Ground Penetrating Radar Data
Brian Karlsen a
, Helge B.D. Srensen a
, JanLarsen b
and Kaj B. Jakobsen a
a
rstedDTU,Technical University of Denmark
rsteds Plads, Building348, DK-2800 Kongens Lyngby, Denmark
b
Informatics and MathematicalModelling,Technical University of Denmark
RichardPetersens Plads, Building321, DK-2800 Kongens Lyngby, Denmark.
ABSTRACT
StatisticalsignalprocessingapproachesbasedonIndependentComponentAnalysis(ICA)algorithmsforclutter
reductionin Stepped-FrequencyGroundPenetratingRadar(SF-GPR)dataarepresented. Thepurposeofthe
clutter reduction is indirectly to decompose the GPR data into clutter reducedGPR data and clutter. The
experimentsindicate thatICAalgorithmscandecomposeGPRdataintosuitablesubspacecomponents,which
makesitpossibleto selectasubset of components containingprimarily target information(likeanti-personal
landmines) and others which contain mainly clutter information. Thepaper compares spatial and temporal
ICA approachesoneld-testdatafrom shallowburiediron andplastic anti-personallandminedummies. The
data areacquired using amonostaticbow-tie antennaoperatingin thefrequencyrange from 500MHzto 2.5
GHz.
Keywords: Anti-personal landmine detection, ground penetrating radar, independent component analysis,
statisticalsignalprocessing,clutterreduction.
1.INTRODUCTION
The Ground PenetratingRadar (GPR) is widelyused in the application of detection of landmines. The ad-
vantage of using a GPR is given by the fact that a GPR is able to detect buried objects in the received
electromagneticeldsscatteredfromtheground. This propertymakestheGPRabletodetectlandmines,and
inparticularanti-personallandminesofplasticwithalowcontentofmetal 1,2
. Mostly,thosekindsoflandmines
are buried close to the surface of the ground, where the detection of objects is very weak due to the strong
clutterscatteringfromthegroundsurface. Clutter hampersthedetectionofthelandminesandthereforegives
a signicant problem for automatic landmine detection systems. In general, the clutter that eects a GPR
canbedened asthose signalsthat areunrelatedtothetargetscatteringcharacteristicsbut occupythesame
frequencybandas thetargets. Clutter canbecausedbymultiplereections,e.g.,intheantenna,betweenthe
antennaandthegroundsurface,and thenon-minetargetsburiedintheground. However,onthedetectionof
shallowburiedlandminesthegroundsurfaceclutteristhestrongestandmostsignicantclutter. Toincreasethe
detectionof shallowburiedobjectsitis thereforenecessaryto deploypropergroundsurfaceclutterreduction
methodsontheGPRsignalstoenhance thedetectionofshallowburiedlandmines.
Theliteraturesuggestsanumberofclutterreductionmethods,suchaslikelihoodratiotesting 3
,parametric
systemidentication 4{7
, waveletpacket decomposition 8,9
, subspacetechniques 10{14
,andsimplemeansubtrac-
tion 1
. However,manyofthese failtodetectshallowburiedlandmines,mostlybecauseofthestatistical nature
of theclutter, e.g.,the groundsurfaceis not perfectly at or evenrelativesmooth. Another problem isthat
manyofthemethodsusereferencesignalestimatesofthesignatureofalandmine. These referencesignalsare
usedto removesignalthat areunrelatedtothereference. However,atargetsignalwhich haslittlecorrelation
withthereferencesignalsmaynotbedetected,hence,beclassiedasclutter.
Further author information on: BK: brk@oersted.dtu.dk, www.oersted.dtu.dk; HBDS: hbs@oersted.dtu.dk,
www.oersted.dtu.dk;JL:jl@imm.dtu.dk,www.imm.dtu.dk/~jl;KBJ:kbj@oersted.dtu.dk,www.oersted.dtu.dk
To reduce the clutter we havesuggested another promising approach basedon decomposition of the
GPR signalsinto clutter and landmine signalsusing Principal Component Analysis (PCA) and Independent
Component Analysis (ICA). In this work we focus on reducing the ground surface clutter using statistical
unsupervisedlearningmethods basedonspatialand temporalICA. ThebasicideausingICAisto decompose
thereceivedGPR signalsinto subspacesof cluttersignalsand landminesignals,respectively. Previouswork 12
addressedtheuseoftemporalICA only.
