NEW RESULTS ON CLUTTER REDUCTION AND PARAMETER ESTIMATION FORLANDMINE DETECTION USING GPR.

L. van Kempen, H. Sahli, J. Brooks, J. CornelisVrije Universiteit Brussel - Faculty of Applied Sciences

ETRO Dept. IRIS Research groupPleinlaan 2, B-1050 Brussels - Belgium

{lmkempen,hsahli,jpcornel}@etro.vub.ac.be, jbrooks@hiwaay.net

ABSTRACT

One of the main problems with the interpretation of GPRdata is the strong ground reflection, obscuring signals arriv-ing from just underneath the surface. The strength of thisreflection can be reduced by deconvolution. This techniqueis especially useful when GPR is used to detect buried land-mines. Parametric and non parametric time variant estimatorsare used for clutter characterization. Wavelet decomposi-tion/reconstruction for noise removal is then applied. Theapplication of the proposed signal processing technique toGPR data yields a substantial enhancement of the target re-flection as well as a good estimation of physical parameterssuch as propagation velocity and target position.

Key words: Clutter Reduction, Parameter Estimation, FeatureExtraction.

INTRODUCTION

Ground Penetrating Radar (GPR) has become widely ac-cepted as a major technique for sub-soil investigations,mainly in civil engineering. Another field of application isthe detection of buried landmines. The clutter and severe at-tenuation, caused by the soil, degrades the target image, ob-tained by the GPR. This leads to an unacceptable number offalse alarms. The clutter varies with soil conditions and sur-face roughness and disrupts the exploitation of measurements.It is therefore necessary to overcome these surrounding ef-fects when processing GPR data for parameter estimation,such as velocity of propagation, target depth, etc... In thispaper we present improved signal processing approaches toreduce clutter due to ground bounce in GPR measurements.First we apply a source signature deconvolution in order toremove the effect of the source waveform from the data. Thenthe clutter contained in the measurements is treated as para-metric (ARMA) and non-parametric (LPC) models. We alsointroduce a wavelet decomposition/reconstruction approach,which can be used for residual noise or clutter reduction. Thepaper is organized as follows: the next section describes anumber of clutter removal approaches, based on system iden-

tification methods. The third section involves the extractionof specific features out of pre-processed B-scan images, andtheir use to estimate target and soil parameters. In the finalsection the presented methods are applied to laboratory data,and the results are discussed.

CLUTTER REMOVAL

Statement of the Problem

The basic structure of the input-output relationship betweenthe radiated electric field and the received one can be writtenas (Daniels, 1996),

~Erec′d(k) = ~Erad(k) ~ (hc(k) + ht(k)) + n (1)

wherehc(n) andht(n) are the impulse responses of the clut-ter and target, respectively, andn represents the measurementnoise.In order to identify the target parameters, the other influenceshave to be eliminated out of the measured signal. In the con-text of this paper, we consider three separate influences to beestimated. Theantenna effects,which are encompassed in theradiated field, can be accurately measured under laboratoryconditions.Clutter includes all environmental effects includ-ing scatterers from the soil and surface interface, and has tobe estimated out of the data.Noisespecifically refers to therandom measurement noise which is added to the compositesignal (Brooks et. al, 1999).

Antenna Deconvolution

Under laboratory conditions the characteristics of the antennacan be determined with great precision (Scheers et. al, 2000).The radiated electric field in a certain point in space and timecan then be calculated on the basis of the convolution of thetime derivative of the electrical signal presented at the antennafeedVant(t) and the antenna impulse response:

~Erad(~r, t) ∼ dVant(t)dt

~ hT (~ar, t) (2)

wherehT is the antenna impulse response, and~ar is the unitvector in the direction of~r.Since this emitted signal will never be a Dirac function, itspresence in the received data will cause a blurring of the re-flected waveforms. Therefore, once the exact emitted signalshape is known, it can be deconvolved from the data. Forthis a basic deconvolution filter is used (Kusama et.al, 1989;Neves and Miller, 1996):

H(ω) =G∗(ω)

|G(ω)|2 + Pn(ω)/Pt(ω) (3)

HereG(ω) is the Fourier transform of the radiated signal, andPn andPt are the power spectra of the noise and target partsof the reflected signal. These can be either estimated out ofthe data, or considered as unknowns, in which case the quo-tient is replaced by a constant water lever parameter.

