Multi-aspect detection of surface and shallow-buried ...

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 39, NO. 6, JUNE 2001 1259

Multi-Aspect Detection of Surface andShallow-Buried Unexploded Ordnance viaUltra-Wideband Synthetic Aperture Radar

Yanting Dong, Student Member, IEEE, Paul R. Runkle, Lawrence Carin, Fellow, IEEE, Raju Damarla,Anders Sullivan, Member, IEEE, Marc A. Ressler, and Jeffrey Sichina

Abstract—An ultra-wideband (UWB) synthetic apertureradar (SAR) system is investigated for the detection of formerbombing ranges, littered by unexploded ordnance (UXO). Theobjective is detection of a high enough percentage of surface andshallow-buried UXO, with a low enough false-alarm rate, suchthat a former range can be detected. The physics of UWB SARscattering is exploited in the context of a hidden Markov model(HMM), which explicitly accounts for the multiple aspects atwhich a SAR system views a given target. The HMM is trained oncomputed data, using SAR imagery synthesized via a validatedphysical-optics solution. The performance of the HMM is demon-strated by performing testing on measured UWB SAR data formany surface and shallow UXO buried in soil in the vicinity ofnaturally occurring clutter.

Index Terms—Detection, scattering, synthetic aperture radar(SAR), wideband.

I. INTRODUCTION

I N MANY former war zones and bombing test ranges, thereare a large number of unexploded ordnance (UXO) that must

be removed before the terrain can be safely returned to civilianuse. There are many sensors that have been developed to ad-dress this problem, including electromagnetic induction (EMI)and magnetometers [1]. While such sensors are often effectivein detecting and discriminating UXO, they generally require thatthe sensor be close to the ground, implying that they are typi-cally employed in a ground-based system. In many cases, theformer bombing ranges have been unused for many years, andtheir location is poorly known. In such situations, wide-areasurveillance is often required to circumscribe local regions inwhich UXO may reside, with such regions sensed subsequentlyvia ground-based sensors.

A wide-area surveillance sensor requires rapid coverage withsignificant standoff. An airborne synthetic aperture radar (SAR)can meet these requirements, but SAR has significant limita-tions for sensing UXO. In particular, it is well known that radarwaves typically suffer significant attenuation upon propagation

Manuscript received June 27, 2000; revised February 12, 2001. This work wassupported by the Strategic Environmental Research and Development Program(SERDP) under Contract DACA72-99-C-0012-CU-1123.

Y. Dong, P. R. Runkle, and L. Carin are with the Department of Electricaland Computer Engineering, Duke University, Durham, NC 27708-0291 USA(e-mail: [email protected]).

R. Damarla, A. Sullivan, M. A. Ressler, and J. Sichina are with the ArmyResearch Laboratory, Adelphi, MD 20783 USA.

Publisher Item Identifier S 0196-2892(01)04845-8.

in soil [2]–[4], severely limiting the utility of SAR for detectingdeeply buried UXO. However, at many former bombing rangesthere are a large number of surface and shallow-buried UXO.It is of interest to quantify whether UWB SAR can detect ahigh-enough percentage of surface and shallow UXO, with alow-enough false-alarm rate, such that such a system can be uti-lized for detection of former bombing ranges (not for detectionof each, possibly deeply buried, individual UXO). The defini-tions of “high-enough” and “low-enough” are dictated by mis-sion requirements and public policy. Rather than attempting todeal with these inchoate terms, we investigate performance ofa particular SAR system at a particular test site (discussed fur-ther below), incorporating the underlying wave physics into thesignal-processing construct. The site considered is relatively fa-vorable for this mission (good soil penetration and relativelybenign clutter), and therefore, the results from this study helpquantify performance under propitious operating characteris-tics.

Having restricted ourselves to surface and shallow-buriedUXO, we must now address the wave phenomenology onemight exploit to reliably detect such targets. For UXO thathave one or more dimension large relative to wavelength,the backscattered waveform is typically a strong function oftarget-sensor orientation. While this aspect dependence maycomplicate target detection, because there is not a single targetsignature representative of all target orientations, the aspectdependence of the target signature is often different than thatof clutter. A large SAR aperture, which manifests looks at thetarget from multiple orientations, provides a natural vehicle forexploiting the aspect dependence of the target signature. Wehave previously developed hidden Markov models (HMMs) forperforming such multi-aspect processing [5]–[7], with thosetools applied here. Since the basic HMM construct has beendescribed by us previously [5]–[7], for target detection andclassification, here we only provide a concise summary, forcompleteness.

Although the scattered waveform (or SAR image) from agiven target is often a strong function of target-sensor orien-tation, there are generally contiguous sets of orientations overwhich the scattering physics is slowly varying (or stationary).Such angular sectors are called “states,” with a given target de-scribed by states, with dictated by the target complexityand sensor bandwidth. When one performs a sequence ofmeasurements, from consecutive target-sensor orientations,we implicitly sample waveforms (or images) from states of

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1260 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 39, NO. 6, JUNE 2001

the target. Some states may be sampled more than once, andsome not all, depending on the target orientation and sensor mo-tion. We have demonstrated that, to a good approximation, thistransitioning from state to state can be modeled as a Markovprocess, which implies that the probability of transitioning intoany given state is approximately dictated entirely by the currentstate being occupied. Moreover, since the target is typically dis-tant or concealed, the actual states being sampled are “hidden,”motivating an HMM. The HMM paradigm has been applied suc-cessfully to several detection and classification problems, basedon processing multi-aspect scattering data [5]–[7].

A limitation of many target-classification algorithms, in-cluding the HMM, is that they often require substantial trainingdata, and in practice, this training data is typically similar to themeasured data on which the algorithm is tested. An advantageof our problem is that electromagnetic models have beendeveloped to simulate UWB scattering from targets such asUXO, in the presence of realistic lossy, dispersive media (soil).In particular, method-of-moments (MoM) [8], fast-multiplemethod (FMM) [9] and finite-difference time-domain (FDTD)[10] models have been developed over the last several years.These models provide the capability of simulating the UWBSAR imagery of a surface or subsurface UXO, with suchsimulated data applicable to training a classifier. In this manner,the classifier is trained and tested on independent data, yieldinga meaningful assessment of classifier performance.

