Imaging is not itself a system goal, but is rather a means to support inference tasks. For data processing with linearized signal models, we seek to report all high-probability interpretations of the data and to report confidence labels in the form of posterior probabilities. A low-complexity recursive procedure is presented for Bayesian estimation in linear regression models. A Gaussian mixture is chosen as the prior on the unknown parameter vector. The algorithm returns both a set of high posterior probability mixing parameters and an approximate minimum mean squared error (MMSE) estimate of the parameter vector. Emphasis is given to the case of a sparse parameter vector. Numerical simulations demonstrate estimation performance and illustrate the distinctions between MMSE estimation and maximum a posteriori probability (MAP) model selection. The proposed tree-search algorithm provides exact ratios of posterior probabilities for a set of high probability solutions to the sparse reconstruction problem. These relative probabilities serve to reveal potential ambiguity among multiple candidate solutions that are ambiguous due to low signal-to-noise ratio and/or significant correlation among columns in the super-resolving regressor matrix.

SAR imaging at low center frequencies (UHF and L-band) offers advantages over imaging at more conventional (X-band) frequencies, including foliage penetration for target detection and scene segmentation based on polarimetric coherency. However, bandwidths typically available at these center frequencies are small, affording poor resolution. By exploiting extreme spatial diversity (partial hemispheric k-space coverage) and nonlinear bandwidth extrapolation/interpolation methods such as Least-Squares SuperResolution (LSSR) and Least-Squares CLEAN (LSCLEAN), one can achieve resolutions that are commensurate with the carrier frequency (λ/4) rather than the bandwidth (c/2B). Furthermore, extreme angle diversity affords complete coverage of a target's backscatter, and a correspondingly more literal image. To realize these benefits, however, one must image the scene in 3-D; otherwise layover-induced misregistration compromises the coherent summation that yields improved resolution. Practically, one is limited to very sparse elevation apertures, i.e. a small number of circular passes. Here we demonstrate that both LSSR and LSCLEAN can reduce considerably the sidelobe and alias artifacts caused by these sparse elevation apertures. Further, we illustrate how a hypothetical multi-static geometry consisting of six vertical real-aperture receive apertures, combined with a single circular transmit aperture provide effective, though sparse and unusual, 3-D k-space support. Forward scattering captured by this geometry reveals horizontal scattering surfaces that are missed in monostatic backscattering geometries. This paper illustrates results based on LucernHammer UHF and L-band mono- and multi-static simulations of a backhoe.

In this paper we present an algorithm for wide-angle synthetic aperture radar (SAR) image formation. Reconstruction of wide-angle SAR holds a promise of higher resolution and better information about a scene, but it also poses a number of challenges when compared to the traditional narrow-angle SAR. Most prominently, the isotropic point scattering model is no longer valid. We present an algorithm capable of producing high resolution reflectivity maps in both space and aspect, thus accounting for the anisotropic scattering behavior of targets. We pose the problem as a non-parametric three-dimensional inversion problem, with two constraints: magnitudes of the backscattered power are highly correlated across closely spaced look angles and the backscattered power originates from a small set of point scatterers. This approach considers jointly all scatterers in the scene across all azimuths, and exploits the sparsity of the underlying scattering field. We implement the algorithm and present reconstruction results on realistic data obtained from the XPatch Backhoe dataset.

If a target's motion can be determined, the problem of reconstructing a 3D target image becomes a sparse-aperture imaging problem. That is, the data lies on a random trajectory in k-space, which constitutes a sparse data collection that yields very low-resolution images if backprojection or other standard imaging techniques are used. This paper investigates two moving-target imaging algorithms: the first is a greedy algorithm based on the CLEAN technique, and the second is a version of Basis Pursuit Denoising. The two imaging algorithms are compared for a realistic moving-target motion history applied to a Xpatch-generated backhoe data set.