Clutter Estimation

The clutter will be characterized using parametric systemidentification, which attempts to determine the parameters(e.g., transfer function coefficients) of a linear time-invariant(LTI) system or signal.

Basic Principles (Farhang-Boroujeny, 1998) Consider adiscrete LTI system described by the difference equation

y(n) + a1y(n− 1) + a2y(n− 2) + . . . + anay(n− na) =b0u(n) + b1u(n− 1) + · · ·+ bnbu(n− nb) (4)

wherey(n) is the output sequence,u(n) the input sequence,andna,nb are theorder of both processes, respectively (nb ≤na). The system described by (4) may be written in transferfunction format as

H(z) =B(z−1)A(z−1)

(5)

where

A(z−1) = 1 + a1z−1 + a2z−2 + · · ·+ anaz−naB(z−1) = b0 + b1z−1 + b2z−2 + · · ·+ bnbz−nb

The more general case includes additional measurement noisesamplese(n) which are assumed to be independent identi-cally distributed with zero mean. In this case, the input-outputrelation is written

Y (z) = H(z)U(z) + E(z) (7)

which is theoutput-error modelin system identification lan-guage. We define theparameter vectorθ as

θ = [a1, a2, . . . ana , b0, b1, · · · bnb ]T (8)

and the elements of this vector are the parameters to be esti-mated.It is shown that an estimation of (8) is given by

θ̂ = (ΨT Ψ)−1ΨT y (9)

whereΨ is the matrix

Ψ =

ψ(n + 1)ψ(n + 2)

...ψ(n + N)

(10)

where

ψ(n + k) =

−y(na + k − 1)...

−y(k)u(nb + k)

...u(k)

T

(11)

whereN is the length of a sliding data window;N À na+nb.Equation (9) is themin-norm solutionto a linear system de-scribed by

y = Ψθ + e, (12)

so Equation (9) may be compactly written as

θ̂ = Ψ†y (13)

whereΨ† is theMoore-Penrose Pseudo-inverseof Ψ .

The Clutter/Noise Model The parameters of the targetmay be estimated only after the clutter/noise parameters aredetermined and removed.The clutter model may be represented by

θ̂c = [a1, a2, . . . ana , b0, b1, · · · bnb ]T (14)

and its block diagram is shown in Figure 1.

δ(n) → Ĥc(z) = B̂(z−1)

Â(z−1)→ ŝc(n)

Figure 1: Representation of Clutter Parametric Model.

The input to the clutter block diagram is aδ-function underthe hypothesis of an ideally deconvolved emitted signal.When modeling real systems, it is usually necessary to in-clude a noise model which will account for any random dis-turbances caused by the measurement equipment, etc. Theinclusion of a (possibly time-varying) noise model is there-fore indicated.Such a noise process model can be described by

θ̂ν =[g1, g2, . . . gng , f0, f1, · · · fnf

]T(15)

The input to the noise model is a vector of independent, iden-tically distributed (i.i.d.) samples with a Gaussian amplitudedistribution of zero mean and constant spectral intensity. Theinput is applied to a filter which provides appropriate spectraland amplitude shaping to represent the measured noise fromA-Scan to A-Scan.Once the clutter estimate and noise processes are determined,the target may be easily extracted by simply subtracting thesum of those estimates from the measured signal.

