phase encoding. Phase encoding is accomplished on receive via a beamforming operation and on transmit via a regularization that enforces a desired phase behavior. We evaluate the method by applying it to multistatic synthetic aperture scenarios where a few sensors travel in formation while collecting data. These scenarios are challenging for conventional LSM, but also potentially desirable due to the limited required hardware resources. We demonstrate with both simulated and experimental data that the proposed technique produces images of fundamentally greater fidelity compared to conventional LSM processing. We demonstrate significantly improved performance both when the aperture completely encircles the target and when the aperture is limited in aspect. The latter result is particularly significant, as limited apertures present significant challenges to LSM imaging.