Linda J. Moore

SAR image formation toolbox for MATLAB

While many synthetic aperture radar (SAR) image formation techniques exist, two of the most intuitive methods for implementation by SAR novices are the matched filter and backprojection algorithms. The matched filter and (non-optimized) backprojection algorithms are undeniably computationally complex. However, the backprojection algorithm may be successfully employed for many SAR research endeavors not involving considerably large data sets and not requiring time-critical image formation. Execution of both image reconstruction algorithms in MATLAB is explicitly addressed. In particular, a manipulation of the backprojection imaging equations is supplied to show how common MATLAB functions, ifft and interp1, may be used for straight-forward SAR image formation. In addition, limits for scene size and pixel spacing are derived to aid in the selection of an appropriate imaging grid to avoid aliasing. Example SAR images generated though use of the backprojection algorithm are provided given four publicly available SAR datasets. Finally, MATLAB code for SAR image reconstruction using the matched filter and backprojection algorithms is provided.

A Challenge Problem for SAR Change Detection and Data Compression.

This document describes a challenge problem whose scope is two-fold. The first aspect is to develop SAR CCD algorithms that are applicable for X-band SAR imagery collected in an urban environment. The second aspect relates to effective data compression of these complex SAR images, where quality SAR CCD is the metric of performance. A set of X-band SAR imagery is being provided to support this development. To focus research onto specific areas of interest to AFRL, a number of challenge problems are defined. The data provided is complex SAR imagery from an AFRL airborne X-band SAR sensor. Some key features of this data set are: 10 repeat passes, single phase center, and single polarization (HH). In the scene observed, there are multiple buildings, vehicles, and trees. Note that the imagery has been coherently aligned to a single reference.

An analytical expression for the three-dimensional response of a point scatterer for circular synthetic aperture radar

Three-dimensional (3-D) spotlight-mode synthetic aperture radar (SAR) images of point scatterers provide insight into the achievable effectiveness of exploitation algorithms given a variety of operating parameters such as elevation angle, azimuth or synthetic aperture extent, and frequency bandwidth. Circular SAR, using 360 degrees of azimuth, offers the benefit of persistent surveillance and the potential for 3-D image reconstruction improvement compared with limited aperture SAR due in part to the increase in favorable viewing angles of unknown objects. The response of a point scatter at the origin, or center of the imaging scene, is known and has been quantified for circular SAR in prior literature by a closed-form solution. The behavior of a point scatterer radially displaced from the origin has been previously characterized for circular SAR through implementation of backprojection image reconstructions. Here, we derive a closed-form expression for the response of an arbitrarily located point scatterer given a circular flight path. In addition, the behavior of the response of an off-center point target is compared to that of a point scatterer at the origin. Symmetries within the 3-D point spread functions (PSFs), or impulse response functions (IPRs), are also noted to provide knowledge of the minimum subset of SAR images required to fully characterize the response of a particular point scatterer. Understanding of simple scattering behavior can provide insight into the response of more complex targets, given that complicated targets may sometimes be modeled as an arrangement of geometrically simple scattering objects.

A framework for rendering high resolution synthetic aperture radar images on heterogeneous architectures

This paper presents a modular, extensible, framework for rendering images from synthetic aperture radar (SAR) data on an array of heterogeneous processor architectures. Our design supports real-time reconstruction of a two-dimensional image from a matrix of echo pulses and their corresponding response values using Backprojection. Key to our design is the division of the Backprojection problem into atoms, which decomposes Backprojection along both its input and output data dimensions, and allows scheduling algorithms to explicitly minimize communication overhead through the deliberate assignment of atoms to processors. Performance analysis on a cluster of 10 Tesla C2050 GPUs, and 5 Intel Xeon Processor X5650 CPUs has shown speedup that closely follows the number of processors in the cluster.

SAR digital spotlight implementation in MATLAB

Legacy synthetic aperture radar (SAR) exploitation algorithms were image-based algorithms, designed to exploit complex and/or detected SAR imagery. In order to improve the efficiency of the algorithms, image chips, or region of interest (ROI) chips, containing candidate targets were extracted. These image chips were then used directly by exploitation algorithms for the purposes of target discrimination or identification. Recent exploitation research has suggested that performance can be improved by processing the underlying phase history data instead of standard SAR imagery. Digital Spotlighting takes the phase history data of a large image and extracts the phase history data corresponding to a smaller spatial subset of the image. In a typical scenario, this spotlighted phase history data will contain much fewer samples than the original data but will still result in an alias-free image of the ROI. The Digital Spotlight algorithm can be considered the first stage in a “two-stage backprojection” image formation process. As the first stage in two-stage backprojection, Digital Spotlighting filters the original phase history data into a number of “pseudo”-phase histories that segment the scene into patches, each of which contain a reduced number of samples compared to the original data. The second stage of the imaging process consists of standard backprojection. The data rate reduction offered by Digital Spotlighting improves the computational efficiency of the overall imaging process by significantly reducing the total number of backprojection operations. This paper describes the Digital Spotlight algorithm in detail and provides an implementation in MATLAB.