Recursive Methods In the case of clutter reduction, a re-cursive algorithm, also known asadaptive algorithmis ap-plied: the Linear Predictive Coding (LPC) Method.LPC is a method of estimating the prediction-error coeffi-cients for a linear regression model. It finds the coefficients

a = [1, a(2), ..., a(N + 1)] (16)

of anN th order forward linear predictor

Xp(n) = −a(2) ∗X(n− 1)− a(3) ∗X(n− 2)−−...− a(N + 1) ∗X(n−N)

such that the sum of the squares of the errors

err(n) = X(n)−Xp(n) (17)is minimized.The coefficients are then used to filter the input data, and theresidual is found by subtracting the original data from the fil-tered estimate.

Wavelet Reconstruction

Another possible clutter reduction algorithm is based onwavelet decomposition and reconstruction (Kaiser, 1994).If x(t) is the real signal in time domain, andψ(t) is an analyt-ical wavelet, then the wavelet transform ofx(t) with respectto ψ(t) is defined as:

Wx(u, s) =1√s

∫ +∞−∞

x(t)ψ∗(

t− us

)dt (18)

In this expressionu is the time delay,s is the scaling factor,andψ∗ is the complex conjugate ofψ.Each of the A-scans can be decomposed into a number oftriplets (u, s, Wx(u, s)). Since each of the triplets expresseshow well that particular wavelet can be found in the signal, alogical choice for the base wavelet will be the emitted signalitself. When the signal is reconstructed using only a limitednumber of these triplets it is possible to reduce the clutter.The problem will then reside in the correct choice of thesereconstructing triplets.An algorithm, based on the Shannon entropy, is proposed(Saito, 1994; van Kempen et al, 1998). A clutter referencesignal and the measured A-scan are decomposed. Each ofthe triplets is linked to a discriminant measure. For the re-construction only those triplets with the highest discriminantvalue are used.Let us consider two nonnegative sequencesp = {pi}ni=1 andq = {qi}ni=1. Thediscriminant measurebetween these se-quences can be chosen as therelative entropyor J-divergencegiven by:

J(p, q) =n∑

i=1

pilogpiqi

+n∑

i=1

qilogqipi

(19)

Measuring discrepancies amongC distributionsp(1), ..., p(C)

can be done using following formula:

J({p(c)}Cc=1) =C−1∑

i=1

C∑

j=i+1

J(p(i), p(j)) (20)

In our case the number of classesC is two, namely the ref-erence clutter signal and the measured A-scan. If more refer-ence signals are added the resulting clutter reduction will beimproved. This algorithm can be either applied to the raw dataas a clutter reduction algorithm, either on ARMA or LPC pro-cessed data. In this case the Wavelet processing will performa residual noise reduction to further clean up the data. Thedifference between the two applications will lie in the choiceof the reference signal.

PARAMETER ESTIMATION

Diffraction Hyperbola

When using a quasi monostatic configuration to acquire theB-scans, a localized reflector will lead to a hyperbolic struc-ture, which can be analytically expressed as:

t2x =x2

v2+ t20, (21)

wherex is the horizontal distance between the object and theantenna,v is the local velocity of propagation,t0 is the per-

pendicular travel-time to the object, andtx is the travel-timeto the object starting from positionx.These structures contain information about the local soil prop-erties, as well as the reflecting object. It is therefore useful toestimate accurately the parameters of the hyperbolas presentin the image. The first step towards this is an edge detection,based on Gabor wavelets.

Gabor Edge Detection

Gabor filters have the possibility of adapting to structureswithin a wide range of spatial frequencies, orientations andFourier spectra (Mehrotra et. al, 1992; van Kempen and Sahli,2000).A Gabor function is a harmonic wave modulated by a Gaus-sian. The most general expression of such a function in twodimensions is:

G(x, y) = A exp

(−

((ax + by)2

σ2x+

(bx− ay)2σ2y

))

∗ exp(−(iωxx + iωyy)) (22)with

ωx = aωωy = bωa = cos(α)b = sin(α)

The general formula contains four parameters:σx and σy,which represent the spatial spread of the Gaussian (a pair ofσx, σy is called a spatial scale),ω the spatial frequency ofthe function, andα, the orientation of the function. Theseparameters are indicated in figure 2.

