Matthew Ferrara

Shape and Motion Reconstruction from 3D-to-1D Orthographically Projected Data via Object-Image Relations

This paper describes an invariant-based shape- and motion reconstruction algorithm for 3D-to-1D orthographically projected range data taken from unknown viewpoints. The algorithm exploits the object-image relation that arises in echo-based range data and represents a simplification and unification of previous work in the literature. Unlike one proposed approach, this method does not require uniqueness constraints, which makes its algorithmic form independent of the translation removal process (centroid removal, range alignment, etc.). The new algorithm, which simultaneously incorporates every projection and does not use an initialization in the optimization process, requires fewer calculations and is more straightforward than the previous approach. Additionally, the new algorithm is shown to be the natural extension of the approach developed by Tomasi and Kanade for 3D-to-2D orthographically projected data and is applied to a realistic inverse synthetic aperture radar imaging scenario, as well as experiments with varying amounts of aperture diversity and noise.

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.

Preliminary experimental results for RF tomography using distributed sensing

Traditional high-value monostatic imaging systems employ frequency-diverse pulses to form images from small synthetic apertures. In contrast, 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 system could use inexpensive sensors with minimal ADC requirements, provide multiple viewpoints into urban canyons and other obscured environments, and offer graceful performance degradation under sensor attrition. However, numerous challenges must be overcome to field and operate such a system, including multistatic autofocus, precision timing requirements, and the development of appropriate image formation algorithms for large, sparsely populated synthetic apertures with anisotropic targets. AFRL has recently constructed an outdoor testing facility to explore these challenges with measured data. Preliminary experimental results are provided for this system, along with a description of remaining challenges and future research directions.

Three-dimensional sparse-aperture moving-target imaging

If a targets 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.

On the Relationship between the Generalized Likelihood Ratio Test and Backprojection for Synthetic Aperture Radar Imaging

In synthetic aperture radar (SAR) imaging, a scene of interest is illuminated by electromagnetic waves. The aim is to reconstruct an image of the scene from the measurement of the scattered waves using airborne antenna(s). There are many imaging systems which are built upon this notion such as mono-static SAR, bi-static SAR, and hitchhiker SAR. For these modalities, there are analytic reconstruction algorithms based on backprojection. Backprojection-based algorithms have the advantage of putting the visible edges of the scene at the right location and orientation in the reconstructed images. On the other hand, there is also a SAR imaging method based on the generalized likelihood-ratio test (GLRT). In particular we consider the problem of detecting a target at an unknown location. In the GLRT, the presence of a target in the scene is determined based on the likelihood-ratio test. Since the location of the target is not known, the GLRT test statistic is calculated for each position in the scene and the location corresponding to the maximum test statistic indicates the location of a potential target. In this paper, we show that the backprojection-based analytic reconstruction methods include as a special case the GLRT method. We show that the GLRT test statistic is related to the reflectivity of the scene when a backprojection-based reconstruction algorithm is used.

Resolution optimization with irregularly sampled Fourier data

Image acquisition systems such as synthetic aperture radar (SAR) and magnetic resonance imaging often measure irregularly spaced Fourier samples of the desired image. In this paper we show the relationship between sample locations, their associated backprojection weights, and image resolution as characterized by the resulting point spread function (PSF). Two new methods for computing data weights, based on different optimization criteria, are proposed. The first method, which solves a maximal-eigenvector problem, optimizes a PSF-derived resolution metric which is shown to be equivalent to the volume of the Cramer–Rao (positional) error ellipsoid in the uniform-weight case. The second approach utilizes as its performance metric the Frobenius error between the PSF operator and the ideal delta function, and is an extension of a previously reported algorithm. Our proposed extension appropriately regularizes the weight estimates in the presence of noisy data and eliminates the superfluous issue of image discretization in the choice of data weights. The Frobenius-error approach results in a Tikhonov-regularized inverse problem whose Tikhonov weights are dependent on the locations of the Fourier data as well as the noise variance. The two new methods are compared against several state-of-the-art weighting strategies for synthetic multistatic point-scatterer data, as well as an ‘interrupted SAR’ dataset representative of in-band interference commonly encountered in very high frequency radar applications.

Single Frequency Inverse Obstacle Scattering: A Sparsity Constrained Linear Sampling Method Approach

The linear sampling method (LSM) offers a qualitative image reconstruction approach, which is known as a viable alternative for obstacle support identification to the well-studied filtered backprojection (FBP), which depends on a linearized forward scattering model. Of practical interest is the imaging of obstacles from sparse aperture far-field data under a fixed single frequency mode of operation. Under this scenario, the Tikhonov regularization typically applied to LSM produces poor images that fail to capture the obstacle boundary. In this paper, we employ an alternative regularization strategy based on constraining the sparsity of the solutions spatial gradient. Two regularization approaches based on the spatial gradient are developed. A numerical comparison to the FBP demonstrates that the new methods ability to account for aspect-dependent scattering permits more accurate reconstruction of concave obstacles, whereas a comparison to Tikhonov-regularized LSM demonstrates that the proposed approach significantly improves obstacle recovery with sparse-aperture data.

Applying Manifold Learning Techniques to the CAESAR Database

Understanding and organizing data is the first step toward exploiting sensor phenomenology for dismount tracking. What image features are good for distinguishing people and what measurements, or combination of measurements, can be used to classify the dataset by demographics including gender, age, and race? A particular technique, Diffusion Maps, has demonstrated the potential to extract features that intuitively make sense [1]. We want to develop an understanding of this tool by validating existing results on the Civilian American and European Surface Anthropometry Resource (CAESAR) database. This database, provided by the Air Force Research Laboratory (AFRL) Human Effectiveness Directorate and SAE International, is a rich dataset which includes 40 traditional, anthropometric measurements of 4400 human subjects. If we could specifically measure the defining features for classification, from this database, then the future question will then be to determine a subset of these features that can be measured from imagery. This paper briefly describes the Diffusion Map technique, shows potential for dimension reduction of the CAESAR database, and describes interesting problems to be further explored.

Shape and Motion Estimation from Near-Field Echo-Based Sensor Data

This paper presents a new approach for reconstructing both shape and motion from data collected by echo-based ranging sensors. The approach is based on geometric invariant theory and exploits object-image relations for near-field (spherical-wavefront) range data. These object-image equations relate the data to a unique matrix of Euclidean invariants that completely describe the object shape. The object-image relations can be used to determine the shape of a scene viewed from unknown vantage points. Specifically, the object-image equations form a linear system of equations whose solution determines the relevant shape parameters for a configuration of features within the scene. Once the shape parameters are estimated, a single shape exemplar from the point in shape space can be used to determine the relative motion (up to an arbitrary rotation) between the sensor and the object. One advantage of this motion-estimation approach is that the geometric-invariant-based strategy allows us to uniquely solve the optimization problem without the need to introduce coordinate-system-dependent “nuisance” parameters. The theorems stated in this paper hold for any range-measurement sensor scenario. As an example of the utility of the given theorems, the object-image relations are used to augment noisy GPS measurements in a circular synthetic aperture radar geometry.

Frequency-dependent reflectivity image reconstruction

We evaluate a recently reported algorithm for computing frequency-dependent radar imagery in scenarios relevant for performing spectral feature identification. For each image pixel in the spatial domain a computed frequency dependent reflectivity is used to produce a corresponding spectral feature identification. We show that this novel image reconstruction technique is capable of considerable flexibility for achieving fine spectral resolution in comparison with previous techniques based on conventional synthetic aperture radar (SAR), yet new challenges are introduced with regard to achieving fine range resolution.