In this paper we extent the work by considering spatial ICA and more elaborate experimental studies.
Section 2presentsthespatial and temporalICA basedclutter reductionmethods and section3 describesfor
selectingofrelevantICAcomponents. Finally,section4providesacomparativestudyofthepresentedmethods,
which aretested onGPR-datacollectedatanindoorGPRmeasurementfacilityattheTechnicalUniversityof
Denmark.
2.CLUTTER REDUCTION USING INDEPENDENT COMPONENT ANALYSIS
To reduce the clutter in the GPR data we focus on unsupervised statistical methods based on spatial and
temporal Independent Component Analysis (s-ICA and t-ICA). The s-ICA and t-ICA method are twocom-
plementary waysto subspacedecompose a multi-channel signalinto a set of weightingvectors(eigenimages)
and aassociated set oftime signalsusing ICA 15{17
. The s-ICAand t-ICA method are inspiredbyarecently
suggestedclutterreductionmethodbasedonPrincipalComponentAnalysis(PCA 11,12
). Thes-ICAandt-ICA
method for clutter reductionresemblesthat of the PCA method. Themajor dierence is that thesubspace
formed by ICA is not orthogonal as in PCA. Moreover, the independent components (IC's), which are the
counterparts of the Principal Components (PC's), are statistically independent. We thus expect the IC's to
haveamoredistincttimeandspatiallocalization. Fromrecentlypresentedwork 12
,t-ICAclearlyshowsamore
distinct time localization than PCA. Briey, the s-ICA and t-ICA basically decomposes GPR signals into a
set ofeigenimagesand associatedtimesignals. Thes-ICA ndsindependent eigenimagesandaassociatedset
of time signals,whereas thet-ICA nds independent timesignals anda associated set of eigenimages. From
thes-ICAandt-ICA, clutterreductionisthenobtainedbyselectingcomponents,which containlandmine-like
signaturesonly.
ToemploytheICAsubspacedecompositionmethodsontheGPRdata,asignalspacemustbedened. The
space observed is spanned by the multi-channel GPR time-domain signalsas expressed by the signalmatrix
X 2R PN
expressedby
X=fX
p;n g=fx
p
(n)g=fx
i;j
(n)g=[x(1);x(2);;x(N)]; (1)
wherePisthenumberoftime-domainsignals,whicharereceivedbyscanningtheGPRabovethegroundsurface
in thex-and y-direction,N isthenumberofsamplesin eachofthe receivedtime-domainsignals,andx
i;j (n)
isthetime-domainsignalreceivedattheantennalocatedatposition x;y
= x =(i 1)4x;y =(j 1)4y
,
where i= 1;2;;I, and j = 1;2;;J. 4x and 4y are the antenna location step size in the x- and y-
direction, respectively, and p = i+(j 1)I. I and J is the number of antenna locations in the x- and
y-direction,respectively. Ingeneralweexpect thatthemeanvalueof X is equalzero, EfXg=0. Hence,we
mayredenex
p
(n)tox
p (n)=x
i;j
(n),where
x
p (n)=x
i;j (n)=x
i;j (n)
1
IJ I
X
i=1 J
X
j=1 x
i;j
(n); p=i+(j 1)I; i2[1;I]; j2[1;J]; p2[i;JI] (2)
That is, in the signal matrix X, i.e., x
p
(n), n = 1;2;;N, is the p'th received time-domain signal, orin
practice,thep'threceivedtime-domainsignalsubtractedby themean valueoftheensembleofreceivedtime-
domainsignals. Equation2isalsoknownasthemean-subtractionclutterreductionmethod 1
.
