A Novel, Fast, Approximate Target Detection Technique for Metallic Target Below a Frequency...

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 58, NO. 5, MAY 2010 1699

A Novel, Fast, Approximate Target DetectionTechnique for Metallic Target Below a Frequency

Dependant Lossy HalfspaceHoi-Shun Lui, Member, IEEE, Nicholas V. Z. Shuley, Member, IEEE, and Aleksandar D. Rakic, Senior Member, IEEE

Abstract—The extinction pulse (E-Pulse) technique has beenwidely applied to problems involving radar target identification.In this paper a fast approximate target detection and recognitionscheme based on the E-Pulse technique is proposed and appliedto a subsurface target detection and recognition scenario. Pre-vious studies have demonstrated that the target resonances forsubsurface targets are closely related to the target resonancesfor a target within a homogenous environment. In the proposedmethod, the target resonance for the target in the homogenousmedium will be used to construct the E-Pulse for target detectionand recognition purposes. The details of the proposed methodwill be described in this paper. The obvious example of a targetbelow a dielectric halfspace is the use of ground penetratingradar (GPR) for detecting and recognizing unexploded ordnance(UXO). However, instead of a GPR related scenario, a numericalexample of a biomedically related problem, of a hip prosthesismodel sited within a halfspace of homogenous human tissue modelwith realistic dielectric properties will be used to demonstrate thefeasibilities of the proposed technique for target detection andrecognition. The reasons for the choice of this particular examplewill also be explained in the paper.

Index Terms—Approximation method, automated target recog-nition, resonance based target recognition, subsurface target de-tection, time domain electromagnetics, transient scattering.

I. INTRODUCTION

R ESONANCE based radar target recognition has beenwidely investigated since the introduction of the singular

expansion method (SEM) in the mid 1970s [1]. SEM con-siders the application of circuital concepts such as the impulseresponse and transfer function directly to electromagneticscattering phenomena. According to the SEM, the complexresonant frequencies (CRFs) extracted from the late time ofthe time domain target signature depend exclusively on thetarget geometry and its associated dielectric properties. Target

Manuscript received November 12, 2008; revised June 12, 2009; acceptedNovember 10, 2009. Date of publication March 01, 2010; date of current versionMay 05, 2010. This work was supported in part from the Australian ResearchCouncil (ARC) under Grant number DP0557169.

H.-S. Lui was with the School of Information Technology and Electrical En-gineering, The University of Queensland, Brisbane 4072, Australia. He is nowwith the Department of Signals and Systems, Chalmers University of Tech-nology, SE-412 96 Gothenburg, Sweden (e-mail: [email protected]).

N. V. Z. Shuley and A. D. Rakic are with the School of Information Tech-nology and Electrical Engineering, The University of Queensland, Queensland4072, Australia (e-mail: [email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TAP.2010.2044317

recognition schemes have been widely applied to pulsed radarapplications such as scaled aircraft model recognition [2].

Since the introduction of the concept of target resonance, ef-fort has largely focused on using the resonant modes as a compactfeature set for target identification. Basically the “free-space”CRFs (CRF for targets in free-space) are a set of target only de-pendent parameters extracted from the late time response and assuch, form a characteristic pattern in the S-plane. Moffatt andMains [3] first proposed the concept of target recognition basedon target dependant resonant frequencies using a predictor-cor-relator approach. Later, various other target recognition schemeswere developed based on the uniqueness of the target resonantfrequencies, for examples the kill pulse (K-Pulse) [4], extinctionpulse (E-Pulse) [2], [5] and single-mode pulse (S-Pulse) [5]. Allof these are synthesized time domain linear filters which anni-hilate some, or all, of the resonant modes of the target responsewhen convolved with the target return.

Resonance based target recognition based on the SEM hasbeen widely applied to targets in free space and successfuldescriptions can be found throughout the considerable litera-ture [1]–[8]. An extensive summary of resonance based targetrecognition in early work from 1970s–1980s can be foundin [2]. Amongst all these filter-based techniques, the E-Pulsetechnique has drawn the most attention and success since itsintroduction. Other than target recognition, studies have alsobeen conducted on improving the E-Pulse performance usingdifferent basis functions [8] and applying the E-Pulse techniquefor resonance extraction [9]. Recently, the E-Pulse techniquehas also been applied to target detection for a target in thepresence of sea clutter [10], monitoring layered materials [11],monitoring target depth changes [12] and geometrical changes[13] for target below a halfspace and target recognition usingthe novel “Banded” E-Pulse technique [14].

Other than targets in free space, target resonances for metallicwires and planar objects sited below a halfspace have beenaddressed in the literature [15]–[17]. With the introduction ofthe discontinuity of the dielectrics for the subsurface problem,the “subsurface” CRF (CRF of subsurface target) are no longerpurely dependent on the shape and dielectric properties of thetarget itself, but also the surrounding environment. In general,as the dielectric properties of the surrounding environment, orthe orientation and the depth of the target vary, the resonantfrequencies correspondingly vary in position in the Laplacedomain (s-plane). Due to the complexity of the problem, thereis, so far, no empirical model to characterize such kind ofchanges for “subsurface” CRF.

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1700 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 58, NO. 5, MAY 2010

Fig. 1. Electromagnetic scattering problems for (a) target in free space, (b) target below an interface, (c) target inside a homogeneous environment.

