Online Dictionary Learning Aided Target Recognition In Cognitive GPR

0.85 MB·

by  Fabio Giovanneschi

ONLINEDICTIONARYLEARNINGAIDEDTARGETRECOGNITIONINCOGNITIVEGPR
FabioGiovanneschi1,KumarVijayMishra2,MariaAntoniaGonzalez-Huici1,YoninaC.Eldar2,
andJoachimH.G.Ender1,3
1FraunhoferInstituteforHighFrequencyPhysicsandRadarTechniques,Germany
2AndrewandErnaViterbiFacultyofElectricalEngineering,Technion-IsraelInstituteofTechnology,Israel
3Centre for Sensor Systems (ZESS), University of Siegen, Germany
7
ABSTRACT Inordertoreducethescantimeornumberofmeasurements,an
1
emergingtrendinGPRresearch[12,13]istoemploytherecently
0
Sparse decomposition of ground penetration radar (GPR) signals proposedcompressedsensing(CS)framework[14, 15]. InCS,a
2
facilitatestheuseofcompressedsensingtechniquesforfasterdata signalcanbereconstructedusingareducednumberofsamplesw.r.t.

n acquisitionandenhancedfeatureextractionfortargetclassification. thetheNyquistraterequirements,providedthesignalissparsein
a In this paper, we investigate use of an online dictionary learning somedomain.However,unlikepointscatterers,themineechoesare
J (ODL)techniqueinthecontextofGPRtobringdownthelearning spatiallyextendedandtheresultingGPRreceivedsignalisnotsparse

5 timeaswellasimproveidentificationofabandonedanti-personnel inconventionalrange-timeandfrequencydomains[16].Therefore,
2 landmines.OurexperimentalresultsusingrealdatafromanL-band ourimmediategoalistofindanefficientsparserepresentation(SR)
GPRforPMN/PMA2,ERAandT72minesshowthatODLreduces whichaccuratelyrepresentsthescatteringbehaviorsrelatedtosoil
] learningtimeby94%andincreasesclutterdetectionby10%overthe type and targets. This has been shown to improve the classifier
T
classicalK-SVDalgorithm.Moreover,ourmethodscouldbehelpful performanceindiscriminatingminesfromclutter[16,17].
I incognitiveoperationoftheGPRwherethesystemadaptstherange
. InSR,thesignal-of-interestistransformedtoadomainwhere
s samplingbasedonthelearneddictionary.
c thesignalcanbeexpressedasalinearcombinationofonlyafew
[ IndexTerms— groundpenetrationradar,onlinedictionarylearn- columnsoratomsofthedictionarymatrix[18].Whenitisinefficient

ing,KSVD,compressedsensing,cognitiveradar topre-definethedictionarytocontainarbitrarybasis(e.g.Fourieror
2
wavelets),theusualresortistolearnthedictionaryfromprevious
v
1. INTRODUCTION measurements. Dictionarylearning(DL)techniquesaimtocreate
7
adapteddictionarieswhichprovidethesparsestreconstructionfor
0 Agroundpenetratingradar(GPR,hereafter)isusedforprobingthe giventraining-sets, i.e., arepresentationwithaminimumnumber
6 undergroundbytransmittingradiowavesinthesubsurfaceandrecord- ofconstitutingatoms. ClassicalDLalgorithmssuchasMethodof
3
ingthebackscatteredreflections. TheinterestinGPRisduetoits OptimalDirections(MOD)[19]andK-SVD[18]operateinbatches
0
abilitytorevealburiedobjectsnon-invasivelyanddetectnon-metallic -dealingwiththeentiretrainingsetineachiteration. Althoughex-
.