Resolution and sidelobe structure analysis for RF tomography

Radio frequency (RF) tomography utilizes a network of spatially diverse sensors to trade geometric diversity for bandwidth, permitting images to be formed with narrowband waveforms. Such a constellation of sensors produces a sparsely and irregularly spaced set of Fourier space samples, complicating the definition and analysis of resolution for these systems. We present an analysis of resolution for RF tomography based on the Cramér Rao Bound (CRB) for estimation of target position and velocity. This approach allows the resolution for a given sensor configuration to be determined with minimal computational cost, thus providing a useful design tool for sensor placement and frequency selection for RF tomography. We also explore the impact of Fourier space “filling” with bistatic geometries on sidelobe structure of the ambiguity function. Several simulation results are presented to validate the resolution calculations from the CRB and to illustrate the importance of sensor placement for RF tomographic imaging.

Blending synthetic and measured data using transfer learning for synthetic aperture radar (SAR) target classification

Convolutional neural networks (CNNs) are state-of-the-art techniques for image classification; however, CNNs require an extensive amount of training data to achieve high accuracy. This demand presents a challenge because the existing amount of measured synthetic aperture radar (SAR) data is typically limited to just a few examples and does not account for articulations, clutter, and other target or scene variability. Therefore, this research aimed to assess the feasibility of combining synthetic and measured SAR images to produce a classification network that is robust to operating conditions not present in measured data and that may adapt to new targets without necessarily training on measured SAR images. A network adapted from the CIFAR-10 LeNet architecture in MATLAB Convolutional Neural Network (MatConvNet) was first trained on a database of multiple synthetic Moving and Stationary Target Acquisition and Recognition (MSTAR) targets. After the network classified with almost perfect accuracy, the synthetic data was replaced with corresponding measured data. Only the first layer of filters was permitted to change in order to create a translation layer between synthetic and measured data. The low error rate of this experiment demonstrates that diverse clutter and target types not represented in measured training data may be introduced in synthetic training data and later recognized in measured test data.

Cramér-Rao lower bound on time of arrival estimates for an envelope-detected pulse

The pulse time of arrival is an important parameter estimated in an electronic warfare receiver. The Cramér-Rao bound provides a lower bound on the variance of unbiased parameter estimates. In the past, time of arrival performance has been compared to a bound derived under Gaussian assumptions. However, these estimates are frequently computed from the pulse envelope, which exhibits Rician statistics that are approximately Gaussian only at high signal-to-noise ratios. This correspondence derives the Rician Cramér-Rao bound on time of arrival estimation accuracy.

Staring RF signal processing challenges

Traditionally, distinct radar modes have been employed to accomplish specific tasks such as imaging an area of interest, or detecting and tracking moving targets. Staring circular synthetic aperture radar (S-CSAR) provides unique opportunities for exploitation of radio frequency (RF) data collected over a large ground spot. The same phase history may be processed in different manners to generate simultaneous S-CSAR products such as 2-D Video SAR, coherent and non-coherent change detection (CCD and NCD), and ground moving target indication (GMTI). Advanced signal processing techniques can take advantage of the S-CSAR geometry to produce 3-D scene reconstructions. The ability to transmit, record and process large volumes of S-CSAR data, to create high fidelity exploitation products, in real-time, poses significant challenges. This paper addresses several open problems in this research area.

Using phase for radar scatterer classification

Traditional synthetic aperture radar (SAR) systems tend to discard phase information of formed complex radar imagery prior to automatic target recognition (ATR). This practice has historically been driven by available hardware storage, processing capabilities, and data link capacity. Recent advances in high performance computing (HPC) have enabled extremely dense storage and processing solutions. Therefore, previous motives for discarding radar phase information in ATR applications have been mitigated. First, we characterize the value of phase in one-dimensional (1-D) radar range profiles with respect to the ability to correctly estimate target features, which are currently employed in ATR algorithms for target discrimination. These features correspond to physical characteristics of targets through radio frequency (RF) scattering phenomenology. Physics-based electromagnetic scattering models developed from the geometrical theory of diffraction are utilized for the information analysis presented here. Information is quantified by the error of target parameter estimates from noisy radar signals when phase is either retained or discarded. Operating conditions (OCs) of signal-tonoise ratio (SNR) and bandwidth are considered. Second, we investigate the value of phase in 1-D radar returns with respect to the ability to correctly classify canonical targets. Classification performance is evaluated via logistic regression for three targets (sphere, plate, tophat). Phase information is demonstrated to improve radar target classification rates, particularly at low SNRs and low bandwidths.