Another closely related problem is the case of a target em-bedded within a homogenous medium [15]–[18]. Physically,comparing the halfspace and fully homogenous media prob-lems, the former has a discontinuity between two media, whilesuch discontinuity does not exist for the latter. Fig. 1 details thedifferences between a target in free space, a target within a halfs-pace and target inside a homogeneous medium. In terms of theirresonant frequencies, these three problems are also closely re-lated to each other. Baum [18] has studied the resonant behaviorof the target within the homogeneous medium analytically. Withthe knowledge of the relative permittivity and conductivity ofthe media together with the resonant frequency of the target infree space, an approximation of the “homogenous” CRF (CRFof the target inside the homogenous medium) can be made usingBaum’s Transform [18]. On the other hand, the behavior of the“subsurface” CRF has been studied numerically using full-wavecomputational electromagnetic tools [15]–[17]. Numerical re-sults show that each “subsurface” CRF varies its position on theS-plane as a spiral pattern around the “homogenous” CRF of thesame target.

Whilst the “subsurface” CRF have certainly been extensivelyevaluated and used for target classification purposes, to ourknowledge, there has not been any target recognition scheme inthe context of resonance based radar target recognition that hasbeen employed for the subsurface target detection or recogni-tion problem. Together with the close relationship between the“subsurface” CRF and the “homogenous” CRF, a resonancebased target detection and recognition scheme for subsurfacetargets is proposed in this paper. Instead of evaluating thesubsurface target resonances using a full wave electromagneticmodel, target detection and recognition will be based on ahomogeneous approximation using Baum’s Transform. TheE-Pulse is then constructed based on the “homogenous” CRFand convolved with the target signatures from subsurfacetargets. It is conjectured that if the E-Pulse is constructed withthe transformed “homogenous” CRF, the convolution withthe halfspace measured or computed signature should providesufficient discrimination to allow target detection. In view ofthis, we examine the possibility of applying this proposedscheme with a number of numerical examples.

The paper is outline as follows. In the next section, a shortreview on resonance based subsurface target detection is given,followed by the details of the E-Pulse technique. The proposedmethod is given in detail in Section IV. In Section V numericalexamples using a model of a hip prosthesis and two cylindricalobjects embedded in human tissue is detailed exemplifying thetechnique. Discussion and conclusions are given in Sections VI

and VII. In this paper, the term “recognition” and “identifica-tion” will be used synonymously.

II. RESONANCE BASED TARGET RECOGNITION FOR A TARGET

BELOW A HALFSPACE

A brief review of the target resonance concept for a subsur-face target is given in this section. This section is divided intothree parts. First, a brief review of the CRF of subsurface tar-gets is given followed by some details and challenges relating toresonance extraction. The relationship between the “free-space”CRF, “subsurface” CRF and “homogenous” CRF, as related toBaum’s transform will be described and explained.

A. Resonances for Subsurface Target

Resonance based target recognition is based on the SEM.Upon excitation of the target in free space using a short elec-tromagnetic pulse, the late time portion of the target signaturecan be expressed as [2]

(1)

where and are the aspect dependent amplitude and phaseof the resonant mode and is the onset of the late timeperiod. It is assumed that only modes are excited by the in-cident field. The CRF are given by , whereand are the damping coefficients and resonant frequenciesrespectively. This description is used for targets in free spacewhere the CRF correspond purely to the physical properties ofthe target geometry including its dielectric properties and asso-ciated loss mechanisms. Theoretically at least, these CRF areaspect independent and can therefore be used as a feature setfor target detection and recognition.

The scattering problem becomes increasingly complicatedwhen the target is buried under a halfspace. The “total target” isthe object in the presence of the environment. Computation ofthe target signature for a target below an interface is much morecomplicated than if the target is in free space. With the introduc-tion of the halfspace, a full wave Sommerfeld analysis in terms ofthe Green’s function is required. This may be achieved in eitherthe frequency domain [19], [20] and then inverse transformedto the time domain or, in the time domain directly [21]. Eitherformulation is complicated and involves considerable effort.

The resonant behavior of the target sited below the halfspaceis also much more complicated than the target in free space.Apart from the constitutive properties of the target itself,the subsurface resonant frequencies were also found to vary

LUI et al.: A NOVEL, FAST, APPROXIMATE TARGET DETECTION TECHNIQUE FOR METALLIC TARGET 1701

according to target depth, target orientation and the dielectricproperties of the surrounding environment in which the targetis embedded [15]–[17]. Among all these variations, the trajec-tories of the resonant modes in the S-plane were studied as afunction of the target depth. Considering the same target andthe same environment in which the target is embedded, pre-vious studies have shown that the subsurface resonant mode(s)position(s) in the S-plane vary in a spiral pattern around the“homogenous” CRF [15]–[17]. However, due to the complexityof the problem, so far there is not any empirical model todescribe the “subsurface” CRF and it has been concluded thatsuch behavior needs to be studied on a case-by-case basis. Interms of numerical computation, information on the dielectricand conductivity profiles of the layers throughout the frequencyrange of interest are also required as well as the depth of thetarget in order to compute the target resonant modes accurately.Since the target recognition process is ultimately based on thefinal extracted resonant modes, it is a costly exercise to re-com-pute the resonant modes if any of the parameters change, andthus target classification and recognition based on the resonantfrequencies is not easy to implement in a practical sense.

Extraction of the CRF can be done using two different ap-proaches. In the first method, as used in previous studies byCarin et al. [15]–[17] for body-of-rotation (BOR) subsurfacetargets, the entire scattering problem is first formulated using afull wave integral equation formulation in the frequency domainat a particular frequency. It is well known that the integral equa-tion can be converted to matrix form using the method-of-mo-ments (MoM) as given by where is anelement matrix, is an N-dimensional vector representing theunknown amplitudes of the N-basis functions (currents), and

is the N-dimensional vector obtained by testing the inci-dent field on the target surface. The CRFs of the subsurfacetarget are essentially the singularities of the matrix, whichcan be solved for using complex root searching schemes suchas Mueller’s method.