As indicated, substantial training data is desirable, with whichthe target can be viewed from all possible target-sensor orienta-tions. Consequently, it is required that the forward solver usedto generate the scattering data be as efficient as possible, whileretaining accuracy. Although well designed MoM, FMM, andFDTD codes are efficient, such numerical algorithms are stillrelatively computationally intensive for the UXO problem. It istherefore desirable to employ an approximate solver, such asphysical optics (PO) [11]. We validate here that the PO approxi-mation accurately generates UWB SAR imagery for surface andburied UXO, in comparison to a rigorous MoM solution, andtherefore employ the PO solutions to train the HMM.

The measured UWB SAR data is collected at the YumaProving Ground, Yuma, AZ, using the U.S. Army ResearchLaboratory (ARL) BoomSAR system, which has been de-scribed elsewhere [12], [13]. The soil at Yuma is relatively dry,providing favorable electromagnetic soil penetration over the50–1200 MHz bandwidth of the ARL system. Moreover, thenaturally occurring clutter at this site provides a significantchallenge, but is relatively benign. In particular, there is littlelarge foliage, with most clutter manifested from small shrubtrees, rocks, subsurface inhomogeneities, and animal burrows.As demonstrated in Section III, even this relatively benignenvironment presents a significant challenge to UWB SARsensing, necessitating a sophisticated processing algorithm.

The remainder of the text is organized as follows. In Sec-tion II, we review the HMM and the key components employedfor its implementation with UWB SAR data. We address HMMtraining, with a validation of the PO forward solver employedin this context. Performance of the HMM on measured UWBSAR data is discussed in Section III, in which we also addressthe use of prescreeners to determine the points of interest subse-

Fig. 1. Schematic of the three states used to characterize a UXO. Stateone (S ) is characterized principally by end scatteringS by diffractivescattering from the two ends, andS by broadside scattering. Due to symmetryassumptions, these three states describe the scattering from any target-sensororientation.

quently interrogated by the HMM. Conclusions from this workare discussed in Section IV.

II. SUMMARY OF HMM CLASSIFIER AND ASSOCIATEDTOOLS

A. Hidden Markov Model (HMM) Basics

Assume that a given target is described bystates, eachstate characteristic of a generally contiguous set of target-sensororientations over which the scattering physics is approximatelystationary as a function of orientation. For the UXO problemconsidered here, we employ an 3 state model. As indi-cated in Fig. 1, state one () corresponds primarily to end-onexcitation, corresponds primarily to oblique excitation, and

corresponds primarily to excitation of the UXO broad side.Note that we are assuming that the UXO has 90symmetry. Al-though this may not be exactly true (a UXO typically has 180symmetry in reality), this is a good approximation over the fre-quencies of interest. The initial state decomposition for the UXOtargets is performed as indicated in Fig. 1, with the details ofthe angles used to define the states not critical, since the entireHMM is subsequently optimized, as discussed further below.The decomposition in Fig. 1 is therefore simply a starting point.

Assume that a sequence of measurements are performed.For the SAR problem of interest here, themeasurements cor-respond to subaperture images. In particular, assume that theSAR aperture defines an angular extentrelative to the targetcenter. The total aperture can be divided intosubapertures,each spanning an angle (here we assume the subaperturesdo not overlap, although this restriction can be loosened). The

subaperture SAR images implicitly “view” the target fromdistinct orientations, and it is these subaperture images that

are processed via the HMM. The images implicitly samplephysics from the target states, with the particular states sam-pled dictated by the details of the target and SAR aperture underconsideration.

The HMM characterizes a doubly stochastic process. Thesequence of measurements sample states of the target,denoted , where the state sequence is treatedstatistically because the absolute target-sensor orientationis “hidden.” Each state is characterized by an ensemble ofscattered waveforms (images), with the selection of a particularsignal from the ensemble also treated statistically. For charac-terization of the HMM, we first define the probability that theinitial subaperture image in the sequence will be in state, or

. For subsequent subaperture images in thesequence, we define the probability of transitioning from state

to state , . The constitutean -dimensional vector , and the an matrix

DONG et al.: MULTI-ASPECT DETECTION OF SURFACE AND SHALLOW-BURIED UXO 1261

. The initial values of these quantities are easily defined interms of the initial state decomposition [5]–[7], with thesealso refined via a subsequent optimization processed. We havediscussed the initial computation of and previously,with the reader referred to [5]–[7] for details.

The HMM is based on the understanding that the scatteringphysics is often a strong function of the target-sensor orienta-tion, but within each of the states, the physics is relativelystationary as a function of orientation. This is addressed here, inthe context of the UXO problem, in the following manner. Weconsider a UXO on the surface of the soil, and producesub-aperture images, from angles uniformly distributed over theextent of the states (over 90, see Fig. 1). These imagesconstitute what is termed a codebook, with composed ofsubaperture images . The elements of thecodebook are termed codes. For each of thesubapertureimages, characteristic of the subaperture sequence under con-sideration, we perform a correlation with each of theimagesin . We associate a given image in the sequence withif, forall the characteristic images in, the correlation is greatest with

. By this process, each of the original subaperture images inthe sequence under test is mapped to one of the codes in, withthis process constituting a generalization of vector quantization[14].

The final HMM element that must be defined is the proba-bility that a given code will be associated with a given targetstate, with denoting the probability that codeis associ-ated with state . These probabilities constitute amatrix . Simple training procedures exist for defining, withthe interested reader referred to [5]–[7] for details.