1 scattererswithincreasedsensitivitytodielectriccontrast[1,2].This tremelysuccessful,thesemethodsarecomputationallydemanding
0 sensingtechniqueis,therefore,attractiveforseveralapplicationssuch andnotscalabletohigh-dimensiontrainingsets. Anefficientalter-
7 asgeophysics,archaeology,forensics,anddefense(seee.g.[1,3]for nativeistheonlinedictionarylearning(ODL)algorithm[20]that
1 somesurveys). Inthiswork,ourfocusisdetectionofburiedland- convergesfast,processessmallsets,andcaninferthedictionaryfrom
v: mines.ItisoneofthemostextensivelyinvestigatedGPRapplications largeortime-varyingtrainingsets[21].
duetoitsobvioussecurityandhumanitarianimportance.
i ImprovedDLmethodscanaidinbettertargetidentificationand
X MinedetectionGPRusuallyoperatesinL-band(1-2GHz)with
subsequentreductioninGPRmeasurementsthroughCS-baseddesign.
r ultra-wideband(UWB)transmitsignalsthatallowresolvingsmalltar- Tothisend,ourworkfocusesonhithertounexaminedapplicationof
a gets(5-10cmdiameter)atshallowdepths(15-30cm)[4,5].Insuch
DLtowardsGPR-basedlandmineclassification.Onlyoneprevious
situations,GPRtargetrecognitionsuffersfromsignaldistortiondue
studyhasemployedDL(K-SVD)usingGPRsignals[16],foridenti-
toinhomogeneoussoilclutter,surfaceroughnessandantennaringing.
fyingbedrockfeatures.WeproposeemployingODLandthenusethe
Moreover,theconstitutingmaterialofmanymodelsoflandminesis
coefficientsoftheresultingsparsevectorsasinputtoaSupportVec-
largelyplasticandhasaveryweakresponsetoradarsignalsdueto
torMachine(SVM)classifiertodistinguishminesfromclutter.Our
itslowdielectriccontrastwithrespecttothesoil[3,6].Avarietyof
comparisonofODLandK-SVDusingrealdatafromL-bandGPR
signalprocessingalgorithmshavebeenproposedfordetectionoflow
showsthatODLenjoysdistinctadvantageinspeedandlowfalse-
metal-contentlandminesinrealisticscenarios;approachesbasedon
alarmrates.FastODLcomputationspavethewaytowardscognitive
featureextractionandclassificationarefoundtobethemosteffective
GPRoperation,whereinthesystemusespreviousmeasurementsto
(seee.g.[7–10]),yetfalse-alarmratesremainveryhigh. Further,a
optimizetheprocessingperformanceandiscapableofsequential
high-resolutionGPRhaslongscantimestherebymakingthedata
samplingadaptationbasedonthelearneddictionary[22–24].
acquisitionbyaportableinstrumentverycumbersome[11].
Inthenextsection,wedescribetheGPRsystemandthedatasets.
InSectionIII,weintroduceourtechniqueforGPRtargetidentifica-
TheauthorswouldliketothankthecolleaguesatLeibnizInstitutefor
tion,withparticularfocusonODL.SectionIVpresentsclassification
AppliedGeophysics(LIAG),Hannover,Germanyfortheirsupportduringthe
measurementcampaign. K.V.M.acknowledgespartialsupportviaAndrew andreconstructionresultsusingrealradardata.Weprovideconclud-
andErnaFinciViterbiFellowshipandLadyDavisFellowship. ingremarksinSectionV.
minimize (cid:107)Y−DX(cid:107)
Parameter Value D,X F
Operatingfrequency 2GHz subjectto (cid:107)x (cid:107) ≤K, ∀1≤i≤L, (3.1)
i 0
PRF 1MHz
where||·|| denotesFrobeniusnorm.SincebothDandXareun-
Pulselength 0.5ns F
known,commonlythisisturnedintoatwo-stepconvexproblemthat
Samplingtime 25ps
alternatelyminimizesX(sparsecodingstep)[26]andD(dictionary
Spatialsampling 1cm
updatestep). ThepopularK-SVDalgorithmsequentiallyupdates
Crossresolution 4cm
alltheatomsforeachalternationbetweentheaforementionedtwo
Antennaheight 5-9cm
steps.Thisisabatchalgorithmthatusestheentiretrainingdatafor
Samples/A-scan 512 updatingthedictionaryateachalternation. TheODLalsoupdates
Fig.1. Testsite(red)withburied theentiredictionarysequentially,butusesoneelementoftraining
mines.InsetshowsGPRsystem. Table1.GPRparameters dataatatimeforthegradientdescent-baseddictionaryupdatestep.