The main limitation of this method is that it is only appli-cable to a particular frequency in the frequency domain. To ex-tract all the CRFs within the excitational bandwidth, the ma-trix needed to be recalculated at other frequencies and the en-tire root searching process needs to be repeated. Furthermore,this method is only applicable to the frequency domain integralequation formulation. Whilst accurate and exhaustive, it cannotbe applied if the target signatures are measured or computedusing other methods.

The CRFs can also be extracted directly from the late timeportion of the target signature using Prony [2], [22] or any ofits related methods such as the matrix pencil method (MPM)[23]. These methods were first applied to free-space scatterers[22], [23] but have recently been applied to extracting “subsur-face” CRF [17]. The advantage of these pole extraction methodsis that only a single time-domain target signature is requiredwithout the necessity of repeating the root searching at differentfrequencies. Furthermore, the target signature could be obtainedfrom any direct time domain method or frequency domain syn-thesis followed by an inverse Fourier transform, either measuredor computed. In this paper resonance extraction using the MPMwill be used.

B. Baum’s Transform

Rather than considering the entire scattering problem in thepresence of a lossy dielectric halfspace, a simpler way to re-gard the problem is to approximate it by considering a targetwithin an equivalent homogeneous space [18]. The relationshipbetween the resonances for a target in free-space, embeddedwithin a halfspace and within a homogenous environment haveall been investigated [18]. It has been found in [15]–[17] that theresonance positions for the latter two cases are closely locatedto each other in the S-domain. Furthermore, for the CRFs fora target in free-space and a target within the homogenous envi-ronment are related by Baum’s transform [18]. Baum analyzedembedded metallic targets (perfectly electric conductor – PEC)[18] within a homogeneous lossy environment. The CRFs forthe subsurface target can be predicted using Baum’s transform,as given by [18], [24]

(2)

where is the CRF and is thecorresponding CRF in the medium of permittivity of and .The transform, or more precisely scaling formula, may be de-rived by equating the propagation coefficients of a lossy mediumto that of free space in the context of complex frequency. Notethat Baum’s transform does not take the air-interface effect intoconsideration. It simply gives an approximation of the resonantfrequencies within a homogeneous halfspace.

III. THE E-PULSE TECHNIQUE

The E-Pulse technique is a radar target recognition schemebased on the aspect independent target CRFs extracted from thelate time of the target signature. It is a time domain filter whichannihilates a finite number of modes when convolved with thetarget response in late time [2], [7]. Mathematically this can bewritten as

(3)

where is the E-Pulse, is the target signature defined in(1) and is the duration of . To quantify the performanceof the E-Pulse technique, the E-Pulse discrimination number

is defined as [5]

(4)

The numerator of corresponds to the energy level ofthe convolution integral for and the denominator is theenergy level of the E-Pulse. The energy level of the E-Pulsedirectly affects the energy level of the convolution and nor-malizing the convolution according to the E-Pulse energy levelconsequently makes it a better measure for the E-Pulse perfor-mance. In the target recognition problem, a library of knowntargets is considered [8]. The CRFs of the targets are known apriori and the various E-Pulses are constructed in advance. The


target signatures are convolved with the E-Pulse. The E-Pulseannihilates the CRFs only when the target signature and theE-Pulse are matched, i.e., the E-Pulse and the target signatureare from the same target and a near zero level results in the latetime portion of the convolution. By thresholding the energy levelof the convolved signal, the one with the lowest energy levelwould be considered as the target. Another numerical measure,called E-Pulse discrimination ratio, is defined as [5]

(5)

IV. PROPOSED METHOD

An approximate subsurface target detection and recognitionscheme based on the E-Pulse technique and Baum’s transformis proposed. With the knowledge of what target we would liketo identify, the “free-space” CRF can easily be extracted fromthe computed or measured target responses. Furthermore, thedielectric properties of the halfspace are also assumed to beknown. With all the information an approximation to the CRFsfor the target within the homogeneous medium with the samedielectric properties of the halfspace can be carried out usingBaum’s transform. The E-Pulse is then constructed using the“homogenous” CRF using the formulation given in [6]. Targetdetection is achieved by convolving the E-Pulse with the “sub-surface” target signatures. It is assumed that the target is sitedbeneath a homogenous halfspace. Both a lossless and lossy half-space will be considered. For the lossy case, realistic dielectricproperties of human tissue (varying as a function of frequency)under microwave frequency excitation will be considered.

In this paper both the detection and recognition problems willbe considered. For the detection problem the target presence orabsence below the interface will be considered. The time do-main response for the target below the interface and the responsesolely from the interface are computed and convolved with theE-Pulse. Similar to the defined in [12], the factor isintroduced and defined as

(6)

where corresponds to the case where the E-Pulse isconvolved with the response from the interface without the pres-ence of the target, while the corresponds to the casewhere the E-Pulse is convolved with the response for the targetbelow an interface. Here the definition of the follows (4).We notice that the “homogenous” CRFs are merely an approx-imation and they are not the “subsurface” CRF extracted fromthe actual target signature. Theoretically null convolution willnot result even for the case when the target is present! However,if the target is present, the procedure should still return a lowervalue of compared to . This assumption isexamined via some numerical examples and indicates how wellthis assumption holds under varying conditions.