We consider three dimensional target construction from SAR data collected on multiple complete circular apertures at different elevation angle. The 3-D resolution of circular SAR systems is constrained by two factors: the sparse sampling in elevation and the limited azimuthal persistence of the reflectors in the scene. Three dimensional target reconstruction with multipass circular SAR data is further complicated by nonuniform elevation spacing in real flight paths and non-constant elevation angle throughout the circular pass. In this paper we first develop parametric spectral estimation methods that extend standard IFSAR method of height estimation to apertures at more than two elevation angles. Next, we show that linear interpolation of the phase history data leads to unsatisfactory performance in 3-D reconstruction from nonuniformly sampled elevation passes. We then present a new sparsity regularized interpolation algorithm to preprocess nonuniform elevation samples to create a virtual uniform linear array geometry. We illustrate the performance of the proposed method using simulated backscatter data.

We consider the problem of automatic parameter selection in regularization-based radar image formation techniques. It has previously been shown that non-quadratic regularization produces feature-enhanced radar images; can yield superresolution; is robust to uncertain or limited data; and can generate enhanced images in non-conventional data collection scenarios such as sparse aperture imaging. However, this regularized imaging framework involves some hyper-parameters, whose choice is crucial because that directly affects the characteristics of the reconstruction. Hence there is interest in developing methods for automatic parameter choice. We investigate Stein's unbiased risk estimator (SURE) and generalized cross-validation (GCV) for automatic selection of hyper-parameters in regularized radar imaging. We present experimental results based on the Air Force Research Laboratory (AFRL) "Backhoe Data Dome," to demonstrate and discuss the effectiveness of these methods.

Fourier analysis based focusing of synthetic aperture radar (SAR) data collected during circular flight path is a recent advancement in SAR signal processing. Fast CSAR algorithm uses the Householder transform to obtain a ground plane circular SAR (CSAR) signal phase history from the slant plane CSAR phase history by inverting the linear shift-varying system model, thereby circumventing the need for explicitly computing a pseudo-inverse. The Householder transform has recently been shown to have improved error bounds and stability as an underdetermined and ill-conditioned system solver, and the Householder transform is computationally efficient.

In this paper we describe an algorithm for fast spotlight-mode synthetic aperture radar (SAR) image formation that employs backprojection as the core, but is implemented such that its compute time is comparable to the often-used Polar Format Algorithm (PFA). (Standard backprojection is so much slower than PFA that it is impractical to use in many operational scenarios.) We demonstrate the feasibility of the algorithm on real SAR phase history data sets and show some advantages in the SAR image formed by this technique.

We develop a linearized imaging theory that combines the spatial, temporal, and spectral aspects of scattered waves. We consider the case of fixed sensors and a general distribution of objects, each undergoing linear motion; thus the theory deals with imaging distributions in phase space. We derive a model for the data that is appropriate for any waveform, and show how it specializes to familiar results when the targets are far from the antennas and narrowband waveforms are used. We develop a phase-space imaging formula that can be interpreted in terms of filtered backprojection or matched filtering. For this imaging approach, we derive the corresponding point-spread function. We show that special cases of the theory reduce to: a) Range-Doppler imaging, b) Inverse Synthetic Aperture Radar (isar), c) Spotlight Synthetic Aperture Radar (sar), d) Diffraction Tomography, and e) Tomography of Moving Targets. We also show that the theory gives a new SAR imaging algorithm for waveforms with arbitrary ridge-like ambiguity functions.

We present a new image reconstruction method for distributed apertures operating in complex environments with additive non-stationary noise. Our method is capable of exploiting information that we might have about: multipath scattering in the environment; statistics of the objects to be imaged; statistics of the additive non-stationary noise. The aperture elements are distributed spatially in an arbitrary fashion, and can be several hundred wavelengths apart. Furthermore, our method facilitates multiple transmit apertures which operate simultaneously, and is thus capable of handling a true multi-transmit-multi-receive scenario. We derive a set of basis functions which is adapted to the given operating environment and sensor distribution. By selecting an appropriate subset of these basis functions we obtain a sub-space reconstruction which is optimal in the sense of obtaining the minimum-mean-square-error for the reconstructed image. Furthermore, as this subspace determines which details will be visible in the reconstructed image, it provides a tool for evaluating the sensor locations against the objects that we would like to see in the image. The implementation of our reconstruction takes the form of a filter bank which is applied to the pulse-echo measurements. This processing can be performed independently on the measurements obtained from each receiving element. Our approach is therefore well suited for parallel implementation, and can be performed in a distributed manner in order to reduce the required communication bandwidth between each receiver and the location where the results are merged into the final image. We present numerical simulations which illustrate capabilities of our method.