For a given target under consideration, the HMM classifieris implemented as follows. Assume that a sequence ofsub-aperture images are considered, with each mapped into one ofthe discrete codes in . We therefore now have an observationsequence , with each of the

. The likelihood that is characteristic of target is given,within the context of the HMM, as

(1)

The conditional probabilities for the codes are defined bythe matrix . In (1), each sum is over all possible state se-quences for the set of subaperture images ( possible statesequences), with each sequence weighted by its likelihood ofoccurrence (quantified throughand ). Although the expres-sion in (1) appears computationally expensive to implement,there is much redundancy in the required summations, and theforward–backward (FB) algorithm [15], [16] has been devel-oped to exploit this fact, making computation of (1) highly effi-cient. The expression in (1) is also often treated in an alternativemanner, through exploitation of the Viterbi algorithm [17]. We

have found that HMM classification performance is generallyinsensitive to whether the FB or Viterbi algorithm is utilized.

In the training phase of the HMM classifier, as many-di-mensional subaperture sequences as possible are utilized, eachmapped into an observation sequencevia vector quantization,as discussed above. In the training phase, the expression in (1) iscomputed for all training sequences, and the HMM parameters

, , and are iteratively optimized to maximize the averagelikelihood from (1). In this process, the state decompositionsthemselves are also optimized (refined), underscoring our ear-lier comment that the initial state decomposition (Fig. 1) neednot be perfect to yield good HMM performance after training.In the testing phase, a given sequence of subaperture images ismapped to an observation sequence, as above, and the likelihood(1) is computed. The sequence of images is deemed associatedwith the target representative of the HMM if the likelihood isabove a prescribed threshold. By varying the threshold, one cangenerate the receiver operating characteristic [18]. If there aremultiple targets of interest, an HMM is designed for each, andthe sequence of images is deemed associated with that targetfor which the respective HMM yields the highest likelihood. Ifthe likelihood of all HMMs is below a given threshold, the se-quence of images is deemed characteristic of clutter (i.e., noneof the targets).

B. Physical-Optics Approximation

A key aspect of the HMM, as implemented here for the UXOproblem, is that all training is performed on computed data (forboth the HMM and prescreeners, see Section IV). All such com-putations have been performed via the PO approximation, dueto its computational efficiency and accuracy (for this problem).To address the latter, we plot in Fig. 3 the backscattered RCSof the PO approximation, relative to a rigorous MoM solution[8], with the meshed target (155 mm shell). This target has amaximum diameter of 155 mm and a length of 58.4 cm. Re-sults are shown for the backscattered RCS from this target, withincidence 30 from grazing, and 45with respect to the targetbroadside. In the results of Fig. 2, the target is buried parallel tothe flat air–ground interface, with the top of the target 2.54 cmbelow the interface (recall that we are focusing on surface andshallow-buried UXO). The soil properties considered are char-acteristic of Yuma soil [12], [13] with 5% water content (3.6 0.12 with 0.005 S/m). Results are shown over thebandwidth of the ARL system [12], [13], and it is demonstratedthat the PO approximation generally matches the MoM solutionwell, for both VV and HH polarizations. We note that, in addi-tion to not modeling the target currents in the shadow region, thePO approximation has the related shortcoming of not modelingmultiple wave interaction between the target and interface. Thisexplains why the PO solutions are still not perfect, even at thehigh-frequency end.

In Fig. 3, we plot SAR imagery computed using scatteredfields from the PO approximation, assuming plane-wave inci-dence, VV polarization, and an incident pulse characteristic ofthe ARL BoomSAR [12], [13]. Results are shown for the targetsituated as in Fig. 2, but from three different target-sensor ori-entations, representative of the three states sketched in Fig. 1.


(a)

(b)

Fig. 2. Comparison of the backscattered RCS computed via a physical optics(PO) and method of moments (MoM) solution, for a 155 mm UXO shellburied parallel to the air–ground interface, at a depth of 2.54 cm. The assumedplane-wave excitation is incident 30from grazing and 45 with respect tobroad side. The target mesh used for these computations is shown in Fig. 3. (a)VV polarization and (b) HH polarization.

These images correspond to a 60SAR aperture, VV polariza-tion, and again are for incidence 30from grazing (details of theimaging procedure are discussed in [12]). These images under-score the strong aspect dependence to the SAR imagery from aUXO, with this exploited explicitly via the HMM. Space limita-tions preclude showing comparisons of these images with sim-ilar images computed using MoM-computed scattered fields.However, we have found that the PO and MoM imagery are, onaverage, correlated to better than 0.95 for the UXO cases con-sidered here. Before closing this section, we note from Fig. 3(a)that the image, when the UXO is parallel to the linear SAR aper-ture, is not absolutely symmetrical in the cross-range direction.This is due to the fact that the end and nose of the UXO are notidentical. This asymmetry vitiates the simple three-state modelused here and depicted in Fig. 1. However, it is felt that the slightasymmetry in Fig. 3 does not warrant additional HMM com-plexity (more states), given that small variations in the targetsignature are likely to be undermined by clutter.

C. Subaperture Images

The HMM processes a sequence of subaperture SAR im-ages (each subaperture image using a subset of the total avail-able SAR aperture). The total aperture from the BoomSAR is

60 [12], [13], dictated by the system antennas, whichonly provide approximate polarization purity over this angularrange. Each of the subaperture images could be formed byusing the UWB scattered waveforms (the “raw” scattering data)measured by antennas within the associated subaperture angularsector. However, this implies that one would have to store all theUWB scattered waveforms for each antenna position along theSAR aperture. Alternatively, we can use all of the available scat-tered-field data to form a single, full-aperture image. A sequenceof two-dimensional (2-D) filters (one filter for each of the de-sired subaperture images) is then utilized on this full-apertureimagery to yield the desired sequence of images applied to theHMM. These filters are simple to design and implement, andhave been described in detail elsewhere [7]. This latter approachis desirable, since it implies that we need only store the full-aper-ture image, after which, the original scattered waveforms can bediscarded for our purposes.

