Abstract-In this paper, we present an analytic, filtered backprojection (FBP) type inversion method for bistatic synthetic aperture radar (BISAR). We consider a BISAR system where a scene of interest is illuminated by electromagnetic waves that are transmitted, at known times, from positions along an arbitrary, but known, flight trajectory and the scattered waves are measured from positions along a different flight trajectory which is also arbitrary, but known. We assume a single-scattering model for the radar data, and we assume that the ground topography is known but not necessarily flat. We use microlocal analysis to develop the FBP-type reconstruction method. We analyze the computational complexity of the numerical implementation of the method and present numerical simulations to demonstrate its performance.
This paper presents an analytic method for synthetic-aperture inversion when the measurements are corrupted with noise and clutter. We use microlocal analysis in a statistical setting to develop filtered-backprojectiontype reconstruction methods. The inversion method is applicable in nonideal scenarios, such as those involving arbitrary source trajectories or variable antenna beam patterns. We show that the backprojection preserves the location and orientation of the singularities of the first-and second-order statistics of the target scene. We derive backprojection filters with respect to different statistical criteria. In particular, if we use a criterion based on first-order statistics, the resulting image can be interpreted as approximately unbiased. Alternatively, if we use a criterion based on second-order statistics to design the backprojection filter, such as a minimum-mean-square error criterion, the strength of the singularities due to noise and clutter is suppressed in the resulting image. Although we have developed our approach specifically for syntheticaperture radar application, the method is also applicable to other inversion problems in which microlocal techniques are relevant, such as geophysics and x-ray tomography.
Abstract-We introduce a novel synthetic-aperture imaging method for radar systems that rely on sources of opportunity. We consider receivers that fly along arbitrary, but known, flight trajectories and develop a spatio-temporal correlationbased filtered-backprojection-type image reconstruction method. The method involves first correlating the measurements from two different receiver locations. This leads to a forward model where the radiance of the target scene is projected onto the intersection of certain hyperboloids with the surface topography. We next use microlocal techniques to develop a filtered-backprojection-type inversion method to recover the scene radiance. The method is applicable to both stationary and mobile, and cooperative and non-cooperative sources of opportunity. Additionally, it is applicable to non-ideal imaging scenarios such as those involving arbitrary flight trajectories, and has the desirable property of preserving the visible edges of the scene radiance. We present an analysis of the computational complexity of the image reconstruction method and demonstrate its performance in numerical simulations for single and multiple transmitters of opportunity.
Computation of first-arrival traveltimes for quasi-P waves in the presence of anisotropy is important for high-end near-surface modeling, microseismic-source localization, and fractured-reservoir characterization — and it requires solving an anisotropic eikonal equation. Anisotropy deviating from elliptical anisotropy introduces higher order nonlinearity into the eikonal equation, which makes solving the eikonal equation a challenge. We addressed this challenge by iteratively solving a sequence of simpler tilted elliptically anisotropic eikonal equations. At each iteration, the source function was updated to capture the effects of the higher order nonlinear terms. We used Aitken’s extrapolation to speed up convergence rate of the iterative algorithm. The result is an algorithm for computing first-arrival traveltimes in tilted anisotropic media. We evaluated the applicability and usefulness of our method on tilted transversely isotropic media and tilted orthorhombic media. Our numerical tests determined that the proposed method matches the first arrivals obtained by wavefield extrapolation, even for strongly anisotropic and highly complex subsurface structures. Thus, for the cases where two-point ray tracing fails, our method can be a potential substitute for computing traveltimes. The approach presented here can be easily extended to compute first-arrival traveltimes for anisotropic media with lower symmetries, such as monoclinic or even the triclinic media.
Abstract-In this paper, we present a novel synthetic aperture radar imaging modality that uses ultranarrowband sources of opportunity and passive airborne receivers to form an image of the ground. Due to its combined passive synthetic aperture and high Doppler resolution of the transmitted waveforms, we refer to this modality as the Doppler Synthetic Aperture Hitchhiker or Doppler-hitchhiker for short. Our imaging method first correlates the windowed signal obtained from one receiver with the scaled and translated version of the received signal in another window from the same or another receiver. We show that this correlation processing removes the transmitter-related variables from the phase of the resulting operator that maps the radiance of the scene to the correlated signals. We define a concept of passive Doppler scale factor using the radial velocities of the receivers. Next, we show that the scaled, translated, and correlated signal is the projection of the scene radiance onto the contours that are formed by the intersection of the surfaces of constant passive Doppler scale factor and ground topography. We use microlocal analysis to design a generalized filtered-backprojection operator to reconstruct the scene radiance from its projections. Our analysis shows that the resolution of the reconstructed images improves with the increased time duration and center frequency of the transmitted ultranarrowband signals. Our reconstruction method is analytic and therefore can be made computationally efficient. Furthermore, it easily accommodates arbitrary flight trajectories, nonflat topography, and system-related parameters. We present numerical simulations to demonstrate the performance of our imaging method.Index Terms-Filtered-backprojection (FBP), passive imaging, passive radar, passive synthetic aperture radar, ultra-narrowband waveforms.
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