For large-scale linear inverse problems, a direct matrix-vector multiplication may not be computationally feasible,
rendering many gradient-based iterative algorithms impractical. For applications where data collection can be
modeled by Fourier encoding, the resulting Gram matrix possesses a block Toeplitz structure. This special
structure can be exploited to replace matrix-vector multiplication with FFTs. In this paper, we identify some
of the important applications which can benefit from the block Toeplitz structure of the Gram matrix. Also,
for illustration, we have applied this idea to reconstruct 2D simulated images from undersampled non-Cartesian
Fourier encoding data using three popular optimization routines, namely, FISTA, SpaRSA, and optimization
Proc. SPIE. 8051, Algorithms for Synthetic Aperture Radar Imagery XVIII
KEYWORDS: Radar, Signal to noise ratio, Detection and tracking algorithms, Scattering, Synthetic aperture radar, Rayleigh scattering, Associative arrays, Reconstruction algorithms, Data centers, 3D image processing
This paper addresses the question of scattering center detection and estimation performance in synthetic aperture
radar. Specifically, we consider sparse 3D radar apertures, in which the radar collects both azimuth and elevation
diverse data of a scene, but collects only a sparse subset of the traditional filled aperture. We use a sparse
reconstruction algorithm to both detect and estimate scattering center locations and amplitudes in the scene.
We quantify both the detection and estimation performance for scattering centers over a high dynamic range of
magnitudes. Over this wide range of scattering center signal-to-noise values, detection performance is compared
to GLRT detection performance, and estimation performance is compared to the Cramer-Rao lower bound.
We present a set of simulated X-band scattering data for civilian vehicles. For ten facet models of civilian
vehicles, a high-frequency electromagnetic simulation produced fully polarized, far-field, monostatic scattering
for 360 degrees azimuth and elevation angles from 30 to 60 degrees. The 369 GB of phase history data is stored
in a MATLAB file format. This paper describes the CVDomes data set along with example imagery using 2D
backprojection, single pass 3D, and multi-pass 3D.
This paper demonstrates image enhancement for wide-angle, multi-pass three-dimensional SAR applications.
Without sufficient regularization, three-dimensional sparse-aperture imaging from realistic data-collection scenarios
results in poor quality, low-resolution images. Sparsity-based image enhancement techniques may be used
to resolve high-amplitude features in limited aspects of multi-pass imagery. Fusion of the enhanced images across
multiple aspects in an approximate GLRT scheme results in a more informative view of the target. In this paper,
we apply two sparse reconstruction techniques to measured data of a calibration top-hat and of a civilian vehicle
observed in the AFRL publicly-released 2006 Circular SAR data set. First, we employ prominent-point autofocus
in order to compensate for unknown platform motion and phase errors across multiple radar passes. Each
sub-aperture of the autofocused phase history is digitally-spotlighted (spatially low-pass filtered) to eliminate
contributions to the data due to features outside the region of interest, and then imaged with <i>l</i><sub>1</sub>-regularized
least squares and CoSaMP. The resulting sparse sub-aperture images are non-coherently combined to obtain a
wide-angle, enhanced view of the target.
Typically in SAR imaging, there is insufficient data to form well-resolved three-dimensional (3D) images using
traditional Fourier image reconstruction; furthermore, scattering centers do not persist over wide-angles. In
this work, we examine 3D non-coherent wide-angle imaging on the GOTCHA Air Force Research Laboratory
(AFRL) data set; this data set consists of multipass complete circular aperture radar data from a scene at AFRL,
with each pass varying in elevation as a result of aircraft flight dynamics . We compare two algorithms capable
of forming well-resolved 3D images over this data set: regularized <i>l</i><sub>p</sub> least-squares inversion, and non-uniform
multipass interferometric SAR (IFSAR).
We study circular synthetic aperture radar (CSAR) systems collecting radar backscatter measurements over a
complete circular aperture of 360 degrees. This study is motivated by the GOTCHA CSAR data collection experiment
conducted by the Air Force Research Laboratory (AFRL). Circular SAR provides wide-angle information
about the anisotropic reflectivity of the scattering centers in the scene, and also provides three dimensional information
about the location of the scattering centers due to a non planar collection geometry. Three dimensional
imaging results with single pass circular SAR data reveals that the 3D resolution of the system is poor due to
the limited persistence of the reflectors in the scene. We present results on polarimetric processing of CSAR
data and illustrate reasoning of three dimensional shape from multi-view layover using prior information about
target scattering mechanisms. Next, we discuss processing of multipass (CSAR) data and present volumetric
imaging results with IFSAR and three dimensional backprojection techniques on the GOTCHA data set. We
observe that the volumetric imaging with GOTCHA data is degraded by aliasing and high sidelobes due to
nonlinear flightpaths and sparse and unequal sampling in elevation. We conclude with a model based technique
that resolves target features and enhances the volumetric imagery by extrapolating the phase history data using
the estimated model.
This paper explores three-dimensional (3D) interferometric synthetic aperture radar (IFSAR) image reconstruction when multiple scattering centers and noise are present in a radar resolution cell. We introduce an IFSAR scattering model that accounts for both multiple scattering centers and noise. The problem of 3D image reconstruction is then posed as a multiple hypothesis detection and estimation problem; resolution cells containing a single scattering center are detected and the 3D location of these cells' pixels are estimated; all other pixels are rejected from the image. Detection and estimation statistics are derived using the multiple scattering center IFSAR model. A 3D image reconstruction algorithm using these statistics is then presented, and its performance is evaluated for a 3D reconstruction of a backhoe from noisy IFSAR data.
In this paper we investigate the use of interferometric synthetic aperture radar (IFSAR) processing for the 3D reconstruction of radar targets. A major source of reconstruction error is induced by multiple scattering responses in a resolution cell, giving rise to height errors. We present a model for multiple scattering centers and analyze the errors that result using traditional IFSAR height estimation. We present a simple geometric model that characterizes the height error and suggests tests for detecting or reducing this error. We consider the use of image magnitude difference as a test statistic to detect multiple scattering responses in a resolution cell, and we analyze the resulting height error reduction and hypothesis test performance using this statistic. Finally, we consider phase linearity test statistics when three or more IFSAR images are available. Examples using synthetic Xpatch backhoe imagery are presented.