It is of interest to examine a typical sequence of subapertureimages, manifested by the sequence offilters applied to theoriginal full-aperture image. In Fig. 4 is shown the full-apertureVV-polarized image of a 155 mm UXO on the surface of theground, oriented at 45with respect to the linear SAR aperture(computed using PO-generated scattering data, assuming an in-cident pulse characteristic of the ARL BoomSAR [12], [13]).Also in this figure is shown a sequence of 7 overlappingsubaperture images of this target, with the center angle of thesubaperture images corresponding to22.5 , 15 , 7.5 , 0 ,7.5 , 15 , and 22.5 (0 is pointing orthogonal to the linear SARaperture, through the target center). Each subaperture image hasan associated aperture of 15( 7.5 about the center angle ofthe subaperture).

We note from Fig. 4 that each subaperture image is character-ized by a loss of cross-range resolution relative to the originalfull-aperture image. This is the price one pays for exploiting theaspect dependence of the target scattering in the context of sub-aperture images, since the cross-range resolution is tied to thesize of the SAR aperture. Nevertheless, one notes that the se-quence of imagery embodies significant information. It is thisphenomenology we seek to exploit, in the context of the HMM,with the goal of distinguishing UXO from clutter.

Before proceeding, it is of interest to address the utility ofpartitioning the original full-aperture image into a sequence ofsubaperture images, given that all information in the sequence ofimages is implicitly contained in the original full-aperture image(and we lose cross-range resolution in the subaperture images).Clutter is likely to undermine some subaperture images morethan others, depending on the clutter position relative to portionsof the full aperture. The HMM is a statistical algorithm that doesnot require that all subaperture images be well matched to thetarget in question [5]–[7], as long as a subset is so matched,and the sequence order of measured images is consistent withthe HMM. By contrast, if one were to build a processor basedonly on the full-aperture image, the latter will be corrupted by


Fig. 3. Computed SAR images for a 155 mm shell buried 2.54 cm in Yuma soil [12], [13], with the target axis parallel to the air–soil interface. The computationsuse pulsed plane-wave excitation at 30from grazing, characterized by the incident pulse described in [12] and [13]. The images use an aperture length that yieldsa 60 angle between the target center and aperture. The images are produced by scattered fields from a physical optics (PO) forward solver. All results are for VVpolarization. (a) Target axis parallel to linear SAR aperture, and (b) target axis 45with respect to linear SAR aperture.

all clutter that appears in the image region under consideration,even if the clutter only contributes from a few subapertures ofthe total measurement.

III. HMM P ERFORMANCE ONMEASUREDUWB SAR DATA

A. Measurements

The UWB SAR measurements were performed by the U.S.Army Research Laboratory at Yuma Proving Ground, Yuma,AZ. The majority of the sensor hardware is mounted to thebasket of a telescoping boom lift capable of moving at approx-imately 1 km/h, while the basket is elevated to 45 m. For a typ-ical collection geometries, down-look angles to the target varyfrom 45 to approximately 10(from grazing), depending on therange to the target and the height of the boom. For all measure-ments reported here, the depression angle was approximately40 and therefore, over the extent of the linear SAR aperture,to a good approximation, only the azimuthal angle is varyingwith respect to a given target (as assumed in the HMM for sim-plicity). The UWB SAR system employed is operated directly in

the time domain, covering a usable bandwidth of approximately50–1200 MHz. Since the sensor is typically distant from the tar-gets under investigation, the target excitation is approximatelya plane wave (it is so modeled in the simulations discussed inSection III). The pulse emitted by the radar, as well as other de-tails of the sensor, are discussed in [12], [13].

At the Yuma test site, a large set of inert ordnance wereburied in the ground at various depths and orientations withrespect to the linear SAR aperture. Although there were manydeeply buried UXO (at 1 m depth or more), only the surfaceand shallow-buried UXO were consistently visible in theSAR imagery, underscoring the difficulty of radar-based UXOdetection and motivating our goal of UXO-range detection,rather than detection of each individual UXO. As indicated inthe introduction, in UXO-range detection, one hopes to detecta large percentage of the surface and flush-buried UXO whilerealizing a low false-alarm rate (FAR). With regard to the latter,the FAR is strongly dictated by the environment in which themeasurements are performed. Yuma is relatively favorable inthis context, since the test site is characterized primarily by


Fig. 3. (Continued.) (c) Target axis perpendicular to linear SAR aperture.

desert conditions in which there are rocks, animal burrows,and relatively benign foliage. The soil conditions at Yuma aredetailed in [12], [13]. However, as indicated below, even thisrelatively propitious environment poses a significant challengeto radar-based sensors. For example, general soil inhomo-geneities constitute clutter to a radar system, with such poorlyunderstood, since such inhomogeneities are often destroyedupon excavation. Consequently, while new electromagneticmodels are yielding increased insight into the phenomenologyof scattering from man-made targets, such as UXO, scatteringfrom naturally occurring clutter is far less understood. Thisis not due to a shortcoming in the electromagnetic modelingtools, but rather to a poor understanding of the subsurfaceenvironment.

B. Prescreeners

A SAR system can quickly collect a large amount of im-agery. It is therefore of interest to develop simple algorithmsthat prescreen the imagery with the goal of eliminating for sub-sequent consideration those regions at which it is relatively clearno target exists. The requirements of a prescreener are that it

be computationally efficient, while yielding a high probabilityof detection (any targets lost to the prescreener cannot be re-covered subsequently). It is acceptable if the FAR of a pre-screener is relatively high, since these false alarms will (ideally)be pruned subsequently by more sophisticated algorithms. In thework considered here, we have considered three prescreenersclasses.

Our first prescreener is based on our ability to model the SARimages of surface and buried UXO. We consider the SAR imageof a flush-buried UXO, from several target-sensor orientations.In particular, we consider the full-aperture imageof the UXO, with the center of the SAR aperture ranging az-imuthally from 0 to 180 . In this way, we produce 181full-aperture SAR images of the UXO (using a 1azimuthalshift between consecutive images). Each of theSAR imagesis arranged as a one-dimensional (1-D) column vector, fromwhich we computed the average correlation between images

(2)

An eigenvector decomposition of (2) yields the principal eigen-vectors characteristic of the space spanned by, with theseeigenvectors associated with the dominant eigenvalues. This isthe Karhunen–Loève transform (KLT) [19]. In Fig. 5, we plotthe eigenvalues associated with the 155 mm UXO shell consid-ered in Figs. 3–5. The first 19 eigenvalues contain 99% of theenergy in the sum of all eigenvalues of, and we use the asso-ciated 19 eigenvectors in our first prescreener.