The most commonly used smoothing algorithms for complex data processing are low pass filters. Unfortunately, an undesired side effect of the aforementioned techniques is the blurring of scene discontinuities in the interferogram. For Digital Surface Map (DSM) extraction and subsidence measurement, the smoothing of the scene discontinuities can cause inaccuracy in the final product. Our goal is to perform spatially non-uniform smoothing to overcome the aforementioned disadvantages. We achieve this by using an Anisotropic Non-Linear Diffuser (ANDI). Here, in this paper we will show the utility of ANDI filtering on simulated and actual Interferometric Synthetic Aperture Radar (IFSAR) data for preprocessing, subsidence measurement and DSM extraction to overcome the difficulties of typical filters. We also compare the results of the ANDI filter with a wavelet filter. Finally, we detail some of our results of the New Orleans IFSAR research project with Canadian Space Agency, NASA, and USGS. The Harris LiteSite^TM Urban 3D Modeling software is used to illustrate some of the results of our RADARSAT-1 processing.

Current SAR imaging techniques assume that radar pulses are reflected from a scene by a single bounce event (reflection from a sphere), or multiple bounces producing a fixed phase-centre (a trihedral). However, scattering is often more complex; e.g. the pulse may reflect off the ground before interacting with a vehicle, leading to additional bright returns in the image which are not located at the position of either bounce. In this paper we use simulation to assess the affect of multipath on vehicle signatures and develop techniques for the identification and removal of multipath returns from SAR imagery.

Through-the-Wall Imaging is emerging as an affordable sensor technology supporting a variety of applications, such as surveillance and reconnaissance, emergency rescue, and firefighting. Motivated by the desire to understand the underlying phenomenology and performance bounds associated with imaging targets behind walls, several through-the-wall imaging experiments were conducted at the Center for Advanced Communications (CAC), Villanova University. These experiments aimed at supporting resolution, polarization, and localization of indoor targets and objects behind walls, and provided valuable dual-polarized synthetic aperture data measurements of indoor scenes of different complexity and population. In this paper, we present full-polarization imaging results, for a setting of calibrated reflectors behind a typical exterior grade wall. These imaging results provide polarimetric scene characterization and are shown to be in good agreement with the ground truth.

Three dimensional (3D) autofocus remains a significant challenge for the development of practical 3D multipass radar imaging. The current 2D radar autofocus methods are not readily extendable across sensor passes. We propose a general framework that allows a class of data adaptive solutions for 3D auto-focus across passes with minimal constraints on the scene contents. The key enabling assumption is that portions of the scene are sparse in elevation which reduces the number of free variables and results in a system that is simultaneously solved for scatterer heights and autofocus parameters. The proposed method extends 2-pass interferometric synthetic aperture radar (IFSAR) methods to an arbitrary number of passes allowing the consideration of scattering from multiple height locations. A specific case from the proposed autofocus framework is solved and demonstrates autofocus and coherent multipass 3D estimation across the 8 passes of the "Gotcha Volumetric SAR Data Set" X-Band radar data.

We investigate a recursive procedure for synthetic aperture imaging. We consider a concept in which a SAR system persistently interrogates a scene, for example as it flies along or around that scene. In traditional SAR imaging, the radar measurements are processed in blocks, by partitioning the data into a set of non-overlapping or overlapping azimuth angles, then processing each block. We consider a recursive update approach, in which the SAR image is continually updated, as a linear combination of a small number of previous images and a term containing the current radar measurement. We investigate the crossrange sidelobes realized by such an imaging approach. We show that a first-order autoregression of the image gives crossrange sidelobes similar to a rectangular azimuth window, while a third-order autoregression gives sidelobes comparable to those obtained from widely-used windows in block-processing image formation. The computational and memory requirements of the recursive imaging approach are modest - on the order of M • N² where M is the recursion order (typically ≤ 3) and N² is the image size. We compare images obtained from the recursive and block processing techniques, both for a synthetic scene and for X-band SAR measurements from the Gotcha data set.

