Quantitative synthetic aperture radar inversion

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.

Imaging in random media by two-point coherent interferometry

This paper considers wave-based imaging through a heterogeneous (random) scattering medium. The goal is to estimate the support of the reflectivity function of a remote scene from measurements of the backscattered wave field. The proposed imaging methodology is based on the coherent interferometric (CINT) approach that exploits the local empirical cross correlations of the measurements of the wave field. The standard CINT images are known to be robust (statistically stable) with respect to the random medium, but the stability comes at the expense of a loss of resolution. This paper shows that a two-point CINT function contains the information needed to obtain statistically stable and high-resolution images. Different methods to build such images are presented, theoretically analyzed and compared with the standard imaging approaches using numerical simulations. The first method involves a phase-retrieval step to extract the reflectivity function from the modulus of its Fourier transform. The second method involves the evaluation of the leading eigenvector of the two-point CINT imaging function seen as the kernel of a linear operator. The third method uses an optimization step to extract the reflectivity function from some cross products of its Fourier transform. The presentation is for the synthetic aperture radar data acquisition setup, where a moving sensor probes the scene with signals emitted periodically and records the resulting backscattered wave. The generalization to other imaging setups, with passive or active arrays of sensors, is discussed briefly.