PCA.Inordertocompareandinordertoprovideatreducedrankdataset 19,20
asinputtothes-ICAand
t-ICA,werstemploythePCAonthedataset. PCAwasexecutedusingsingularvaluedecomposition(SVD),
X =UDV
>
= N
X
u
i D
i;i v
>
i
; X
p;n
= N
X
U
p;i D
i;i V
n;i
(3)
p;i 1 2 N n;i 1 2 N
representorthonormalbasisvectors,i.e.,eigenvectorsofthesymmetricmatricesXX T
andX T
X,respectively.
D=D
i;i
isanN N diagonalmatrixofsingularvaluesrankedin decreasingorder,asshown byD
i 1;i 1
D
i;i
;8i 2 [2;N]. The SVD identies a set of uncorrelated time signals, the principal components (PC's):
y
i
=D
i;i v
i
, enumeratedbythe componentindex i =1;2;:::;N and y
i
=[y
i
(1);;y
i (N)]
>
. That is, from
the PCA we canwrite the observedsignalmatrix asaweighted sumof xed eigenvectors(eigenimages), u
i ,
that oftenlendthemselvesintodirect interpretation. ThePC'sand theeigenimagesareused asinputstothe
t-ICA ands-ICA,respectively. ThedimensionofthePCA dataset willbedN. That is, wemodelX only
fromnon-zeroeigenvalues 20
.
Temporal ICA.t-ICAembodiestheassumptionthateachPC,y
i
,isalinearcombinationofM temporal
independenttime signals,the IC's. The t-ICA isprocessed in twosteps. First,X is projected toasubspace
spannedbyM,M d,selectedPC's.,e.g.,therstM PC's. Thatis,Y = e
U
>
X,where e
U =[u
1
;u
2
;;u
M ]
andY isanMN matrix,Y =[y
1
;y
2
;;y
m ]
>
. Hence,thet-ICAproblemisdened as
Y =A
t S
t
; (4)
whereA
t
istheMM matrixofmixingcoeÆcientsandS
t
istheMN matrixofindependenttimesignals,
(IC's). Secondly, the mixing matrix, A
t
, and the matrix of independent time series, S
t
, are estimated 16,17
.
The original signal matrix is reconstructed as b
X = W
t S
t
= P
M
i=1 w
ti s
ti
, where W
t
= e
UA
t
is the matrix
of eigenimages. s
t
i
=[s
t
i
(1);;s
t
i
(N)] and w
t
i
=[w
t
i
(1);;w
t
i (P)]
>
is thei'th independent timesignal
and associated eigenimage, respectively. Fromthe t-ICA clutter reductioncanthen beobtained byselecting
componentswhichmainlycontainlandmine-likesignaturesandthenreconstructthesignalmatrix, b
X. Amore
detaileddescriptionofthisprocedure isgiveninSection3.
SpatialICA.s-ICAembodiestheassumptionthateacheigenimage,u
i
,iscomposedofalinearcombination
of M spatially IC eigenimages. Thes-ICA isdone in twosteps. First isX projectedto a subspacespanned
byM selectedPC's.,e.g.,therstM PC's,i.e.,similar tothet-ICA,where wegetY andhave e
U. Then,the
s-ICAproblemisdened as
e
U
>
=A
s S
s
; (5)
whereA
s
istheMMmatrixofmixingcoeÆcientsandS
s
istheMP matrixofindependenteigenimages,
IC's. Secondly,themixingmatrix,A
s
,andthematrixofindependenteigenimages,S
s
,areestimated 16,17
ina
similarwayasforthet-ICA.Theoriginalsignalmatrixisreconstructedas b
X
>
=W
s S
s
= P
M
i=1 w
s
i s
s
i ,where
W
s
=YA
s
isthematrixoftimesignals. s
s
i
=[s
s
i
(1);;s
s
i
(P)]andw
s
i
=[w
s
i
(1);;w
s
i (N)]
>
isthei'th
independenteigenimageandassociatedtimesignal,respectively. s-ICAclutterreductionresemblesthatofthe
t-ICAclutterreduction(referto Section3).