One could apply these 19 characteristic images in the contextof a matched filter. However, it is well known that matched fil-ters are only optimal for signals in white Gaussian noise [19].The clutter in the SAR imagery mitigates the utility of a matchedfilter. Alternatively, one can design a Wiener filter [18] to mit-igate the effects of clutter and to produce better discriminationthan a simple matched filter. This extension of the traditionalmatched filtering has been termed expansion matching (EXMfilters) in the signal processing community [20]. Such EXM fil-ters, based on the aforementioned eigenvectors, have been ap-plied here in the context of our initial prescreener. The EXMfilters must be implemented for all 2-D shifts across the SARaperture, with this implemented efficiently via a 2-D FFT (onboth the EXM filters and the SAR image). At each pixel value,we consider the output from the 19 EXM filters that are max-imum (using full-aperture imagery) and a threshold is set, withall pixels below a particular threshold discarded for subsequentconsideration. The selection of the threshold is based on a com-promise between retaining as many targets as possible, whileeliminating as much of the image that is clearly devoid of tar-gets.

While the EXM filters (based on the reduced set of mod-eling-generated eigenvectors) produce relatively good results,such filters have limitations. In particular, any large-amplitudeportion of the SAR image will produce a relatively large outputfrom an EXM filter, even if the correlation between the filter andimage is low. We therefore consider a subsequent class of pre-screeners, based on the spatial extent of energy in the image. Asseen from Fig. 3, the spatial extent of energy in a UXO image


Fig. 4. Original (top left) full-aperture VV-polarized image of a 155 mm UXO on the surface of the ground, oriented at 45with respect to the linear SARaperture (computed using PO-generated scattering data, assuming an incident pulse characteristic in [12], [13]). Also shown are a set of overlapping subapertureimages of this target, with the center angle of the subaperture images indicated. Each subaperture image has an associated aperture of 15.

Fig. 5. Eigenvalues corresponding to the surface 155 mm shell atop Yumasoil [12], [13], as computed from the correlation matrix of the full-aperture VVpolarized SAR imagery, considering center angles of the SAR image rangingfrom 0 to 180 , in 1 increments.

is relatively small, dictated by the relatively small target size(relative to system wavelength). Consequently, for each regionin the SAR image that passed through the first prescreener, wecompute the standard deviation of the image strength, about themean energy position in a prescribed area (this area made con-sistent with the size of the target images, as in Fig. 3). Thissimple prescreener efficiently eliminates any portions of theSAR image that have energy extent too large to be consistentwith a UXO. All portions of the image that pass through thisstage are then sent to another prescreener of the same genre. Inparticular, we consider templates as shown in Fig. 6. The totalenergy from the SAR image inside the circle (“inner” energy)is compared to the energy in the area between the circle and el-lipse (“outer” energy). The feature applied from this template isthe ratio of the inner to outer energy, with a threshold again seton the output from this parameter. A proper threshold is againdetermined by consideration of the variability of this feature for

Fig. 6. Template applied in one of the prescreeners, used to eliminate clutterthat occupy a spatial extent in the SAR imagery that is too large to be consistentwith a UXO. The sizes of the template components are dictated by the expectedextent of UXO in the SAR imagery (see Fig. 3). The diameter of the inner circleis 0.6 m and the outer-circle diameter is 2.25 m.

computed data of the form in Fig. 3. The size of the inner circleis chosen such that it encloses the target image (Fig. 3).

The three prescreeners discussed above are computationallyvery efficient, and therefore easily implemented. A subse-quent more computationally expensive prescreener involvescalculating correlations between a library of characteristic(full-aperture) image templates and the measured SAR image(this requires more than a simple 2-D FFT). However, afterhaving implemented the three prescreeners above, the spacethat need be interrogated with the more sophisticated correla-tion filter is much reduced. We therefore consider the modeledfull-aperture image of the UXO, with center aperture positionoriented at 0, 10 , 30 , 180 with respect to the target(this number of templates is consistent with the 19 eigenvaluesdiscussed above for the 155 mm shell). We compute the corre-lation of the remaining portions of the measured SAR image(after the initial prescreeners) with these 19 templates, yielding19 correlation values for each point of interest. If the maximumcorrelation of this set is above a prescribed threshold, thisregion of the image passes on to the more sophisticated HMMtest.

C. HMM Implementation

The correlation matrix used to implement the first prescreeneris implemented using computed imagery for the 155 mm shell,


Fig. 7. Photographs of the three UXO in the measured SAR imagery used to test the performance of the classifier.

for VV polarization. The correlation filters, for the last pre-screener, were also implemented based on computed imageryfor the same scattering scenario. The HMM is likewise trainedentirely on computed data from the 155 mm shell, with VV po-larization. In particular, the codebook discussed in Section III-Awas implemented with 10 overlapping subaperture im-ages, with center angles at 0, 10 , 20 , 90 , each with a15 angular aperture. Concerning training with the computed155 mm shell data, we considered all possible 7 lengthsubaperture sequences (as in Fig. 4), with the center of the firstsubaperture image in the sequence ranging over the angles 0,1 , 2 , 179 , 180 . The HMM parameters , and wereoptimized using the above training data, through application ofthe Viterbi algorithm [17]. After the HMM for the 155 mm shellwas so trained, its performance is tested on measured data, asdiscussed below.

D. Algorithm Performance

We address performance of the detector through considera-tion of three distinct UXO, with each shown in Fig. 7. The 155mm shell, 105 mm shell, and 81 mm shell are all of approxi-mately the same length, with distinct maximum-diameter sizes.These targets look very similar to a radar system operating at thebandwidth considered. Therefore, as discussed above, we builda single HMM (and a single set of prescreeners), based on com-puted training data from the 155 mm shell on the soil surface.The full classifier (prescreeners and HMM) is tested on mea-sured SAR data from Yuma, and if the HMM correctly declares

a particular region occupied by one of thethreetargets, this istermed a detection. At regions for which the classifier declares aUXO, but none exists, a false alarm is declared. It is necessary toplace a “hallow” around a given declaration, to define the spatialregion in which a target is deemed present. In the work reportedhere, we have used circular regions of diameter 5 m. All resultsreported here are for VV polarization.