Forthesparsecodingstep,K-SVDemploysOrthogonalMatching
2. SYSTEMANDFIELDTESTS
Pursuit(OMP)withtheformulation:
WeusedacommercialGPRsystemandcarriedoutthefieldcam-
minimize (cid:107)x (cid:107)
paignatLeibnizInstituteforAppliedGeophysics(LIAG),Hannover xi i 0
(Germany)[8].Wenowprovidedetailsforthesystemanddata.
subjectto (cid:107)y −Dx (cid:107)2 ≤α, ∀1≤i≤L, (3.2)
i i 2
2.1. L-bandGPR
whereαisthemaximumresidualerrorusedasastoppingcriterion.
TheGPRsystem(seeFig. 1inset)isanimpulseradarwithcentral TheODL,ontheotherhand,usesCholesky-basedimplementationof
frequency of 2 GHz.The frequency of the pulse repetition (PRF) theLARS-LASSOalgorithm[27].Thelattersolvesa(cid:96) -regularized
1
andthesamplingofthereceiverADCisof1MHz. Table1lists least-squaresproblem:
thesalienttechnicalparametersofthesystem.Thescanrateofthe
system is ∼ 1 m/s with sampling resolution of 1 cm towards the x (cid:44) min1||y −D x||2+λ||x|| , (3.3)
perpendicularbroadside(orXdirection)and4cmtowardsthecross- T x∈Rn2 T T−1 2 1
beam(Ydirection).Theradarusesa8cm×8cmdualbow-tiedipole
wherethesubscriptsT −1andT denotelastandcurrentiterations.
antennaforbothtransmit(Tx)andreceive(Rx)sealedinametallic
shieldingandaninternalabsorber.Therawdataconsistsofsamples 3.2. Signalclassification
ofcomplexenvelopeofthereceivedsignal.
WeuseSVMtoclassifythesparselyrepresentedGPRrangeprofiles.
2.2. Minesdata
Given a pre-defined collection of labeled observations, namely a
Thetestbedwasagrassy,moderatelyroughsurfacecontainingland- “classificationset”, SVMsearchesforafunctionalf : Rn → R
minesimulantsofdifferentsizesthatintheorderofdecreasingsize thatmapsanygivenobservationxi toaclassc ∈ R. Inourwork,
arePMN/PMA2,ERAandT72,allburiedatadepthof5-10cm[25]. theclassificationsetisalabeledcollectionofGPRrangeprofiles
Duringthefieldtests,theGPRscanneddifferent1m×1msections oftargets/clutterwhichhavebeensparselydecomposedusingthe
ofthetest-bed.Thesoiltexturewassandyandhighlyinhomegeneous learned dictionary D. We refer the reader to [28] for details of
(duetothepresenceofmaterialsuchasorganicmatterandstones), SVM. Briefly, SVM transforms the data into a high dimensional
therebyleadingtoahighvariabilityintheelectricalparameters.We featurespacewhereitiseasiertoseparatebetweendifferentclasses.
measuredthedielectricconstantatthreedifferentlocationsofthe Thekernelfunctionthatweusetocomputethehighdimensional
testbedwithaTimeDomainReflectometer(TDR)toobtainanesti- operationsinthefeaturespace,istheRadialBasisFunction(RBF).To
mateofitsmeanvalueandvariability.Theaveragevalueoscillated optimallyselecttheSVMinputparameters,wearrangedtheoriginal
between4.6and10.1with15%standarddeviationandcorrelation classificationsetintotrainingandvalidationvectorsinν different
length[8]of20cm. Suchbigvariationsinsoilcompositionspose ways(ν-foldcross-validationwithν=10)toarriveatacertainmean
difficultiesinminedetectionwithexistingmethods. cross-classificationaccuracyofthevalidationvectors.