But how do we get A
s , A
t , S
s and S
t
? The literature provides a number of algorithms for estimating
theA mixing matrixand theS sourcematrix
. Basicallytheycanbedividedinto twofamiliesin which the
rstdeployhigher(or lower)order momentsofnon-Gaussiansources, whereastheotherfamilyuses thetime
correlation of the source signals. In the present casewe expect that the sources are bothnon-Gaussian and
colored. Wedeployamemberfromtherst family: thewidelyused Bell-Sejnowski 16
algorithmusing natural
gradientlearning.
3.SELECTION OF COMPONENTS AND RECONSTRUCTION
Theclutterreductionisobtainedbyselectingcomponentsthathavelandmine-likesignaturesonly. Thefeatures
we canbase ourselectionon aretemporalfeatures and spatial features. Wesuggestthree selectionmethods,
which arebasedontemporalfeatures,spatialfeatures,and combinedtemporalandspatialfeatures.
Temporal Features: selecting components only using information from W
s and S
t
. Considerthe pro-
jection onto the subspace spanned by K selected time signals which mainly contain information about the
Foraresentreviewthereaderisreferredto 21
.
landmine object, i.e., W
t
= X e
S
>
t ,
e
S
t
= [s
ti
1
;s
ti
2
;;s
ti
K ]
>
for the t-ICA, and S
s
= f
W
s X
>
, f
W
s
=
[w
si
1
;w
si
2
;;w
si
K
]forthes-ICA. Theselectionofthecomponentscanbedonebyinspectingthetimesig-
nalsonly. Ifweknowwerethegroundsurfaceislocatedintime,wethenremovethosetimesignalcomponents
thatpeaksbeforeandatthegroundsurface. TheclutterissubsequentlyreducedbyreconstructingXfromthe
subspaceas givenby
b
X =W
t e
S
t
; b
X
>
= f
W
s S
s
(6)
fort-ICAands-ICA, respectively.
Spatial Features. Selecting components only using information from W
t and S
s
. Consider the pro-
jection onto the subspace spanned by K selected eigenimages which mainly contain information about the
landmine object, i.e., S
t
= f
W
>
t X,
f
W
t
= [w
ti
1
;w
ti
2
;;w
ti
K
] for the t-ICA, and W
s
= X
>
e
S
>
s ,
e
S
s
=
[s
s
i
1
;s
s
i
2
;;s
s
i
K ]
>
for thes-ICA. Theselection of thecomponentscanbedoneby inspecting theeigenim-
ages only. We then remove those components that show no spatial landmine-like signatures. The clutter is
subsequentlyreducedbyreconstructingX from thesubspaceasgivenby
b
X = f
W
t S
t
; b
X
>
=W
s e
S
s
(7)
fort-ICAands-ICA, respectively.
Spatial Temporal Features. Selecting components only using information from W
s and S
t , W
t , and
S
s
. That is,selectionofcomponentsthat showsbothtemporalandspatial landmine-likesignatures. Consider
a subspace spanned by K components asin the spatial and the temporal feature selection methods. Then
weselectcomponentsthat showlandmine-likesignaturesin botheigenimagesandtimesignals. Theclutter is
subsequentlyreducedbyreconstructingX from thesubspaceasexpressedbyequation6and7.
TheoverallobjectiveoftheICAmethodsisautomaticdetectionofthelandminesbyautomaticselectionof
thecomponentsbasedonW
s ,S
s ,W
t ,andS
t
. However,thisworkisdoneonaverysmalldataset. Therefore,
theselectionofthecomponentsis donebyvisualinspectionofeigenimagesandtimesignals.