In the following, we present receiver operating characteristic(ROC) performance for subsets of the target classes considered,because we have found that the algorithms detect some typesof targets better than others. Such performance characteristicsyield insight into the types of scattering physics for which thealgorithms work particularly well.

In our first set of results, we consider UXO that are in theground at a 45 angle, with the top of the target flush buriedwith the interface (nose down). There were 36 such targets. Thealgorithms performed best for this target class, with this dis-cussed further in Section III-E. In Fig. 8, we plot the ROC forthe last three prescreeners discussed above. The ROC quanti-fies the probability of detection as a function of the FAR, thelatter quantified in terms of false alarms/km(the total regionconsidered for this test encompassed 0.23 km). We see fromFig. 8 that the performance of the prescreeners improves as theprescreener complexity increases. In particular, we see that theworst performance occurs for the standard-deviation test, withsignificant improvement demonstrated by the energy ratio sum-marized in Fig. 6. Finally, the most-complex, correlation-basedprescreener, which uses computed full-aperture imagery, yields


Fig. 8. Receiver operating characteristic (ROC) for three of the prescreeners,as scored by only considering the angled-entry UXO with the top of the targetflush buried.

the best performance. The advantage of pruning via a sequenceof prescreeners is realized by the fact that the most complexprescreener need only be performed over a small subset of theoriginal data.

One issue that must be discussed is that, although the ROCsin Fig. 8 demonstrate performance as a function of the detectorthreshold, when one transitions from one prescreener to thenext, a particular threshold must be selected for the former, thisdictating which parts of the image are discarded, and which goon to the next phase. This implies that the final performance ofsubsequent detectors may not achieve a probability of detectionof unity, since targets may not be passed forward from anearlier prescreener. This explains why the correlation-basedprescreener in Fig. 8 does not reach a detection probabilityof unity. Care must be take in selection of these prescreenerthresholds, with the latter dictated by the clutter statistics.

The composite performance of the prescreeners summarizedin Fig. 8 is relatively good. However, note that we are achievinga probability of detection of 0.97 with approximately 1000false alarms/km. This FAR is likely too high to reliablyperform UXO-range detection, especially given the relativelybenign clutter environment considered here (likely to be worsefor other cases). This motivates the HMM, the performanceof which we now address. In Fig. 9, we plot the ROC for theHMM as scored with the angle-entry targets. For comparison,in Fig. 9, we also plot the results of the correlation detector fromFig. 8. We note that the HMM yields a substantial improvementin classifier performance, especially at the low FAR values.

The next set of ROC curves are as in Figs. 8 and 9, but now,in addition to considering the angle-entry UXO, we considerUXO parallel to the air–ground interface (both on the surfaceand flush-buried). With regard to the latter, we only considerthose interface-parallel targets for which, for some portion ofthe SAR aperture, the target axis is parallel to or orthogonal tothe linear sensor path. For this target class, we have a total of54 targets. Again, we discuss in Section III-E the reasons forconsidering these special cases. In Figs. 10 and 11, we show the

Fig. 9. As in Fig. 8, but here we consider the performance of the HMM,compared to the correlation-based prescreener.

Fig. 10. Receiver operating characteristic (ROC) for three of the prescreeners,as scored by only considering the angled-entry UXO with the top of the targetflush buried, as well as the UXO for which the target was either parallel orperpendicular to some part of the linear SAR aperture.

results of the prescreeners and of the HMM, as in Figs. 8 and9, respectively. We notice that, by inclusion of this additionaltarget class, the overall ROC performance deteriorates, althoughthe relative trends between different algorithm types are as inFigs. 8 and 9. In particular, note in Fig. 11 that at an FAR of40/km , the HMM correctly detects over 40% of the targets,with the performance of the correlation detector significantlylower (about 10%).

In Figs. 12 and 13, we plot the results of the prescreeners andof the subsequent incorporation of the HMM, as applied to allsurface and flush-buried UXO, constituting a total of 84 targets.The principal difference between Figs. 12 and 13 and Figs. 10and 11 is the inclusion of surface and flush UXO that are notat some point oriented parallel to or orthogonal to the linearSAR aperture. The performance of the classifiers is now further


Fig. 11. As in Fig. 10, but here we consider the performance of the HMMcompared to the correlation-based prescreener.

Fig. 12. Receiver operating characteristic (ROC) for three of the prescreeners,as scored by considering all surface and flush-buried UXO.

degraded, although the HMM is still correctly identifying overa fourth of the targets at a FAR of 40/km.

E. Discussion

We have broken the above presentation into the three por-tions, with the goal of delineating the types of targets for whichthe SAR system is particularly effective. In particular, we foundthat best performance was achieved for angle-entry targets, withthe top of the target flush buried. We explain this phenomenonas follows. The portion of the target nearest the surface producesan end-diffracted component, that looks approximately the samefrom all antenna positions along the linear SAR aperture. Thisimplies that the response from this component is approximatelythe same for each of the antenna positions used to form the fulland subaperture images, yielding a strong signature that is rela-tively less sensitive to competing clutter.

Fig. 13. As in Fig. 12, but here we consider the performance of the HMMcompared to the correlation-based prescreener.

In this same context, if the target broadside is parallel to thelinear SAR aperture for some antenna positions, at these po-sitions the UXO signature will be strong, and less sensitive toclutter. Moreover, for such targets, as one moves along the se-quence of subaperture images, the signature will increase asbroadside excitation is approach, at which point the signaturewill be maximized in strength, and then the image strength willdiminish as one moves away from this cardinal angle. This se-quence produces a very distinctive signature, exploited effec-tively via the HMM. Similar issues hold for the case in whichthe target is orthogonal to the portion of the linear SAR aperture.