For the recognition problem, a number of targets will be con-sidered. We have picked one of them as the “true” target that wewould like to identify. The E-Pulse is again constructed usingthe “homogenous” CRFs of the “true target” and convolved with

the responses from all other targets. The is introduced anddefined as

(7)

where corresponds to the convolution of the E-Pulseand the response of the target that we are not interested in, whilethe corresponds to the convolution of the E-Pulse andtarget response from the true target. Once again, null convolu-tion will not result even when the E-Pulse is convolved withthe true target under the transform approximation. However,

should still returns a lower value numerically thanand we examine this assumption with some numer-

ical examples given in the next subsection.

V. NUMERICAL EXAMPLES

One of the most common examples of subsurface target de-tection/recognition is the GPR problem for detecting landmines.This topic has received significant treatment throughout the lit-erature. Recently biomedical and microwave engineers have no-ticed that the problem of detecting dielectric targets embeddedin another dielectric, as is the case of the plastic landmine buriedclose to the soil surface, is very similar to that of detecting a can-cerous lesion in female breast tissue. Moreover, provided thedielectric contrast between the two dielectrics is sufficient, thesame techniques should indeed apply. In this biological contextwe therefore tackle a somewhat easier but related problem con-cerned with the presence, or not, of an in vivo implanted hipprosthesis. This problem is of interest to biomedical scientistswho wish to know quickly the presence of the prosthesis, or not,and do not want to resort to ionizing X-ray methods. Apart fromthis application, the problem is significant in itself. In this casethe target is metallic and large compared to a breast tissue lesionand can be easily incorporated into a finite-difference time do-main (FDTD) simulator when dealing with the heterogeneousmedia. As such, the problem forms the first step towards usingthe previously outlined techniques in a biological context.

This section is divided into five parts with the first two partson target detection, one part on target recognition and one partconcerned with the use of the “single-mode” E-Pulse. First ofall, to demonstrate the detection application of the technique,a hip prosthesis model embedded inside a lossless halfspace isconsidered. In the second part, the same prosthesis model em-bedded inside a model of human tissue is treated. In particular,a dispersive Cole-Cole-4 model is used to approximate the fre-quency dependent dielectric properties of the human tissue. Inthe third part, the target recognition applicability of the proposedtechnique is examined with a number of “scaled” versions1 ofprosthesis models. In the fourth part, the “single-mode” E-Pulseis proposed. The E-Pulse is only constructed with the first domi-nant “homogenous” CRF and then convolved with various tran-sient signatures. The target detection and recognition perfor-mance of this “single-mode” E-Pulse will be evaluated in thissection. Lastly, numerical examples of the hip prosthesis model

1The “scaled” version of the target means that the entire target geometry isbeing increased or decreased by a factor of K. In this work K ranges from 0.5to 2.


Fig. 2. Cross sectional view of the hip prosthesis model. The original hip pros-thesis implant is given by � � �� , � � � �� and � �� . The alteredgeometry has the same dimensions of the figure but with � � � ��, � � � ��

and � � �� .

Fig. 3. The hip prosthesis in free space. The target is excited at � � � andmeasured in the forward scattering direction, i.e., � � � .

and metallic cylinder targets will be used to demonstrate thetarget recognition feasibility of the proposed method.

A. Detection of the Hip Prosthesis Embedded Within aLossless Halfspace

A cross section of the model is shown in Fig. 2 with, and . The prosthesis model is

the target that we are interested in whether or not this target iseither present or absent below the halfspace. First, the hip pros-thesis model in free space in the FEKO environment shown inFig. 3 is considered. This is essentially the same configuration asthe prosthesis sited below the halfspace of human tissue shownin Fig. 4 except that the layered Green’s function is replacedby the free space Green’s function. The target signature of theprosthesis model in free space is computed in the frequency do-main with 512 equally spaced samples fromto using FEKO [25]. The frequency samples

Fig. 4. Hip prosthesis model sited � cm depth below under the halfspace inFEKO. For the lossless and human tissue examples, there is no skin layer.

Fig. 5. Target response of the hip prosthesis model in free space.

TABLE IRESONANT MODES FOR THE HIP PROSTHESIS IN FREE SPACE

are then windowed by a Gaussian shaped window in the fre-quency domain and transformed to the time domain via an In-verse Fourier transform. The target signature in both time andfrequency domain are shown in Fig. 5. The “free space” CRFsare then extracted using the MPM [23] and they are tabulatedin Table I. As shown in Fig. 5, resonant peaks are clearly ob-served around 1 GHz and 2 GHz, which correspond to mode 1and 2 respectively as listed in Table I. Mode 3 with a resonantfrequency of 4.98 GHz has a high damping factor and thus doesnot appear as a sharp peak in the frequency response, but ratheras a relatively flat response in the frequency domain.

Baum’s transform is then applied to the “free-space” CRFto approximate the resonances of the target within the homo-geneous environment with the same dielectric properties of the


Fig. 6. Target response of the hip prosthesis sited at 8 cm depth below thelossless halfspace of � � �, � � � �� with � � �� .

halfspace, in this case , which is a simple as-sumption of the dielectric properties of the human tissue undermicrowave frequency excitation [26]. The E-Pulse is then con-structed using the “homogeneous” CRFs, and function as thetarget detection tool. The E-Pulse will then be convolved withthe time domain target signature considering cases of with andwithout the prosthesis model below the human tissue. The de-tection performance of the proposed technique is evaluated nu-merically based on the s and values.