4.CASE STUDY: M56 IRON AND PLASTIC LANDMINE DUMMIES
Thecomparativestudyof thet-ICAand s-ICAmethods forclutterreductionin GPRdatawasperformedon
eld-testStepped-FrequencyGPR data. Theeld-testdata wascollectedusing amonostaticbow-tie antenna
operatinginthefrequencyrangefrom500MHzto2.5GHz. ThedatawasacquiredusingaHP8753Anetwork
analyzer. Thebandwidthoftheantennadeterminestheresolution,whichisapproximately7.5cminfree-space.
Thefrequency-domain data wasFouriertransformedto the time-domainusing asampling frequencyof 10.24
GHz,whichcorrespondstoafree-spacesamplingof2.9cminthedepthdirection,whichisbelowtheresolution
setbytheantennabandwidth. Inameasurementareaof126cm90cmM56landminedummiesofironand
plastic (lledwith bees wax) were buriedin thecenteroftheeld in relativewet soil5cm belowthesurface.
Thedimension ofthelandmine dummiesare: diameter 5.4 cm,and height4cm. The measurementareawas
scannedsoeveryantennapositionswerelocated(4x=1cm)(4y=1cm)fromeachother.
In Figure 1 and Figure 2 are the PCA results shown. The Figures show the rst M = 21 eigenimages,
u
i
, i = 1;2;:::;M, and associated PC's, y
i
, i = 1;2;:::;M, for the iron dummy and the plastic dummy,
respectively. In totalwegotd=24andd=23eigenimagesandassociatedPC'sfor theirondummy andfor
theplasticdummy,respectively. However,thelasteigenimagesandPC'sshowsonlynoise-liketextures,asalso
are shown from therst 21eigenimagesand PC's due to thefact that the latereigenimagesand PC's shows
noise-liketextureonly. All thecomponentsaresortedaftervariance. Thatis, therstcomponentcontributes
mostto X, where as thelast componenthasthe lowest contribution to X. The varianceisgivenbyD
i;i for
thei'th component. Forthe signalmatrix,X, wehaveP =12791=11557antennapositions. Thatis, P
receivedtime-domain signalsatP locations. Thenumberof samples, N, was62. Theeigenimagesand PC's
areusedasinputstothes-ICAand t-ICAmethods.
ThePCAendupwithadatasetofdimensiond=24andd=23fortheironandplasticdummy,respectively.
rathercomplex. Thesolutiontothis istocompress theinformationinto fewercomponents. That is,havinga
subspacedecompositionmethodthatisabletolowerthedimensionofthedatasetwithoutloosinginformation,
e.g., asubspacedecomposition method that seeks themost optimaldimension. However, theBell{Sejnowski
ICA (BS-ICA)is notableto reduce thedimension ofthedata set in that way. Therefore, one way to reduce
thenumberofdimensionsistoreduce thenumberofinputs,withthecostof information. Inorderto seehow
theICA performsonsmallersubspaces,e.g.,isitpossibletocompress thelandmine-likesignaturesinto fewer
components, the t-ICA and s-ICA were tested on subspaces using the rst M = 15, M = 10, and M = 5
eigenimages,u
i
,andassociatedPC's, y
i
. TheseeigenimagesandPC'swere selecteddue tothefact thatlater
eigenimagesand PC's than M = 15 showsonly clutter-like signatures and that the contribution from those
componentsin X issmall(lowvariance).
InFigure3andFigure4areshowntherst12componentsfromthet-ICAands-ICAusingtherstM=15
PC's, e
Y =[y
1
;y
2
;;y
15 ]
>
, asinput to thet-ICA and rstM =15 eigenimages, e
U =[u
1
;u
2
;;u
15 ], as
inputtothes-ICA.InFigure3someoftheeigenimagesoftheirondummyexperimentsshowsstronglandmine-
signatures, inparticular eigenimagenumber5and 6forthet-ICA andnumber6forthes-ICA. However,the
signaturesaremoreclearlypronouncedforthes-ICA.Further,fewereigenimagesforthes-ICAshowslandmine-
likesignatures. Thatis,thet-ICAspreadthelandmineinformationoutinmanycomponents,whereasthes-ICA
is ableto compress theinformation in to few components. Thetime signalsshowsbetter localization forthe
t-ICA than for thes-ICA. That is, for the t-ICA theeigenimages canbe associatedwith aparticular depth.