a bFigure 2: An example of a general Gabor filter. (a) the four

parameters, (b) three dimensional view

When selecting certain values for the four parameters inGσx,σy,α,ω(x, y), and convolving the resulting function withthe input imageI(x, y), the input image structures that cor-respond to the selected scale and orientation are enhanced,while others are reduced. The results given by the differentscales and orientations are combined in one gradient mag-nitude image. The final edge detection is performed usingCanny’s criteria (Canny, 1986):

1. Good Detection: Maximize the signal to noise ratio.

2. Good Localization: Minimize the variance of the posi-tion of the zero crossings.

3. Non multiplicity of the responses: Put a limitation onthe number of maxima, detected in response to a singlecontour.

Hough Transform

Once the binary edge image is found, the hyperbolas are esti-mated, using a modified Hough Transform (Capineri, Grande,and Temple, 1998).

If z is the depth of the scattering object,x its horizontal posi-tion, andxa the horizontal position of the antenna, the TimeOf Flight t of the wave is:

t = 2(z2 + (xa − x)2)1/2/v (23)

with v the velocity of propagation of the electromagneticwaves in the medium. Since all axes are displayed with dis-crete values one can write:t = jdt, xa = iadx andx = idx(dt, dx are the horizontal and vertical scanning steps). Thisdiscretisation will lead to the following parametric equationof the hyperbola:

j2 = α + β(i− γ)2 (24)

with the three parametersα, β andγ given by:

α = 4z2/dt2v2

β = 4dx2/dt2v2

γ = i (25)

By randomly picking three distinct points in the edge image,one can obtain the values forα, β andγ

The accumulation of votes of the tripletsα, β, γ, correspond-ing to possible hyperbolic arcs occurs in a 3D array whilescanning over the edge pixels. The high peaks in the accumu-lator space (α, β, γ) provide the parameters that identify themost likely hyperbolic arcs.

Figure 4 shows an example of the results of edge detectionand hyperbola estimation.

(a) (b) (c)Figure 4: Edge detection and hyperbola estimation results.

(a) The results of edge detection, (b) the estimatedhyperbolas, (c) the detected hyperbolas, after correlation

between several neighbor B-scans.

Parameter Estimation

Out of the estimated diffraction hyperbola several parameterscan be deduced. The horizontal object positionx is directlygiven byx = γ. The velocity of propagation in the mediumis given by:

v =2dx

dt√

β(26)

and the depth of the object is given byz = v√

α.This is valid in the assumption that the wave travels in a con-tinuous, homogeneous medium. In practice, however therewill be some travel in air before the wave will reach themedium. So for both the estimation of the velocity, as forthe depth this has to be accounted for. Figure 3 shows thesituation.

Figure 3: The situation for the estimation of the velocity ofpropagation.

√α is known out of the hyperbola. Distanced2 characterizes

the travelpath in the soil with the unknown velocityv2. Thedistanced1 corresponds to air with the approximate velocity

v1 = c. The algorithm estimates the average velocityvav,defined as:

vav =d1 + d2t1 + t2

=v1v2(d1 + d2)v2d1 + v1d2

(27)

with t1 = d1/v1 andt2 = d2/v2.We wish to estimatev2:

v2 =vavv1d2

v1(d1 + d2)− vavd1 (28)

vav is estimated, andv1 = c is known, so one still needs toestimated1 andd2. Essentially this corresponds to the esti-mation of the position of the air-soil interface reflection. Thiscan be done either during the scanning, either estimated outof the data itself.Finally, the hyperbolae that belong to the same object showa certain amount of correlation over the B-scans of a singleC-scan. This correlation can then be used to distinguish be-tween the object hyperbolae and the other noisy ones, thusfurther cleaning up the images.

RESULTS ON LABORATORY DATA

The proposed algorithms were applied to a data set that wasacquired under laboratory conditions (Scheers et.al, 2000).The setup consisted out of a bistatic pair of UWB GPR anten-nae. The objects were buried in a sandbox, filled with localsoil. The characteristics of the antennae were measured. Fig-ure 5 shows a three dimensional representation of the sameB-scan after the different algorithms are applied.

