A Time-Domain Multigrid Solver With Higher-Order Born Approximation for Full-Wave Radar Tomography of a Complex-Shaped Target

This article introduces and evaluates numerically a multigrid solver for non-linear tomographic radar imaging. Our goal is to enable the fast and robust inversion of sparse time-domain data with a mathematical full-wave approach utilizing a higher-order Born approximation (BA). Full-wave inversion is computationally expensive, hence techniques to speed up the numerical procedures are needed. To model the wave propagation effectively, we use the finite element time-domain (FETD) method, which is equipped with a multigrid scheme to enable the rapid evaluation of the higher-order BA. As a potential application, we consider the tomography of small solar system bodies (SSSBs) and asteroid interiors particular, the latter of which can contain internal details observable by radar, e.g., layers, voids and cracks. In the numerical experiments, we investigated monostatic, bistatic and multistatic measurement configurations. The results obtained suggest that, with a relevant noise level, the tomographic reconstruction quality can be improved by applying the higher-order BA in comparison to the first-order case, which we interpret as a linearization of the inverse problem. Our open multigrid-FETD solver for Matlab (The Mathworks Inc.) is available online. It applies Matlabs features for graphics computing unit acceleration to enhance computational performance.