Synthetic-aperture radar imaging through dispersive media

Abstract

In this paper we develop a method for synthetic-aperture radar (SAR) imaging through a dispersive medium. We consider the case when the sensor and scatterers are embedded in a known homogeneous dispersive material, the scene to be imaged lies on a known surface and the radar antenna flight path is an arbitrary but known smooth curve. The scattering is modeled using a linearized (Born) scalar model. We assume that the measurements are polluted with additive noise. Furthermore, we assume that we have prior knowledge about the power-spectral densities of the scene and the noise. This leads us to formulate the problem in a statistical framework. We develop a filtered-back-projection imaging algorithm in which we choose the filter according to the statistical properties of the scene and noise. We present numerical simulations for a case where the scene consists of point-like scatterers located on the ground, and demonstrate how the ability to resolve the targets depends on a quantity which we call the noise-to-target ratio. In our simulations, the dispersive material is modeled with the Fung-Ulaby equations for leafy vegetation. However, the method is also applicable to other dielectric materials where the dispersion is considered relevant in the frequency range of the transmitted signals.

Ultra-Wideband Electromagnetic Pulse Propagation through Causal Media

“…The question of whether or not the Brillouin precursor is the ideal waveform for synthetic aperture radar imaging through dispersive material was partially addressed by Varslot, Morales, and Cheney [5,6] in a pair of papers appearing in 2010 and 2011. These authors used a filtered back-projection algorithm to derive an optimal filter and its associated optimal waveform.…”

“…Formulation. We adopt the assumptions and formulation of [5,6], one of which assumes the sensor and scatterers are located within in a homogeneous, isotropic, locally linear dispersive material with a known relative dielectric permittivity ǫ(ω). Under the assumptions of a scalar model of wave propagation and single-scattering, the electric field component of the scattered field is given by…”

“…The dielectric permittivity of the dispersive material is modeled by the Fung-Ulaby model [7] for vegetation with the same material parameters as used in [5,6]. The Fung-Ulaby model gives the relative dielectric permittivity as a mixing formula for water and leaf as…”

“…Comparison to Previous Work. The optimal waveform of Varslot et al [5] is obtained by minimizing the mean-square error between the reconstructed image Eq. (2) and the ideal image where Ω z defines the data collection manifold, the set of Fourier components of T that are present in the data, and (ω, s) → ξ is a Stolt change of variables.…”

Waveform Design for Synthetic-Aperture Radar Imaging through Dispersive Media

“…The theory was extended to propagation through a dispersive medium in [8] and [30]. This paper builds on the foundation of [30] to develop a theory for the design of waveforms that are optimal for forming a SAR image through a dispersive medium. Our results suggest that under certain conditions, precursors may indeed be useful for SAR imaging.…”