In this paper we show that the technique for spotlight-mode SAR image formation generally known as "backprojection" or "time-domain" is most easily derived and described in terms of the well-known methods of phased-array beamforming. By contrast, backprojection has been typically developed via analogy to tomographic imaging, which restricts this technique to the case of planar wavefronts. We demonstrate how the very simple notion of delay-and-sum beamforming leads directly to the backprojection algorithm for SAR, including the case for curved wavefronts. We further explain why backprojection offers a certain elegant simplicity for SAR imaging, and allows direct one-step computation of several useful SAR products, including an orthographically correct image free of any geometric or defocus effects from wavefront curvature and also free of the effects of terrain-elevation-induced defocus. (This product requires as an input a pre-existing digital elevation map (DEM) of the scene to be imaged.) In addition, we'll demonstrate why beamforming yields a mode-independent SAR image formation algorithm, i.e. one that can just as easily accommodate strip-map or spotlight-mode phase histories collected on an arbitrary flight path.

A multi-stage Synthetic Aperture Radar (SAR) Automatic Target Recognition (ATR) system is analyzed across images of various pixel areas achieved by both square and non-square resolution. Non-square resolution offers the ability to achieve finer resolution in the range or cross-range direction with a corresponding degradation of resolution in the cross-range or range direction, respectively. The algorithms examined include a standard 2-parameter Constant False Alarm Rate (CFAR) detection stage, a discrimination stage, and a template-based classification stage. Performance for each stage with respect to both pixel area and square versus non-square resolution is shown via cascaded Receiver Operating Characteristic (ROC) curves. The results indicate that, for fixed pixel areas, non-square resolution imagery can achieve statistically similar performance to square pixel resolution imagery in a multi-stage SAR ATR system.

This paper describes the automatic target recognition (ATR) challenge problem which includes source code for a baseline ATR algorithm, display utilities for the results, and a high range resolution (HRR) data set consisting of 10 civilian vehicles. The Ku-band data in this data set has been processed into 1-dimensional range profiles of vehicles in the open, moving in a straight line. It is being released to the ATR community to facilitate the development of new and improved HRR identification algorithms which can provide greater confidence and very high identification performance. The intent of the baseline algorithm included with this challenge problem is to provide an ATR performance comparison to newly developed algorithms. Single-look identification performance results using the baseline algorithm and the data set are provided as a starting point for algorithm developers. Both the algorithm and data set can support single look and multi-look target identification.

Joint tracking and ATR with HRR radar is an important field of research in recent years. This paper addresses the issue of end-to-end performance modeling for HRR radar based joint tracking and ATR system under various operating conditions. To this end, an ATR system with peak location and amplitude as features is considered. A complete set of models are developed to capture the statistics in all stages of processing, including HRR signal, extracted features, Baysian classifier and tracker. In particular, we demonstrate that the effect of operating conditions on feature can be represented through a random variable with Log-normal distribution. Then, the result is extended to predicting the system performance under specified operating conditions. Although this paper is developed based on a type of ATR and tracking system, the result indicates the trend of the performance for general joint ATR and tracking system over operating conditions. It also provides guidance to how the empirical performance model of a general joint tracking and ATR system shall be constructed.

Tracking is widely used in a variety of computer vision applications, ranging from video surveillance to medical imaging. The principal goal of tracking is to first identify regions of interest in a scene, and to then monitor the movements or changes of the object through the image sequence. In this paper, we focus on unsupervised vehicle tracking for low resolution aerial images taken from an urban area. Various optical effects have traditionally made this tracking problem very challenging. Objects are often lost in tracking due to intensity changes that result from shadowed or partially occluded regions of an image. Additionally, the presence of multiple vehicles in a scene can lead to mistakes in tracking and significantly increased computation time. We propose a feature-based tracking algorithm herein that will seek to mitigate these limitations. To first isolate vehicles in the initial frame, we apply three-frame change detection to the registered images. Feature points are identified in the labelled regions using the Harris corner criteria. To track a feature point from one frame to the next, we search for the point around a predicted location, determined from the feature's previous motion, that minimizes the sum-of-squared-differences value. Finally, during the course of the image sequence, our algorithm constantly searches for new objects that might have entered the scene. We will demonstrate the success of our tracking approach through experimental considerations.