3. GPRTARGETIDENTIFICATIONMETHOD 4. EXPERIMENTALRESULTSANDANALYSIS
Wenowdescribeourmethodfordictionarylearningandclassification WedividedtheentireLIAGdataintothreedifferentsets:thetraining
for GPR target identification. The literature for DL and SVM is settolearnthedictionary,theclassificationsetfortheSVMclassifier
extensive, and hence we only summarize these methods here. In andthetestset. Wedevisedastatisticalapproachtoselectthebest
thefollowing,weuseboldfacelowercaseanduppercaselettersfor parametersforDLwithGPRminesdata,andthenusetheresultant
vectorsandmatrices,respectively. dictionaryfortheclassificationprocedure.
3.1. Dictionarylearning 4.1. Dictionarycomparison
Adictionarylearningalgorithmfindsanover-completedictionary ThetrainingsetYconsistedofmorethantwothousandrangeprofiles
D ∈ Rm×n, m < n that can sparsely represent measurements thatwererandomlyselectedfromacollectionofGPRresponsesin
y ∈ Rm. ForthetrainingdataY = [y ,··· ,y ], wecallX = proximity of the buried targets; these areas belonged to different
1 L
[x ,··· ,x ] ∈ Rn×L a sparse representation of Y over D = surveysofthetestsite.Inordertocomparethedictionariesobtained
1 L
[d ,··· ,d ], ifY (cid:39) DX. Here, d , j = 1,··· ,niscalledan fromODLandK-SVD,weuseasimilaritymeasurethatquantifiesthe
1 n j
atomofthedictionary.Eachofthevectorsx isasparserepresenta- closenessofthereconstructedvectorsyˆ obtainedusingthesparse
i i
tionofy withonlyK nonzeroentries. Atractableformulationof coefficientsofthelearneddictionaryDwiththeoriginaltraining
i
thisproblemisthefollowingnon-convexoptimization set vectors y . Let the cross-correlation between the two vectors
i
Wearelookingforsetofvalues{T,K,λ,α}forwhichthep
sDL
isskewedtowardsunityandhassmallvariance.Theindividualcom-
parisonsofmean(µ)andstandarddeviation(σ),asusedinprevious
GPRDLstudies[16],arenotsufficienttoquantifytheobserveddis-
persionintheepdfsobtainedbyvaryinganyoftheparametervalues.
We,therefore,simultaneouslycomparebothstatisticsbyusingthe
coefficientofvariation,CV =σ/µ;inouranalysis,itrepresentsthe
extentofvariabilityinrelationtothemeanofthesimilarityvalues.
Figure3ashowsthevariationofCVforODLandK-SVDfordiffer-
entvaluesoftrainedatomsandfixedvaluesofλ=0.1andα=0.1.
TheODLshowsthatafter40iterations,thevariationintheepdfis
negligibleandtheimpactofincreasingthenumberoftrainedatoms
grows.WenotethatK-SVDdoesn’tshowanysuchtrend.
Oursecondmetrictocomparethedistributionsofthesimilarity
measureobtainedbysuccessivechangesinparametervaluesisthe
Kolmogorov-Smirnov(K-S)distance[29],whichisthemaximum
distancebetweentwogivenempiricalcumulativedistributionfunc-
tions(ecdf).LargervaluesofK-Sdistanceindicatethatsamplesare
Fig.2. Normalizedhistogramsofsimilaritymeasure. Here,T = 40,K = 512, drawnfromdifferentunderlyingdistributions.SupposeP andP
λ=0.1,andα=0.1. s1 s2
aretheecdfsofthesamelengthcorrespondingtoepdfsp andp ,
s1 s2
respectively.ThenK-SdistanceD(P ,P )is
s1 s2
D(P ,P )= sup |P (i)−P (i)|, (4.2)
s1 s2 s1 s2
1≤i≤N
wheresupdenotesthesupremumoveralldistances.Figure3bshows
thevariationofK-Sdistancefortheidenticalvaluesofparametersas
usedforCVevaluationinFig.3a.Wekepttheecdfcorresponding
toK = 128atomsandT = 1iterationasareference. Wethen
computedtheK-Sdistanceofecdfsobtainedwithotherparameter
valueswithrespecttothisreference.Astheparametervaluesmove
awayfromthisreference,theK-Sdistanceincreases.However,for
(a)Coefficientofvariation (b)Kolmogorov-Smirnovdistance
bothDLmethods,wenoticethefollowingtrend: asthenumberof
iterationsincrease,thedifferenceinK-Sdistancebetweensuccessive
Fig.3. Statisticsofsimilaritymeasuredistributionsforλ=0.1andα=0.1and
iterationsisnegligibleandisinfluencedmostlybythenumberof
varyingnumberofiterationsandtrainedatoms.