IV. CONCLUSIONS

The utility of employing UWB SAR for detection of UXOhas been investigated. We have emphasized that a SAR-basedsystem is unlikely to find all UXO, especially those burieddeeply. However, at a former bombing range, there is often alarge amount of surface and flush-buried UXO. The goal of thework reported here was investigation of whether a UWB SARsystem can detect a “large enough” percentage of such UXO,at a “low enough” false-alarm rate, such that a former bombingrange can be detected. The answer to this question involvesboth engineering and policy issues. We have sought to focus onthe former, with the goal of developing algorithms that providean optimal utilization of the wave physics, explicitly utilizingmodels that simulate electromagnetic scattering from suchtargets.

We have considered several prescreeners and have imple-mented an HMM, with all of these algorithms trained entirelyon computed data. We have demonstrated that the performanceis a strong function of the UXO position in the ground or on thesurface. This underscores that it is salutary to view the UXOfrom as many target-sensor orientations as possible. Here wehave considered a single linear aperture. However, the workpresented here suggests that it may be desirable to considermultiple linear sensor paths, or perhaps a circular SAR, to


improve the likelihood that one or more of the favorabletarget-sensor orientations discussed in Section III-E is realized.

The work reported here constitutes only a beginning of moreresearch that should be directed at this problem. For example,we have only considered imagery from a single polarization(VV). Although not presented here, we have also addressedfusing the performance of prescreeners based on both VV andHH polarized fields, and have witnessed further improvementsin performance. We have not discussed such results further, be-cause a significant issue in UWB SAR sensors involves accuratepolarization calibration. This is an ongoing topic of research, butit is expected that the fusion of multiple polarizations will fur-ther improve the detection results.

The SAR-based detection of UXO, with the goal of bombingrange detection, is a clutter-limited problem. In particular, thesuccess of such a system is predicated on realizing measureddata from UXO with signature amplitudes and features (as afunction of target-sensor orientation) that allow one to separatetargets from clutter. This implies that performance is stronglylinked to the clutter characteristics. The test conditions at YumaProving Ground were relatively favorable in this connection, thesoil being relatively low-loss and the clutter generally benign.Nevertheless, desirable performance was only achieved afterimplementing sophisticated detectors that explicitly accountedfor the wave physics. To further quantify the utility of such asystem, more challenging clutter scenarios must be considered.Moreover, since the number of different environments that canbe considered empirically is limited, further insight is requiredinto the clutter sources, with this insight transitioned to the elec-tromagnetic models.

REFERENCES

[1] Y. Das, J. E. McFee, J. Toews, and G. C. Stuart, “Analysis of an elec-tromagnetic induction detector for real-time location of buried objects,”IEEE Trans. Geosci. Remote Sensing, vol. 28, pp. 278–287, May 1990.

[2] R. W. P. King and C. W. Harrison, Jr., “The transmission of electro-magnetic waves and pulses into the earth,”J. Appl. Phys., vol. 39, pp.4444–4452, Aug. 1968.

[3] J. A. Fuller and J. R. Wait, “Electromagnetic pulse transmission inhomogeneous dispersive rock,”IEEE Trans. Antennas Propagat., vol.AP-20, pp. 530–533, July 1972.

[4] D. L. Moffat and R. J. Puskar, “A subsurface electromagnetic pulseradar,”Geophysics, vol. 41, pp. 506–518, June 1976.

[5] P. Runkle, P. K. Bharadwaj, L. Couchman, and L. Carin, “HiddenMarkov models for multiaspect target classification,”IEEE Trans.Signal Processing, vol. 47, pp. 2035–2040, July 1999.

[6] P. Runkle, L. Carin, L. Couchman, T. Yoder, and J. Bucaro, “Multiaspecttarget identification with wave-based matched pursuits and continuoushidden Markov models,”IEEE Trans. Pattern Anal. Machine Intell., vol.21, pp. 1371–1378, Dec. 1999.

[7] P. Runkle, L. Nguyen, J. McClellan, and L. Carin, “Multiaspect targetdetection for SAR imagery using hidden Markov models,”IEEE Trans.Geosci. Remote Sensing, to be published.

[8] J. Q. He, T. J. Yu, N. Geng, and L. Carin, “Method of moments analysisof electromagnetic scattering from a general three-dimensional dielec-tric target embedded in a multilayered medium,”Radio Sci., vol. 35, pp.305–313, Mar.–Apr. 2000.

[9] N. Geng, A. Sullivan, and L. Carin, “Multi-level fast multipole algorithmfor conducting targets embedded above or within a lossy half space,”IEEE Trans. Geosci. Remote Sensing, vol. 38, pp. 1561–1573, July 2000.

[10] J. M. Bourgeois and G. S. Smith, “A fully three-dimensional simulationof ground penetrating radar: FDTD theory compared with experiment,”IEEE Trans. Geosci. Remote Sensing, vol. GE-34, pp. 36–28, Jan. 1996.

[11] R. F. Harrington,Time-Harmonic Electromagnetic Fields. New York:McGraw Hill, 1961.

[12] L. Carin, N. Geng, M. McClure, J. Sichina, and L. Nguyen, “Ultra-wide-band synthetic-aperture radar for mine-field detection,”IEEE An-tennas Propagat. Mag., vol. 41, pp. 18–33, Feb. 1999.

[13] S. Vitebskiy, L. Carin, M. A. Ressler, and F. H. Le, “Ultra-wideband,short-pulse ground-penetrating radar: Simulation and measurement,”IEEE Trans. Geosci. Remote Sensing, vol. 35, pp. 762–772, May 1997.

[14] Y. Linde, A. Buzo, and R. M. Gray, “An algorithm for vector quantizerdesign,”IEEE Trans. Commun., vol. COM-28, pp. 84–95, Jan. 1980.

[15] L. E. Baum, T. Petrie, G. Soules, and N. Weiss, “A maximization tech-nique occurring in the statistical analysis of probabilistic functions ofMarkov chains,”Ann. Math. Statist., vol. 41, pp. 164–171, 1970.