From theresultsit isshown that thet-ICA providesabettertime separation,whereasthes-ICA provides at
betterspatialseparation. FortheM56plasticdummyresults,shownin Figure4,similarresultsareobtained.
However,thelandmine-signatureislesspronouncedduetothelowscatterfrom thelandmine.
In Figure 5to Figure 7arethe resultsof theclutter reductionshown. Theimages showsthe totalpower
oftherst30samplesofthereceivedGPRtime signalat eachantennalocation. That is, b
X
ppow
= P
L
n=l
^ x 2
p;n .
The power is calculated using a rectangular window of size L = 30. By using the window size L = 30, we
covertheareafrom theinputof theantennato approx.20 cmunder thegroundsurface. Fromthe resultsin
general it is clearthat theselection method based on combined spatial and temporal features givesthe best
performance, particular when choosing M = 15 components. It is also shown that the t-ICA has a better
performancethanthes-ICA, whenusing onlytemporalfeatures, andthes-ICA hasbetterperformance when
usingonlyspatial features. Thisistrueforboththeirondummyandplastic dummy. Howeverfortheplastic
dummythebest resultisobtainedwhenchoosingasubspaceofM =5components. Whytheperformanceis
poorat small subspacesmay befound in thesimple way we selectthe inputsto the s-ICA and t-ICA. From
Figure1andFigure2itisclearthatmostofthelandmineinformationisin component5to12. Byremoving
those components, which we do when we select the rst M = 5components, we will loose information. In
Figure6andFigure7aremeshplotsshown,theyclearlyshowsthattheclutterisreducedintheGPRdata.
5.CONCLUSION
ThispaperprovidedacomparativestudyofspatialandtemporalICAforclutterreduction. TheICAmethods
were based on the Bell{Sejnowski ICA. From the results we havethat the t-ICA provides more peaky time
signalsthanthes-ICA,duetothefactthat thet-ICA givesindependenttimesignals. Hence,thet-ICAshows
betterperformanceintimelocalization.However,s-ICAshowsmorelandmine-likeeigenimagesthanthet-ICA,
due to the fact that the eigenimagesare independent in the s-ICA. Hence, s-ICA showsbetter performance
in spatiallocalization. Threecomponentselectionmethods weresuggestedandcompared. Theywere baseon
temporal featureselection,spatialfeature selection,andcombinedspatialandtemporalfeatureselection. The
combinedshowedbestperformance. Thatis, thebestclutterreductionisobtainbyselectingcomponentswere
botheigenimagesand associatedtime signalsshowslandmine-like signatures. Futurestudies will concentrate
onICA methodsbasedonbothspatialandtemporalfeaturesandmethodsforautomaticcomponentselection.
6.ACKNOWLEDGEMENT
We thankOleNymann forenthusiastic andsteady support of our work in humanitarianlandmine detection.
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EI 1 EI 2 EI 3
EI 4 EI 5 EI 6
EI 7 EI 8 EI 9
EI 10 EI 11 EI 12
EI 13 EI 14 EI 15
EI 16 EI 17 EI 18
EI 19 EI 20 EI 21
1 2 3
0.5 1 1.5 2
x 10 −3
S 1
1 2 3
2 4 6 8 10 12 14
x 10 −4
S 2
1 2 3
0.5 1 1.5 2 2.5
x 10 −4
S 3
1 2 3
5 10 15
x 10 −5
S 4
1 2 3
1 2 3 4 5
x 10 −5
S 5
1 2 3
2 4
x 10 −5
S 6
1 2 3
0.5 1 1.5 2
x 10 −5 S 7
1 2 3
5 10 15
x 10 S 8 −6
1 2 3
2 4 6 8
x 10 −6 S 9
1 2 3
2 4
x 10 S 10 −6
1 2 3
1 2 3
x 10 S 11 −6
1 2 3
5 10 15
x 10 S 12 −7
1 2 3
2 4 6 8 10
x 10 S 13 −7
1 2 3
2 4 6
x 10 S 14 −7
1 2 3
1 2 3 4 5
x 10 S 15 −7
1 2 3
1 2 3 4 5
x 10 S 16 −7
1 2 3
1 2 3
x 10 S 17 −7
1 2 3
2 4 6 8 10 12
x 10 S 18 −8
1 2 3
2 4 6
x 10
S 19 −8
1 2 3
2 4 6 8
x 10
S 20 −8
1 2 3
1 2 3
x 10
S 21 −8
Figure 1. Eigenimages (xy-plane), ui, and associated PC's, y
i
, for the M56 iron dummy. Only the rst M = 21
eigenimages and associated PC's are shown. It should be noticed that it is the power of the PC's that are shown.