Next we simulate the response of the target below the half-space of human tissue. The same hip prosthesis model sitedbelow a homogeneous halfspace of and atthe depth of 8 cm is considered and shown in Fig. 4. The samecomputation procedures for the target in free space are repeatedin FEKO, except that the halfspace Green’s function is used forthe target below the human tissue. The angle of incidence variedfrom to and the response was measured in theforward scattering direction. The target response foris shown in Fig. 6. In time domain, we note that in the FEKOsimulation for plane wave excitation and far-field reception, thereference point is at the interface. Thus the scattered field fromthe induced current on the surface of the target and the multiplereflections between the target and the air-dielectric interface areall accounted for, but the dielectric boundary is not seen in thefar-field plots. In the frequency domain, the first dominant reso-nant peak is clearly observed at around 0.33 GHz which roughlycorresponds to the mode 2 in column 2 and 3 in Table II.

The response from the air-dielectric interface without thetarget present needs now to be considered and is shown in Fig. 7.The reflected field from a homogeneous lossless interface withplane wave incidence may be described using a Fresnel reflec-tion coefficient [27], [28]. For a lossless non-ferromagneticdielectric interface with parallel polarized incidence, this isgiven by

(8)

TABLE IIRESONANT MODES FOR THE HIP PROSTHESIS IN HOMOGENOUS ENVIRONMENT

OF (I) LOSSLESS HALFSPACE OF � � �, � � � ��, (II) COLE-COLE-4 FAT

INFILTRATED HUMAN TISSUE, THE DIELECTRIC PROPERTIES GIVEN IN FIGURE.THIS IS ACHIEVED BY APPLYING BAUM’S TRANSFORM TO THE RESONANT

MODES IN TABLE

Fig. 7. Incident, reflected and transmitted parallel (TM) polarized plane waveat the interface.

Here, it is assumed that the relative permittivity is constant andthus the reflection is frequency independent. To compute thetime domain signature with the same Gaussian pulse incidentas in the previous cases, the reflection coefficient is computedfrom and with 512 equallyspace samples, then Gaussian windowed and inverse Fouriertransformed to the time domain.

As the sampling rate of the E-Pulse and the target signa-tures are usually different, the signals are first resampled [29].The E-Pulse is then convolved with the late-time responses (awindow from 12.5 ns to 33.3 ns) for the two cases of bothwith and without the target present. The early-time responsehas been removed due to the fact that the E-Pulse null convo-lution acts only on the late-time period, and at the same time theearly-time dielectric interface reflection has been suppressed asthe reference point of the MoM calculation. s and sare computed over a range of incidence angles and are plotted inFig. 8. On average, is around whileis around respectively. This is a significant difference andit demonstrates that the proposed technique is capable of de-tecting the existence of the target below the interface over arange of incidence angles. It also may be noticed that the min-imum value of occurs at . This is due tothe fact that the reflection coefficient at this angle is very smalland it would become zero at , which is the Brewsterangle of incidence for the dielectric of and .The corresponding was also computed for each angle of


Fig. 8. ��s and �� s for the hip prosthesis below a lossless halfspace of� � � at various angles of incidence.

Fig. 9. Conductivity and relative permittivity of human tissue and the skin layerusing the Cole-Cole-4 model.

incidence and on average a figure of 30.79 dB is achieved witha minimum of 15.67 dB at .

As demonstrated, the proposed technique is capable of de-tecting the existence of the target below a homogeneous loss-less halfspace. Next, the dispersive nature of the human tissueis taken into consideration and the detection possibilities are fur-ther investigated.

B. Detection of the Hip Prosthesis Target Sited Within HumanTissue

The same hip prosthesis model is now sited within disper-sive homogeneous human tissue. In the microwave frequencyregion, numerous studies on measuring and modelling the di-electric properties of human tissue can be found in the literature[26], [30]. Here the Cole-Cole-4 model of fat infiltrated tissueis used [30]. A plot of the relative permittivity and conductivityof the fat filtrated tissue up to 10 GHz is shown in Fig. 9.

To investigate the target detection performance at varioustarget depths, the angle of incidence is fixed at inthe forthcoming examples, and the target signatures for thetarget at various depth positions below the halfspace will be

studied. To approximate the prosthesis within the homogeneousenvironment of the tissue accurately it is necessary to evaluatethe relative permittivity and conductivity at each resonantfrequency (Fig. 9) using the Cole-Cole-4 model and then applyBaum’s transform to each CRF individually. Once again, theE-Pulse is then constructed from the “homogeneous” CRFstabulated in Table II.

To compute the target signature for the prosthesis below thehalfspace of frequency dispersive human tissue, the dielectricproperties at each frequency point are extracted from the Cole-Cole-4 model in Fig. 9 and are imported into FEKO to model thedispersive nature of the tissue. Again, the frequency domain datais then Gaussian windowed and inverse Fourier transformed tothe time domain. Various target depths from 2.5 cm to 12 cmwith a step size of 0.5 cm are considered.

To simulate the case in which the target is absent, the Fresnelreflection coefficient is again required, but is now modified forthe lossy case. Recent efforts have been focused on directlycomputing the transient reflection coefficient in the time domain[31]–[38]. In particular Suk [34] has extensively addressed thisissue for both perpendicular (TE) and parallel (TM) polariza-tion with finite conductivity. However, he assumed that the rel-ative permittivity and conductivity is constant throughout thefrequency range of interest, and therefore his results cannot beapplied here. Recent efforts by Rothwell et al. [35]–[38] haveextended Suk’s work into Lorentz and Debye halfspaces. Due tothe frequency dependent properties of relative permittivity andnon-zero conductivity of the human tissue, a frequency domainapproach with an inverse Fourier transform is the preferred op-tion. The details of the formulation can be found in [39, Ch. 2].While not included in this paper, we have verified the frequencydomain formation of [39] by comparing it with the results ofSuk [34]. The dielectric profiles are constant over the frequencyrange of interest and the former produces the same results as thelatter.