• Subplot (a) shows the original B-scan as it is measured.The object here was a PRB-M409 mine buried at 5 cmdepth in a soil that contains small inhomogeneities. Theair-soil interface is at sample 100, while the mine sig-nature is situated around sample 150, in the center ofthe B-scan. In this image a lot of clutter is present,especially at and immediately underneath the air-soilinterface. Remark also that although during the exper-iments the soil surface was made smooth, the surfacereflection is not constant over the B-scan.

• Subplot (b) shows the result after mean A-scan Sub-traction. This image was added for comparison, be-cause this is a very commonly used technique to reduceair soil interface effects. The resulting low target con-trast has two main reasons. First the non-smoothness ofthe surface results in a residual clutter at the interfaceposition. Further, since the target response is spreadover a relatively large part of the B-scan, the averageA-scan will contain too much target information, whichis therefore also removed from the data.

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• Subplot (c) shows the results when the wavelet decom-position and reconstruction is directly applied to theoriginal data. It is clear that most of the clutter is re-moved, although a small part of the surface reflectionremains. The target response is enhanced, but severelydeformed. The hyperbolic shapes that were present inthe original image are reduced to small areas near theapexes. This processing will help to locate targets, butdoes not allow to extract specific target features.

• Subplot (d) shows the results after deconvolution. Thepurpose of deconvolution is not to reduce the clutter.The energy present at the air soil interface has remainedunchanged. The shape of this reflection however, whichin the original B-scan contains the emitted pulse, isreduced to a single dip. The multiple hyperbolas forthe target are here reduced in a single positive-negativepair.

• Subplot (e) shows the results after the ARMA clutterreduction is applied on the deconvolved data. The clut-ter is clearly reduced, both at the interface and aroundthe target. Although some clutter remains, the enhance-ment of the target is greatly improved, compared withthe simple average subtraction of subplot (b).

• Subplot (f) shows the results of the wavelet decompo-sition and reconstruction applied on the ARMA results.The gain in clutter reduction is minimal, while again thedeformation of the hyperbolic shapes is very severe.

• Subplot (g) shows the results of the LPC clutter reduc-tion algorithm on the deconvolved data. Here, in com-parison with ARMA, the clutter is more reduced, butthe enhancement of the target is less clear.

• Subplot (h) shows the results of the wavelet decompo-sition and reconstruction on the LPC data. Note againthe severe deformation of the target response, while theextra clutter reduction is negligible.

Finally on the four resulting C-scans (ARMA, LPC and bothreconstructions) the estimation of the hyperbolae and the cal-culation of the parameters was executed. The results are sum-marized in the following table:

Processing Vel Dep Pos

ARMA 1.45108 5.95 25ARMA + REC 7.64107 1.78 23

LPC 1.25108 5.05 26LPC + REC 4.49107 2.06 27

Table 1: Results of parameter estimation. Velocity inm/s,depth in cm and horizontal position in cm.

The estimated horizontal position (25 cm) is satisfactory in allcases. The estimation of the depth (5 cm) is found to be mostaccurate for the LPC processing and for the ARMA process-ing. The reconstructed data lead, as can be seen in figure 5, toa narrowing of the hyperbolas. A hyperbola with less eccen-tricity results in a lower estimate for the velocity, and thus alsoto a more shallow estimate of the target depth. This is exactlywhat can be seen in the table. Finally the estimated velocitiescan be compared to the velocities of the same soil, which weremeasured in laboratory conditions (Storme, 1998). Compari-son reveals that both estimated velocities (ARMA and LPC)fall within the velocity range that was measured for a6 to 9%humid soil.

CONCLUSIONS

A number of clutter estimation and reduction mechanismswere introduced and applied to a set of laboratory data. Out ofthe comparison between the estimated features and the knownreal ones, it was concluded that both ARMA and LPC meth-ods are an improvement on the existing methods. They resultin a reduction of the clutter without deformation of the targetfeatures. Further improvement will lie in the dynamic estima-tion of the reference clutter sample. The wavelet reconstruc-tion method gives best results when applied directly on theraw data. The resulting target enhancement is large, but thedeformation leads to the loss of specific target features.