trainedatoms. TheK-Sdistancequantifiesthedifferencebetween
+∞
be r (m) = (cid:80) y (n)yˆ (n+m). The normalized cross- ODLandK-SVDdistributionsratherthanstatingwhichoneisbetter.
yi,yˆi i i
n=−∞ CombiningthisinformationwithFig.3a,itisevidentthatODLhas
correlationis lowerCVandisalsomorerobusttoparameterchangesthanK-SVD.
r (m)
r (m)= yi,yˆi (4.1) 4.3. Classificationandcomputationalefficiency
yi,yˆi (cid:112)r (0)r (0)
yi,yi yˆi,yˆi AfterexaminingthethresholdsatwhichtheCVandK-Sdistance
Wedefinethesimilaritymeasuresitobethemaximumoftheabsolute stabilize,weselectedthefollowingvaluesfordictionarylearning:
valueofthenormalizedcrosscorrelationbetweenyiandyˆi: si = T =40,K =512,λ=0.1,andα=0.1.Forthissetofvalues,Fig.
max|ryi,yˆi(m)|.Thesetofsimilaritymeasurevalues{si}Ni=1form 2showstheepdfsofsimilaritymeasuresforODLandK-SVD.Ina
an empirical probability density function (epdf), psDL where the landmineclearancecampaign,theseparameterswillbelearnedoffline
subscriptDLrepresentsthemethodused(K-SVDorODL).Asan andwillremainfixedduringtheclassificationprocedure.Thetestset
example, Fig. 2 shows the epdfs for the dictionaries learned for contains2differentsurveysforeachtypeofmineclassforatotalof
theGPRminesdata. WenotethatpsODL ismoreskewedtowards fivethousandrangeprofiles.Oncethetest-setissparselydecomposed
unitythanpsKSVD,therebydemonstratingsimilarityofthelearned usingthelearneddictionary,weestimatedameansparsitytobe≈4
ODLdictionarywiththeoriginaltrainingset.Toarriveatoptimum forODLand≈6forK-SVD.Inordertofindthebestfunctionalfor
parametervaluesaffectingtheseepdfs,wenowusestatisticalmetrics. theSVMclassifier,weconductedacross-validationonthesparsely
decomposed classification set using a set of different RBF kernel
parameters.Afterobtainingthefunctional,weusedittoclassifythe
4.2. Parameteranalysis
sparselydecomposedtestset.
TheparameterswhichpredominantlyaffecttheresultsofODLand Figure4showstherawdataforPMA/PMNminesat15cmdepth
K-SVDalgorithmsarethenumberofiterations(T),thenumberof andtheclassificationmapsobtainedwithalearneddictionaryusing
trainedatomsK,theregularizationparameterλintheSDstep,and ODLandK-SVDmethods.Itisclearthattargetandclutterrecogni-
theerrorparameterαtosparselydecomposethetrainingsetviaOMP. tionaredrasticallyimprovedusingadictionarylearnedwithODL
Theepdfp isthenafunctionofthesefourparameters.Foragiven when compared with K-SVD. Table 2 compares the performance
s
DLmethod,ourgoalistocomparetheepdfsofsimilaritymeasure ofclassificationusingthetwoDLmethods.Usingaccurateground
byvaryingtheseparameters,andarriveatthethresholdsofparameter truthinformation,wedefinedtargethalosastheboundariesofthe
valuesafterwhichthechangesinp areonlyincremental. buriedlandmines. Letthenumberofpixelsandthedeclaredmine
sDL
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