The E-Pulse is convolved with the responses for cases bothwith and without the target. The corresponding s and sare computed and plotted in Figs. 10 and 11 and are denoted as“real tissue.” The angle of incidence is fixed at 20 and the pros-thesis models at the depths from 2.5 to 12 cm are considered.With the existence of the target a level of to is ob-tained for and a level of results forwhen the target is absent. As for shown in Fig. 11, a min-imum of around 40 dB results at 2.5 cm depth. This demon-strates that there is a significant difference in energy level in theresultant convolved signals for the case of the target present andabsent, again supporting the detection capabilities of the pro-posed technique.

It is also noticed that varies as a function of target depth.This is due to the fact that the position of the “subsurface” CRFsin the S-plane varies as a function of target depth. The E-Pulse isconstructed based on the “homogenous” CRFs listed in Table II.As the actual CRF is located close to the approximated CRF alower value of results and consequently a higher valueof , as the remains the same for all cases.

To better model the human tissue, a skin layer is added asshown in Fig. 4. A thickness of 1 mm and 5 mm are consid-ered separately. The dielectric properties of the skin layer from


Fig. 10. �� values for the hip prosthesis below a halfspace of human tissueat various depths with � � �� .

Fig. 11. �� values for the hip prosthesis below a halfspace of human tissueat various depths with � � �� .

19.5 MHz to 10 GHz are shown in Fig. 9, again using a Cole-Cole-4 model. The entire computation procedures are repeated,except that a layered Green’s function is used in FEKO to modelthe prosthesis model below the layered halfspace, and the reflec-tion coefficient of the multi-layer structure is used [39] to simu-late the absence of the prosthesis. The same E-Pulse is used forthe convolution with the two cases (both with and without pros-thesis). It should be noted that Baum’s transform does not takethe skin layer into consideration. However, with the prosthesissited in the tissue layer it is reasonable to assume that the entireresonant behavior will be dominated by the dielectric propertiesof the tissue as the skin layer is relatively thin.

The s and values are also listed in Figs. 10 and 11respectively. Similar results are obtained compared to the casewithout the skin layer. Comparing the values of the twocases in Fig. 10, they both have a similar value at thelevel of . However, for the values drop slightlywith the introduction of the 1 mm layer compare to the casewithout the skin, and as the thickness of the skin increases to

5 mm, the values further decrease. The degradation inperformance compared to the case without the skin layer is notsurprising given the fact that the skin layer has a higher relativepermittivity (about 5 times that of the tissue) and conductivitythroughout the frequency range of interest (as shown in Fig. 9)resulting in higher attenuation of the transmitted wave. Due tothe small changes in and the significant drop for

, the value, which essentially is the ratio of theand the , result in higher values for

the 5 mm cases than the values of the 1 mm cases. Overallthe minimum values of are above 30 dB.

C. Recognition of the Hip Prosthesis Target Below the HumanTissue

Next, recognition of the hip prosthesis below the humantissue with the skin layer is considered. The hip prosthesismodel in Figure with , andis considered as the reference. “Scaled” versions of the hipprosthesis models with the factor of to 2 times areconsidered. As previously noted, the basis of the proposedtechnique depends on the scaling the “free-space” CRFs to ap-proximate the “subsurface” CRFs using the transform. Here, weconsider a library of targets that are “scaled.” For the “scaled”target below the dielectric halfspace, the “subsurface” CRFsare the same as the original target under the same halfspaceexcept they have been scaled by a factor of “1/K” due to the ge-ometrical changes. Consider the case of . The geometryof the target has been doubled but the resonance frequencieshave been divided by 2. If the second harmonics of particularresonant modes of the “scaled” target are being excited, theresonance frequency could be close to the fundamental resonantmode of the original target. As a result, the proposed techniquemay fail due to the situation of the original (transformed) CRFsbeing close to the position of the CRFs of the scaled target. Asimilar situation may occur for the factor of . Thisproblem is more difficult than considering a totally differenttarget with different resonant behavior as the resonance modesare totally different and chances for successful recognition ishigher. In view of this, instead of using a prosthesis model witha different geometry with different resonance modes, the scaledversion of the original target is first considered for the identifi-cation problem. The limitations of the proposed technique ontarget recognition will also be shown in the examples and theensuing discussion towards the end of the section.

Throughout this example, the hip prosthesis models (bothoriginal and scaled) are sited at a depth of 8 cm. The same nu-merical computation is again repeated for the three cases ofhuman tissue: 1) human tissue model without skin layer; 2)human tissue model with 1 mm and 3) 5 mm skin layer.

The E-Pulse in the previous subsection is convolved with thetarget responses of the original and the scaled version of thetarget. Fig. 12 shows the values. For all 3 cases thevalues in general increase as the target size increases from

and decreases for the original model . As the sizefurther increases, the values increase, except for the caseof the 1 mm skin layer where the values for 1.1 and 1.2times are smaller than that of the 1 time model. Comparing thethree different cases of human tissue, the results are in line with


Fig. 12. �� values for the original and scaled version of the hip prosthesismodel buried below the halfspace. The �� values corresponds to the E-Pulseconvolved with the original target (1 time) is regarded as �� and the�� values corresponds to the E-Pulse convolved with the scaled version ofthe target is regarded as �� .

Fig. 13. �� values for the original and scaled version of the hip prosthesismodel buried below the halfspace. The �� values are calculated with�� as the reference.

the one in the previous example, i.e., the s decrease as thethickness of the skin layer increases.