[16] L. R. Rabiner, “A tutorial on hidden Markov models and selected appli-cations in speech recognition,”Proc. IEEE, vol. 77, pp. 257–285, Feb.1989.

[17] A. Viterbi, “Error bounds for convolutional codes and an asymptoticallyoptimum decoding algorithm,”IEEE Trans. Inform. Theory, vol. 13, pp.260–269, Apr. 1967.

[18] S. M. Kay,Fundamentals of Statistical Signal Processing. EnglewoodCliffs, NJ: Prentice-Hall, 1998, vol. 2, Detection Theory.

[19] S. S. Haykin,Adaptive Filter Theory. Englewood Cliffs, NJ: Prentice-Hall, 1995.

[20] D. Nandy and J. Ben-Arie, “Generalized feature extraction using expan-sion matching,”IEEE Trans. Image Processing, vol. 8, pp. 22–32, Jan.1999.

Yanting Dong (S’00) received the B.S. degree in electrical engineering and theM.E. degree in automation from Tianjin University, China, in 1993 and 1996,respectively. She received the M.S. degree in electrical engineering from DukeUniversity, Durham, NC, in 2000, and is now pursuing the Ph.D. degree in theDepartment of Electrical and Computer Engineering, Duke University.

From 1996 to 1998, she was with the Department of Automation, TianjinUniversity, working on electromagnetic tomography systems. Since 1999, shehas been working as a Research Assistant with Duke University. Her researchinterests are in statistical signal processing, information theory, detection andestimation, tomographic technique, and applied electromagnetics.

Paul R. Runkle received the B.S. degree in applied mathematics and physicsfrom the University of Wisconsin, Madison, in 1988, and the M.S. and Ph.D.degrees in electrical engineering from the University of Michigan, Ann Arbor,MI, in 1992 and 2000, respectively.

Since 1998, he has been a Research Associate in the Department of Electricaland Computer Engineering, Duke University. His research interests include sta-tistical signal processing and modeling, multichannel signal processing, imageprocessing, and related applications.

Lawrence Carin (SM’96–F’01) was born March 25, 1963 in Washington, DC,and earned the B.S., M.S., and Ph.D. degrees in electrical engineering at theUniversity of Maryland, College Park, in 1985, 1986, and 1989, respectively.

In 1989, he joined the Electrical Engineering Department, Polytechnic Uni-versity, Brooklyn, NY, as an Assistant Professor, and became an Associate Pro-fessor there in 1994. In September 1995, he joined the Electrical EngineeringDepartment, Duke University, Durham, NC, where he is now a Professor. Heis currently the Principal Investigator on a Multidisciplinary University Re-search Initiative (MURI) on demining. His current research interests includeshort-pulse scattering, subsurface sensing, and wavebased signal processing.

Dr. Carin is an Associate Editor of the IEEE TRANSACTIONS ONANTENNAS

AND PROPAGATIONand is a member of Tau Beta Pi and Eta Kappa Nu.

Raju Damarla received the B.Sc. degree (hons.) in mathematics, the B.Tech.degree (hons.) in electronics and electrical communication engineering, and theM.Tech. degree in controls and computation engineering from the Indian Insti-tute of Technology, Kharagpur, India. He received Ph.D. in engineering fromBoston University, Boston, MA.

He was an Assistant Professor in the Electrical Engineering Department, Uni-versity of Kentucky, Lexington, until 1994. He is currently an Electronics En-gineer with the U.S. Army Research Laboratory, Adelphi, MD. His interestsinclude signal processing, automatic target detection and recognition algorithmdevelopment, and neural networks.


Anders Sullivan (M’93) was born August 9, 1963, in Staten Island, NY. Hereceived the B.S. and M.S. degrees in aerospace engineering from the GeorgiaInstitute of Technology, Atlanta, GA, in 1985 and 1987, respectively, and thePh.D. degree in electromagnetics from Polytechnic University, Brooklyn, NY,in 1997.

From 1988 through May 1998, he was with the Air Force Research Labo-ratory, Eglin AFB, FL. From June 1998 through September 1999, he was withthe Electrical Engineering Department, Duke University, Durham, NC, as a Re-search Associate. Since September 1999, he has been with the Army ResearchLab, Adelphi, MD. His current research interests include modeling complex tar-gets and short-pulse scattering.

Dr. Sullivan is a member of Tau Beta Pi and Sigma Gamma Tau.

Marc A. Ressler received the B.S. degree in electrical engineering from theUniversity of Maryland, College Park, in 1969, and the M.S. degree in electricaland computer engineering from the University of Michigan, Ann Arbor, in 1973.

He has been with the Army Research Laboratory (ARL) and one of its prede-cessors, the Harry Diamond Laboratories, since 1969, where he worked on a va-riety of programs including battlefield data processing and fusion, and low-fre-quency and microwave radar systems.

Mr. Ressler is currently assigned to the Sensors and Electron Devices Direc-torate of ARL, where his area of interest is low frequency, ultra-wideband radarfor foliage and ground penetration applications.

Jeffrey Sichina received the B.S.E.E. degree in 1975 from the University ofPittsburgh, Pittsburgh, PA. He subsequently undertook graduate study at theUniversity of Maryland, College Park.

In 1974, he joined Harry Diamond Laboratories, Adelphi, MD, a componentof the U.S. Army Materiel Command. From 1974 through 1985, he was a StaffEngineer, working on a variety of electronic fuzing programs. His primary re-search interest included digital signal processing, FM/CW systems, and elec-tronic counter-counter measures. In 1988, he joined the Radar Branch, and wasresponsible for development of a miniature moving-target-indicator radar forunmanned air vehicles. In 1992, he was named Chief of the Radar Branch andwas responsible for a variety of long-term applied research undertakings withinthe Army. Among these was an effort aimed at determining the effectiveness ofultra-wideband (UWB) radar for detection of concealed objects such as buriedmines and UXO. His current research interests include algorithm developmentand detection theory.

Mr. Sichina is a member of Eta Kappa Nu.

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