Thepower iscalculated usinga non-causalKaiser windowof size 3with thecharacteristic parameterset to2. The
eigenimages shows verystronglandmine signaturesinafew eigenimages, e.g., eigenimage5and 6,andthe associated
PC'salsopeaksinadepthcorrespondingtotheburieddepth(1.8nanosec.). Eigenimage1,2,and3andassociatedPC's
showsstronggroundsurfacesignature. Theeigenimagesshowsthevariationsintheground surfaceand theassociated
PC'speaksatthegroundsurface(1.0nansec.). TheremainingeigenimagesandPC'sshowsmoremixedclutter-landmine
signals. However,theyhavemuchlesspower. Itisclearthattheseparationintimeispoor. TheeigenimagesandPC's
areusedasinputstothes-ICAandt-ICA.
Eigenimages Principal Components
EI 1 EI 2 EI 3
EI 4 EI 5 EI 6
EI 7 EI 8 EI 9
EI 10 EI 11 EI 12
EI 13 EI 14 EI 15
EI 16 EI 17 EI 18
EI 19 EI 20 EI 21
1 2 3
0.5 1 1.5 2
x 10 −3
S 1
1 2 3
2 4 6 8
x 10 −4
S 2
1 2 3
0.5 1 1.5 2 2.5
x 10 −4
S 3
1 2 3
5 10 15
x 10 −5
S 4
1 2 3
1 2 3 4 5
x 10 −5
S 5
1 2 3
1 2 3
x 10 −5
S 6
1 2 3
0.5 1 1.5 2
x 10 −5 S 7
1 2 3
2 4 6 8 10 12 14
x 10 S 8 −6
1 2 3
2 4 6
x 10 −6 S 9
1 2 3
2 4
x 10 S 10 −6
1 2 3
1 2 3
x 10 S 11 −6
1 2 3
0.5 1 1.5 2
x 10 S 12 −6
1 2 3
2 4 6
x 10 S 13 −7
1 2 3
2 4 6
x 10 S 14 −7
1 2 3
2 4 6
x 10 S 15 −7
1 2 3
1 2 3 4 5
x 10
S 16 −7
1 2 3
1 2 3
x 10
S 17 −7
1 2 3
2 4 6 8 10 12
x 10
S 18 −8
1 2 3
2 4 6
x 10
S 19 −8
1 2 3
2 4 6 8
x 10
S 20 −8
1 2 3
1 2 3
x 10
S 21 −8
Figure 2. Eigenimages(xy-plane),ui,andassociatedPC's, y
i
,fortheM56 plasticdummy(lledwithbeeswax). As
fortheM56irondummy,itisonlytherstM =21eigenimagesandassociatedPC'sthatareshown. Againitshouldbe
noticedthatitisthepowerofthePC'sthatareshown. Thepoweriscalculatedusinganon-causalKaiserwindowofsize
3withthecharacteristicparametersetto2. Duetotheweakscatteringfromtheplasticdummytheeigenimagesshows
veryweaklandmine signatures. However,eigenimage5and6showslandminesignatures, andtheassociatedPC's also
peaksinadepthcorrespondingtotheburieddepth(1.8nanosec.). Eigenimage1,2,and3andassociatedPC's shows
stronggroundsurface signature. Theeigenimages shows the variations intheground surfaceandthe associatedPC's
peaks at the groundsurface (1.0 nansec.). The remaining eigenimages and PC's shows more mixedclutter-landmine
signals. However,theyhavemuchlesspower. Itisclearthattheseparationintimeispoor. TheeigenimagesandPC's
areusedasinputstothes-ICAandt-ICA.