The values are then computed with value of theoriginal target as reference and are shown in Fig. 13. The re-sulted values ranged from 12 dB up to about 12 dB.Negative values of imply that numerically the value of

is smaller than that of the , which also im-plies an incorrect recognition given the prior knowledge of the“true” target. Such cases occurs for the cases of 0.5, 0.6, 0.7times for real tissue and tissue with 1 mm skin layer, 1.1 and1.2 times for tissue with 1 mm skin layer, and 0.5, 0.9 times fortissue with 5 mm skin layer examples.

The results above can be explained by the resonant behaviorof this target. As shown in Table I, the wavelengths at the reso-nant frequencies of the hip prosthesis in free space roughly cor-

Fig. 14. Frequency response of the prosthesis at 8 cm depth below the humantissue model, (i) Fat infiltrated tissue, (ii) Tissue with 1 mm skin layer, (iii)Tissue with 5 mm skin layer.

responds to 0.5 times, 1 time and 2 times the projected lengthof the target. When the size of the target is scaled by a factorof 0.5, the resonant frequencies of the scaled target doubledand the second harmonics of the scaled target would be roughlythe same as the first harmonic of the original model. The reso-nant modes approach values corresponding to Baum’s transform“homogenous” CRFs and thus fail the identification. Higherorder modes with higher order resonant frequencies may not bewell excited due to the significant attenuation of human tissueas frequency increases. In addition, for the cases where the sizeof the target is smaller than the original model, the smaller phys-ical size results in a smaller amount of energy being transmittedto the free space in the late-time, which would also degrade theE-Pulse performance. In summary, the proposed technique isable to identify the correct target provided that the target reso-nances are well excited and the location of their CRFs are notclose to the approximated “homogenous” CRFs of the correcttarget.

D. Target Detection and Recognition Using “Single Mode”E-Pulse

To gain further insight into the scattering phenomena, the fre-quency response of the original prosthesis model at 8 cm depthbelow the human tissue is shown in Fig. 14. As observed, thefirst dominant frequency peak is observed at around 0.5 GHzwhich has a similar resonant frequency to the “homogenous”CRFs of mode 2 in Table II. This indicates that only this par-ticular mode is well excited when the target is sited below thehalfspace. As a result, the proposed target detection techniqueusing only one transformed CRF is considered. The detectionand recognition problems for the prosthesis for the previous 3different situations are repeated and the and valuesare shown in Figs. 15 to 18, respectively.

For the detection problem, the is at the level of, which is slightly higher than that of the detection exam-

ples shown in Section V-C. However, the values for


Fig. 15. �� values for the hip prosthesis below a halfspace of human tissueat various depths with � � �� using “single-mode” E-Pulse. (a) �� ;(b) �� .

Fig. 16. �� values for the hip prosthesis below a halfspace of human tissueat various depths with � � �� , using a “single-mode” E-Pulse.

are increased to the levels of and , for the cases withand without skin layer respectively. As a result, higher values of

result. In addition, and values are relativelystable as the target depth changes for all 3 different human tis-sues compared to the previous example. This seems to indicatethat the “single-mode” E-Pulse provides a more stable detectionperformance compared to the “all-modes” E-Pulse. As for theidentification problem, again higher values of result forthe cases where the target is larger than the correct target. Asfor the case which the targets are smaller than the correct target,only the cases of 0.7 to 0.9 times of the target below the real and1 mm layered human tissue resulted a positive value of ,and for other cases the proposed technique fails to identify thetarget.

Fig. 17. �� values for the original and scaled version of the hip prosthesismodel buried below the halfspace using “single-mode” E-Pulse. The ��values corresponds to the E-Pulse convolved with the original target (1 time)is regarded as �� and the �� values corresponds to the E-Pulseconvolved with the scaled version of the target is regarded as �� .

Fig. 18. �� values for the original and scaled version of the hip prosthesismodel buried below the halfspace using “single-mode” E-Pulse. The ��values are calculated with �� as reference.

TABLE III�� VALUES FOR THE HIP PROSTHESIS MODEL AND THE PEC CYLINDERS

BURIED BELOW THE HALFSPACE USING THE E-PULSE AND “SINGLE-MODE”E-PULSE. THE PEC CYLINDERS ARE WITH THE LENGTH � � � � AND

RADIUS OF (1) � � �� AND (2) � � �� . THE �� VALUES ARE

CALCULATED WITH �� AS REFERENCE


E. Target Recognition of the Hip Prosthesis Model VersusCylindrical Object

Lastly, target recognition examples of the original hip pros-thesis model and two PEC cylindrical targets are considered.This is essentially the same as the previous two subsections ex-cept that cylindrical targets are used instead of the “scaled” ver-sion of the prosthesis, so as to give a clearer picture of the targetrecognition performance of the proposed methods. The cylin-ders are sited at a depth of 8 cm below the interface and areof length with radius of (1) and (2)

respectively. The s are computed and tabu-lated in Table III. The results show that both the E-Pulse and“Single-mode” E-Pulse are able to recognize the hip prosthesismodel from the cylinders under different human tissue models.

VI. DISCUSSION

The examples show that the proposed technique is capableof detecting the existence of a target below a layered, homoge-neous, lossy, and frequency dependent environment. It is alsocapable of recognizing the correct target below the halfspacewith scaled versions of the target. Given the known target in freespace, an approximation of the target inside the homogeneousmedium can be made using Baum’s transform. The E-Pulse isconstructed and convolved with measured target returns. For de-tection application, if the target exists below the interface, a lowvalue of the parameter results as expected. As for recogni-tion application, a lower value of should still result. How-ever, for the case in which the target is smaller than the originaltarget, the resonant frequencies increases and at the same timedue to the increase in attenuation at higher frequencies, the res-onant frequencies are not well excited and thus the proposedscheme fails to detect the target.

