Quantitative synthetic aperture radar inversion

TL;DR

This paper introduces a novel two-step approach for SAR inverse scattering that improves target support estimation and wave speed quantification by combining a non-iterative internal wave computation with iterative Maxwell's equation-based optimization.

Contribution

It proposes a new two-step method that enhances SAR inversion by decoupling internal wave estimation from Maxwell's equation-based refinement, improving accuracy and computational efficiency.

Findings

Better support estimation of targets compared to standard methods

Quantitative wave speed estimation improved through iterative refinement

Method performs well in numerical simulations, outperforming standard inversion

Abstract

We study an inverse scattering problem for monostatic synthetic aperture radar (SAR): Estimate the wave speed in a heterogeneous, isotropic and nonmagnetic medium probed by waves emitted and measured by a moving antenna. The forward map, from the wave speed to the measurements, is derived from Maxwell's equations. It is a nonlinear map that accounts for multiple scattering and it is very oscillatory at high frequencies. This makes the standard, nonlinear least squares data fitting formulation of the inverse problem difficult to solve. We introduce an alternative, two-step approach: The first step computes the nonlinear map from the measurements to an approximation of the electric field inside the unknown medium aka, the internal wave. This is done for each antenna location in a non-iterative manner. The internal wave fits the data by construction, but it does not solve Maxwell's equations. The second step uses optimization to minimize the discrepancy between the internal wave and the solution of Maxwell's equations, for all antenna locations. The optimization is iterative. The first step defines an imaging function whose computational cost is comparable to that of standard SAR imaging, but it gives a better estimate of the support of targets. Further iterations improve the quantitative estimation of the wave speed. We assess the performance of the method with numerical simulations and compare the results with those of standard inversion.