ACKNOWLEDGEMENTS. The authors wish to acknowl-edge the support of the DEMINE project (EU:HPCN 29902).The experimental data, used in the paper, were acquiredwithin the Belgian HUDEM project. The authors would liketo thank in particular Bart Scheers for his collaboration.

REFERENCES

Brooks, J.W., van Kempen, L., and Sahli, H., 1999. GroundPenetrating Radar Data Processing: Clutter Characteri-zation And Removal, Technical Report IRIS-TR-0059,Vrije Universiteit Brussel ETRO department, Belgium,44pp.

Canny, J., 1986. A Computational Approach To Edge De-tection, IEEE Transactions on Pattern analysis andMachine Intelligence, Vol. PAMI-8, No. 6, pp. 679-697

Capineri, L., Grande, P., and Temple, J., 1998. AdvancedImage-Processing Technique For Real-Time Interpre-tation Of Ground-Penetrating Radar Images,IEEETransactions, Vol. 9, pp. 51-59

Daniels, D., 1996.Surface Penetrating Radar, IEE, London,UK

Farhang-Boroujeny, B., 1998.Adaptive Filters: Theory andApplications, John Wiley & Sons, Inc., New York,ISBN 0-471-98337-3

Kaiser, G., 1994.A Friendly Guide To Wavelets, Birkhauser,Boston, ISBN 0-8176-3711-7

Kusama, K., Arai, I., Motomura, K., Wu, X., and Suzuki, T.,1989. Compression Of Radar Beam By Deconvolution,Proceedings of the 1989 international symposium onnoise and clutter rejection in radars and imaging sen-sors, pp. 767-772

Mehrotra, R., Namuduri, K., and Ranganathan, N., 1992. Ga-bor Filter-Based Edge Detection,Pattern Recognition,Vol. 25, No. 12, pp. 1479-1493

Neves, F., and Miller, J., 1996. Source Signature Decon-volution Of Ground Penetrating Radar Data,6th In-ternational Conference on Ground Penetrating Radar(GPR96), pp. 573-578

Saito, N., 1994. Local Feature Extraction And Its Applica-tions Using A Library Of Bases, PhD. Thesis, YaleUniversity.

Scheers, B., Plasman, Y., Piette, M., Acheroy, M., and Van-der Vorst, A., 2000. Laboratory Uwb Gpr System ForLandmine Detection,Proceedings GPR2000.

Storme, M., 1998. Microwave Characterization Of Wet Soils:Experimental Results And Comments, Technical Re-port HUDEM F97-06, Université Catholique de Lou-vain, Belgium, 34pp.

van Kempen, L., and Sahli, H., 2000. Multiscale Edge De-tection On Ground Penetrating Radar Images, UsingGabor Wavelets, And The Subsequent Parameter Es-timation Based On A Generalized Hough Transform,Submitted

van Kempen, L., Sahli, H., and Nyssen, E., and Cornelis,J., 1998. Signal Processing And Pattern RecognitionMethods For Radar Ap Mine Detection And Identi-fication, IEE Second International Conference on theDetection of Abandoned Landmines (MD’98), Edin-burgh, UK, pp. 81-85

New Results on Clutter Reduction and Parameter Estimationfor Landmine Detection Using GPR.

L. van Kempen, H. Sahli, J. Brooks, and J. Cornelis

Department of Electronics - ETRO-IRIS

Vrije Universiteit Brussel

Pleinlaan 2, 1050 Brussel - Belgium

tel. +32 2 629 28 58 fax. +32 2 629 28 83

email : {lmkempen,hsahli,jpcornel}@etro.vub.ac.be,jbrooks@hiwaay.net

Submitted to:

GPR2000Eighth International Conference on Ground Penetrating Radar

23-26 May, 2000

Gold Coast, Australia

pp

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