Rotation of targets pose great a challenge for the design of an automatic image-based target detection system. In this paper, we propose a target detection algorithm that is robust to rotation of targets. Our key idea is to use rotation invariant features as the input for the classifier. For an image in Radon transform space, namely R(b,θ), taking the magnitude of 1-D Fourier transform on θ, we get |F_θ{R(b,θ)}|. It was proved that the coefficients of the combined Radon and 1-D Fourier transform, |F_θ{R(b,θ)}| is invariant to rotation of the image. These coefficients are used as the input to a maximum-margin classifier based on I-RELIEF feature weighting technique. Its objective is to maximize the margin between two classes and improve the robustness of the classifier against uncertainties. For each pixel of a sample SAR image, a feature vector can be extracted from a sub image centered at that pixel. Then our classifier decides whether the pixel is target or non-target. This produces a binary-valued image. We further improve the detection performance by connectivity analysis, image differencing and diversity combining. We evaluate the performance of our proposed algorithm, using the data set collected by Swedish CARABAS-II systems, and the experimental results show that our proposed algorithm achieves superior performance over the benchmark algorithm.

Efficient representation of images usually leads to improvements in storage efficiency, computational complexity and performance of image processing algorithms. Efficient representation of images can be achieved by transforms. However, conventional transforms such as Fourier transform and wavelet transform suffer from discontinuities such as edges in images. To address this problem, we propose a new transform called ripplet transform. The ripplet transform is a higher dimensional generalization of the wavelet transform designed to represent images or two-dimensional signals at different scales and different directions. The ripplet transform is also a generalization of the curvelet transform. Specifically, the ripplet transform allows arbitrary support c and degree d while the curvelet transform is just a special case of the ripplet transform (Type I) with c = 1 and d = 2. Our experimental results show that the ripplet transform can provide efficient representation of images that contain edges. The ripplet transform holds great potential for image denoising and image compression.

Detection of targets concealed in foliage is a challenging problem and is critical for ground surveillance. To detect foliage-concealed targets, we need to address two major challenges, namely, 1) how to remotely acquire information that contains important features of foliage-concealed targets, and 2) how to distinguish targets from background and clutter. Synthetic aperture radar operated in low VHF-band has shown very good penetration capability in the forest environment, and hence the first problem can be satisfactorily addressed. The second problem is the focus of this paper. Existing detection schemes can achieve good detection performance but at the cost of high false alarm rate. To address the limitation of the existing schemes, in this paper, we develop a target detection algorithm based on a supervised learning technique that maximizes the margin between two classes, i.e., the target class and the non-target class. Specifically, our target detection algorithm consists of 1) image differencing, 2) maximum-margin classifier, and 3) diversity combining. The image differencing is to enhance and highlight the targets so that the targets are more distinguishable from the background. The maximum-margin classifier is based on a recently developed feature weighting technique called I-RELIEF; the objective of the maximum-margin classifier is to achieve robustness against uncertainties and clutter. The diversity combining utilizes multiple images to further improve the performance of detection, and hence it is a type of multi-pass change detection. We evaluate the performance of our proposed detection algorithm, using the SAR image data collected by Swedish CARABAS-II systems which operates at low VHF-band around 20-90 MHz. The experimental results demonstrate superior performance of our algorithm, compared to the benchmark algorithm associated with the CARABAS-II SAR image data. For example, for the same level of target detection probability, our algorithm only produces 11 false alarms while the benchmark algorithm produces 86 false alarms.

At high frequencies, synthetic aperture radar (SAR) imagery can be represented as a set of points corresponding to scattering centers. Using a collection of sequential azimuths with a fixed aperture we build a cube of points for each of seven civilian vehicles in the Gotcha public release data set (GPRD). We present a baseline study of the ability to discriminate between the vehicles using strictly 2D geometric information of the scattering centers. The comparison algorithm is independent of pose and translation using a novel application of the partial Hausdorff distance (PHD) minimized through a particle swarm optimization. Using the PHD has the added benefit of reducing the effects of occlusions and clutter in comparing vehicles from pass to pass. We provide confusion matrices for a variety of operating parameters including azimuth extent, various amplitude cutoffs, and various parameters within PHD. Finally, we discuss extension of the approach to near-field imaging and to additional point attributes, such as 3D location and polarimetric response.