Lastly, the proposed technique has been simplified by usingthe first dominant resonant frequency, and the “single-mode”E-Pulse is applied for both detection and recognition prob-lems. Numerical results demonstrated that relatively higherenergy levels result for most values when compared tothe E-Pulse using all the “homogenous” CRFs, however thedifferences between the and , as well asthe and for the detection and recogni-tion problems respectively, are more significant when using“single-mode” E-Pulse. This reveals that the proposed tech-nique should still function even if only the dominant resonantmode is considered when formulating the E-Pulse.

In this example, only the one dominant mode is observedwhen the prosthesis target is sited below the lossy halfspace ofhuman tissue. The proposed technique may function better ifmore resonant modes are excited. For example, consider a targetsize of the order of metres. This of course may not seem to befeasible for a biomedical application but it could be feasible forsome GPR problems.

VII. CONCLUSION

A novel subsurface target detection method based on theE-Pulse technique is proposed and investigated. The targetembedded in a halfspace medium is approximated by thatof a homogeneous medium using the same properties of thehalfspace. Using Baum’s transform, an E-Pulse is constructed

from the “homogenous” CRFs and convolved with the targetreturn. Examples of a metallic hip prosthesis embedded in ahomogeneous halfspace show that the proposed technique iscapable of detecting the existence of the target, and recognizingthe correct target when the target is sited beneath a lossy andlayered medium.

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Hoi-Shun Lui (S’06–M’09) received the Bachelor ofEngineering degree (with first class honors) and thePh.D. degree in electrical engineering from the Uni-versity of Queensland, Brisbane, Australia, in 2003and 2008, respectively.

During his candidature, he has carried out consul-tancy work with Filtronics Australia Ltd. In 2008, hewas a Research Fellow with the Microwave and RFGroup, National University of Singapore. He is nowan Assistant Professor with the Department of Sig-nals and Systems at Chalmers University of Tech-

nology, Gothenburg, Sweden. He also serves as a project leader in the VINN Ex-cellence Centre CHASE that is financed by the Swedish Governmental Agencyfor Innovation Systems (VINNOVA), industry and Chalmers.

Dr. Lui is an active reviewer in various international refereed journals such asIEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION and IEEE ANTENNAS

AND WIRELESS PROPAGATION LETTERS. His research interest includes res-onance-based radar target recognition, transient electromagnetic scattering,mutual coupling of antenna arrays and direction-of-arrival estimation.

Nicholas V. Z. Shuley (S’80–M’86) received theB.E. and M.Eng.Sc. degrees from the Universityof New South Wales, Australia, in 1973 and 1975,respectively, and the Ph.D. degree from ChalmersUniversity of Technology, Gothenburg, Sweden, in1985, all in electrical engineering.

From 1977 to 1978, he was with Microwave Asso-ciates, Dunstable, U.K. From 1979 to 1988, he was aResearch and Teaching Assistant and later a Postdoc-toral Scientist with the Division of Network Theory,Chalmers University of Technology, Gothenburg,

Sweden. From 1988 to 1998, he was with the University of Queensland,Queensland, Australia, working within the Microwave Group and during 1996he was awarded a Visiting Scientist Stipend by the Spanish Government towork on electromagnetic related problems at the Department of Electronicsand Electromagnetics, Department of Physics, University of Seville, Spain.From 1999 to 2001, he was Head of the Electronics discipline within theSchool of Electrical and Computer Systems Engineering, RMIT University,Melbourne, Australia. He returned in 2002 to the University of Queensland tothe School of Information Technology and Electrical Engineering where he iscurrently teaching and supervising research in the areas relating to time-domainelectromagnetics and non-cooperative object identification. He has carried outconsulting work for the European Space Agency.

Dr. Shuley has been a member of the editorial board of THE IEEETRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES since 1992 andshared a Best Paper Award at JINA 1988. He has published extensively in bothinternational journals and conference proceedings concerned with electromag-netic phenomena and has successfully supervised either (jointly or solely) 18Masters or Ph.D. students to completion.

Aleksandar D. Rakic (S’93–M’99–SM’08)received the Dipl.-Ing. degree in electrical engi-neering/engineering physics and the M.Eng.Sci.degree in optoelectronics from the University of Bel-grade, Yugoslavia, and the Ph.D. degree in electricalengineering from The University of Queensland,Queensland, Australia.

He has over 15 years of experience working in thefield of photonics. He is recognized for his contribu-tions in the areas of semiconductor lasers and lasersensing and has more than 140 papers and one book

chapter to his credit. He currently leads a cross-disciplinary R&D team devel-oping hardware and software for self-mixing sensors. He is the Director of Elec-trical Engineering and an Associate Professor with the School of InformationTechnology and Electrical Engineering, The University of Queensland.

Dr. Rakic served as the General Chair for the 2004 Conference on Optoelec-tronic and Microelectronic Materials and Devices (COMMAD04), the Co-Chairof the Symposium on Molecular and Organic Electronics and Organic Displayswithin the 2006 International Conference on Nanoscience and Nanotechnology(ICONN 2006), and the Co-Chair “Symposium on Compound SemiconductorMaterials and Devices” within the 2008 International Conference on ElectronicMaterials ICEM 2008. He is currently Chair of the IEEE AP/MTT QueenslandChapter.

A Novel, Fast, Approximate Target Detection Technique for Metallic Target Below a Frequency...

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