Christian D. Austin

GOTCHA experience report: three-dimensional SAR imaging with complete circular apertures

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.

On the Relation Between Sparse Reconstruction and Parameter Estimation With Model Order Selection

We examine the relationship between sparse linear reconstruction and the classic problem of continuous parametric modeling. In sparse reconstruction, one wishes to recover a sparse amplitude vector from a measurement that is described as a linear combination of a small number of discrete additive components. Recent results in the compressive sensing literature have provided fast sparse reconstruction algorithms with guaranteed performance bounds for problems with certain structure. In this paper, we show an explicit connection between sparse reconstruction and parameter/order estimation and demonstrate how sparse reconstruction may be used to solve model order selection and parameter estimation problems. The structural assumption used in compressive sensing to guarantee reconstruction performance-the Restricted Isometry Property-is not satisfied in the general parameter estimation context. Nonetheless, we develop a method for selecting sparsity parameters such that sparse reconstruction mimics classic order selection criteria such as Akaike information criterion (AIC) and Bayesian information criterion (BIC). We compare the performance of the sparse reconstruction approach with traditional model order selection/parameter estimation techniques for a sinusoids-in-noise example. We find that the two methods have comparable performance in most cases, and that sparse linear modeling performs better than traditional model-based parameter/order estimation for closely spaced sinusoids with low signal-to-noise ratio.

Sparse Signal Methods for 3-D Radar Imaging

Synthetic aperture radar (SAR) imaging is a valuable tool in a number of defense surveillance and monitoring applications. There is increasing interest in 3-D reconstruction of objects from radar measurements. Traditional 3-D SAR image formation requires data collection over a densely sampled azimuth-elevation sector. In practice, such a dense measurement set is difficult or impossible to obtain, and effective 3-D reconstructions using sparse measurements are sought. This paper presents wide-angle 3-D image reconstruction approaches for object reconstruction that exploit reconstruction sparsity in the signal domain to ameliorate the limitations of sparse measurements. Two methods are presented; first, we use ℓp penalized (for p ≤ 1) least squares inversion, and second, we utilize tomographic SAR processing to derive wide-angle 3-D reconstruction algorithms that are computationally attractive but apply to a specific class of sparse aperture samplings. All approaches rely on high-frequency radar backscatter phenomenology so that sparse signal representations align with physical radar scattering properties of the objects of interest. We present full 360° 3-D SAR visualizations of objects from air-to-ground X-band radar measurements using different flight paths to illustrate and compare the two approaches.

Civilian vehicle radar data domes

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.

Sparse multipass 3D SAR imaging: applications to the GOTCHA data set

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 lp least-squares inversion, and non-uniform multipass interferometric SAR (IFSAR).

Enhancement of multi-pass 3D circular SAR images using sparse reconstruction techniques

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 l1-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.

Dynamic Dictionary Algorithms for Model Order and Parameter Estimation

In this paper, we present and evaluate dynamic dictionary-based estimation methods for joint model order and parameter estimation. In dictionary-based estimation, a continuous parameter space is discretized, and vector-valued dictionary elements are formed for specific parameter values. A linear combination of a subset of dictionary elements is used to represent the model, where the number of elements used is the estimated model order, and the parameters corresponding to the selected elements are the parameter estimates. In static-based methods, the dictionary is fixed; while in the dynamic methods proposed here, the parameter sampling, and hence the dictionary, adapt to the data. We propose two dynamic dictionary-based estimation algorithms in which the dictionary elements are dynamically adjusted to improve parameter estimation performance. We examine the performance of both static and dynamic algorithms in terms of probability of correct model order selection and the root mean-squared error of parameter estimates. We show that dynamic dictionary methods overcome the problem of estimation bias induced by quantization effects in static dictionary-based estimation, and we demonstrate that dictionary-based estimation methods are capable of parameter estimation performance comparable to the Cramér-Rao lower bound and to traditional ML-based model estimation over a wide range of signal-to-noise ratios.

On the Relation Between Sparse Sampling and Parametric Estimation

We consider the relationship between parameter estimation of an additive model and sparse inversion of an under-determined matrix (dictionary) in a linear system. The dictionary is constructed by sampling parameters of the additive model. Parameters and model order are estimated using regularized least-squares inversion. We investigate equi-spaced and Fisher information inspired parameter sampling methods for dictionary construction, and present an example quantifying parameter estimation error performance for the different sampling methods. These results indicate that estimation performance is degraded by sampling the parameter space either too finely or too coarsely.

Synthetic aperture radar visualization

We investigate methods for two-dimensional and three-dimensional reconstruction of objects from radar backscatter measurements taken over wide angles. Radar backscattering is characterized by several variables: object location, complex amplitude, polarization and the aspect (azimuth and elevation) of the interrogating sensor. This high-dimensional data is typically projected into a two-dimensional image. As next-generation radar systems become increasingly capable, the assumptions and algorithms for traditional imaging need to be reconsidered. We propose new imaging techniques that accommodate limited persistence scattering on objects and use these techniques to develop two-dimensional and three-dimensional object reconstructions from wide-aperture radar measurements. Finally, we explore phase and polarization stability of scattering centers at the high resolutions afforded by wide-angle apertures.

Parameter estimation using sparse reconstruction with dynamic dictionaries

We consider the problem of parameter estimation for signals characterized by sums of parameterized functions. We present a dynamic dictionary subset selection approach to parameter estimation where we iteratively select a small number of dictionary elements and then alter the parameters of these dictionary elements to achieve better signal model fit. The proposed approach avoids the use of highly oversampled (and highly correlated) dictionary elements, which are needed in fixed dictionary approaches to reduce parameter bias associated with dictionary quantization. We demonstrate estimation performance on a sinusoidal signal estimation example.