Waymond R. Scott

A Compressive Sensing Data Acquisition and Imaging Method for Stepped Frequency GPRs

A novel data acquisition and imaging method is presented for stepped-frequency continuous-wave ground penetrating radars (SFCW GPRs). It is shown that if the target space is sparse, i.e., a small number of point like targets, it is enough to make measurements at only a small number of random frequencies to construct an image of the target space by solving a convex optimization problem which enforces sparsity through lscr 1 minimization. This measurement strategy greatly reduces the data acquisition time at the expense of higher computational costs. Imaging results for both simulated and experimental GPR data exhibit less clutter than the standard migration methods and are robust to noise and random spatial sampling. The images also have increased resolution where closely spaced targets that cannot be resolved by the standard migration methods can be resolved by the proposed method.

Multistatic Ground-Penetrating Radar Experiments

A multistatic ground-penetrating radar (GPR) system has been developed and used to measure the response of a number of targets to produce data for the investigation of multistatic inversion algorithms. The system consists of a linear array of resistive-vee antennas, microwave switches, a vector network analyzer, and a 3-D positioner, all under computer control. The array has two transmitters and four receivers which provide eight bistatic spacings from 12 to 96 cm in 12-cm increments. Buried targets are scanned with and without surface clutter, which is a layer of rocks whose spacing is empirically chosen to maximize the clutter effect. The measured responses are calibrated so that the direct coupling in the system is removed, and the signal reference point is located at the antenna drive point. Images are formed using a frequency-domain beamforming algorithm that compensates for the phase response of the antennas. Images of targets in air validate the system calibration and the imaging algorithm. Bistatic and multistatic images for the buried targets are very good, and they show the effectiveness of the system and processing.

Compressive Sensing for GPR Imaging

The theory of compressive sensing (CS) enables the reconstruction of sparse signals from a small set of non-adaptive linear measurements by solving a convex lscr1 minimization problem. This paper presents a novel data acquisition and imaging algorithm for ground penetrating radars (GPR) based on CS by exploiting sparseness in the target space, i.e., a small number of point-like targets. Instead of measuring conventional radar returns and sampling at the Nyquist rate, linear projections of the returned signal with random vectors are taken as measurements. Using simulated and experimental GPR data, it is shown that sparser and sharper target space images can be obtained compared to standard backprojection methods using only a small number of CS measurements. Furthermore, the target region can even be sampled at random aperture points.

Design of a resistively loaded vee dipole for ultrawide-band ground-penetrating Radar applications

A new resistively loaded vee dipole (RVD) is designed and implemented for ultrawide-band short-pulse ground-penetrating radar (GPR) applications. The new RVD is improved in terms of voltage standing wave ratio, gain, and front-to-back ratio while maintaining many advantages of the typical RVD, such as the ability to radiate a short-pulse into a small spot on the ground, a low radar cross section, applicability in an array, etc. The improvements are achieved by curving the arms and modifying the Wu-King loading profile. The curve and the loading profile are designed to decrease the reflection at the drive point of the antenna while increasing the forward gain. The new RVD is manufactured by printing the curved arms on a thin Kapton film and loading them with chip resistors, which approximate the continuous loading profile. The number of resistors is chosen such that the resonant frequency due to the resistor spacing occurs at a frequency higher than the operation bandwidth. The antenna and balun are made in a module by sandwiching them between two blocks of polystyrene foam, attaching a plastic support, and encasing the foam blocks in heat-sealable plastic. The antenna module is mechanically reliable without significant performance degradation. The use of the new RVD module in a GPR system is also demonstrated with an experiment.

Robust Estimation of the Discrete Spectrum of Relaxations for Electromagnetic Induction Responses

The electromagnetic induction response of a target can be accurately modeled by a sum of real exponentials. However, it is difficult to obtain the model parameters from measurements when the number of exponentials in the sum is unknown or the terms are strongly correlated. Traditionally, the time constants and residues are estimated by nonlinear iterative search. In this paper, a constrained linear method of estimating the parameters is formulated by enumerating the relaxation parameter space and imposing a nonnegative constraint on the parameters. The resulting algorithm does not depend on a good initial guess to converge to a solution. By using tests on synthetic data and laboratory measurement of known targets, the proposed method is shown to provide accurate and stable estimates of the model parameters.

Analysis of the Equiangular Spiral Antenna on a Dielectric Substrate

While the first equiangular spiral antennas were slots cut from a thin conductive sheet, the widespread availability of cheap photoetching fabrication has made it more common for the spiral to be printed on a dielectric substrate. This paper examines the effects of the substrate on the spirals performance. The finite-difference time-domain (FDTD) technique is used to model the spiral over a range of configurations. The results are used to construct a design graph that shows that the substrate significantly affects the impedance of the antenna. The results also show that the substrate can negatively impact the bore-sight gain and radiation patterns. Measurements from two spirals are used to verify the accuracy of the numerical model.

A finite-difference model to study the elastic-wave interactions with buried land mines

A two-dimensional (2-D) finite-difference model for elastic waves in the ground has been developed. The model uses the equation of motion and the stress-strain relation, from which a first-order stress-velocity formulation is obtained. The resulting system of equations is discretized using centered finite-differences. A perfectly matched layer surrounds the discretized solution space and absorbs the outward traveling waves. The numerical model is validated by comparison to an analytical solution. The numerical model is used to study the interaction of elastic waves with a buried land mine. It is seen that the presence of an air-chamber within the mine gives rise to resonant oscillations that are clearly visible on the surface above the mine. The resonance is shown to be due to flexural waves being trapped within the thin layer between the surface of the ground and the air chamber of the mine. The numerical results are in good qualitative agreement with experimental observations.

A scale model for studying ground penetrating radars

A scale model developed for experimentally studying ground penetrating radars is described. The model is one-third full size and is used with transient signals that have significant frequency content within the range 150 MHz to 1.5 GHz. A unique feature is that the soil in the model is represented by an emulsion, which is mixture of mineral oil, saline solution, and a stabilizing agent. This emulsion is a scale model for red clay soil; it matches the electrical parameters of the clay, including the dispersion in the conductivity, over a ten-to-one frequency range. Typical results measured with the model are discussed. These include the measurement of the electric field transmitted by the radar into the soil and the measurement of radar signatures for pipes of various composition buried in the ground. >

Broadband Array of Electromagnetic Induction Sensors for Detecting Buried Landmines

A broadband electromagnetic induction (EMI) sensor is developed to help discriminate between buried landmines and metal clutter. The detector uses a single dipole transmit coil and an array of three quadrapole receive coils. The sensor operates in the frequency domain and collects data at 21 logarithmically spaced frequencies from 300 Hz to 90 kHz. Experimental results are presented for several targets.

An investigation of numerical dispersion in the vector finite element method using quadrilateral elements

The discretization inherent in the vector finite element method results in the numerical dispersion of a propagating wave. The numerical dispersion of a time-harmonic plane wave propagating through an infinite, two-dimensional, vector finite element mesh composed of uniform quadrilateral elements is investigated. The effects on the numerical dispersion of the propagation direction of the wave, the order of the polynomials used for the basis functions, and the electrical size of the elements are investigated. Simple formulas are presented which are excellent approximations to the exact numerical dispersion. The numerical dispersion is validated by a numerical example. >