Eigenimages,t-ICA IndependentComponents, t-ICA
EI 1 EI 2 EI 3
EI 4 EI 5 EI 6
EI 7 EI 8 EI 9
EI 10 EI 11 EI 12
1 2 3
50 00 50
S 1
1 2 3
50 100 150 200
S 2
1 2 3
20 40 60 80 100
S 3
1 2 3
20 40 60 80 00 20 40
S 4
1 2 3
20 40 60 80 100
S 5
1 2 3
20 40 60 80 100 120
S 6
1 2 3
20 40 60 80 00
S 7
1 2 3
20 40 60 80 100
S 8
1 2 3
20 40 60 80
S 9
1 2 3
20 40 60 80
S 10
1 2 3
20 40 60
S 11
1 2 3
20 40 60
S 12
IndependentComponents, s-ICA Time signals,s-ICA
EI 1 EI 2 EI 3
EI 4 EI 5 EI 6
EI 7 EI 8 EI 9
EI 10 EI 11 EI 12
1 2 3
1 2 3 4
x 10 −8
S 1
1 2 3
2 4 6 8 10
x 10 −9
S 2
1 2 3
1 2 3 4 5 6
x 10 −9
S 3
1 2 3
1 2 3 4
x 10 −9 S 4
1 2 3
5 10 15
x 10 −9 S 5
1 2 3
2 4 6 8 10 12 14
x 10 −10 S 6
1 2 3
2 4 6 8
x 10 −10 S 7
1 2 3
5 10 15
x 10 −10 S 8
1 2 3
1 2 3 4 5 6
x 10 −9 S 9
1 2 3
0.5 1 1.5 2 2.5
x 10 −9 S 10
1 2 3
0.5 1 1.5 2 2.5 3
x 10 −9 S 11
1 2 3
1 2 3 4
x 10 −9 S 12
Figure 3. Eigenimages (xy-plane) and associated timesignals for thet-ICA and the s-ICA havingthe rst M =15
PC's,y
i
,andeigenimages,ui,asinput,respectively. Onlythersteigenimagesandtimesignalsareshown. Fromthe
eigenimagesandtimesignalsitisclearthatthet-ICAprovidesagoodtimeseparation,andthes-ICAprovidesagood
spatialseparation.
Eigenimages,t-ICA IndependentComponents, t-ICA
EI 1 EI 2 EI 3
EI 4 EI 5 EI 6
EI 7 EI 8 EI 9
EI 10 EI 11 EI 12
1 2 3
50 00 50
S 1
1 2 3
50 100 150 200
S 2
1 2 3
20 40 60 80 100
S 3
1 2 3
20 40 60 80 00 20 40
S 4
1 2 3
20 40 60 80 100
S 5
1 2 3
20 40 60 80 100 120
S 6
1 2 3
20 40 60 80 00
S 7
1 2 3
20 40 60 80 100
S 8
1 2 3
20 40 60 80
S 9
1 2 3
50 00 50
S 10
1 2 3
10 20 30 40 50 60
S 11
1 2 3
20 40 60
S 12
IndependentComponents, s-ICA Time signals,s-ICA
EI 1 EI 2 EI 3
EI 4 EI 5 EI 6
EI 7 EI 8 EI 9
EI 10 EI 11 EI 12
1 2 3
1 2 3
x 10 −8 S 1
1 2 3
2 4 6 8
x 10 −9 S 2
1 2 3
2 4 6 8
x 10 −9 S 3
1 2 3
1 2 3 4
x 10 −9
S 4
1 2 3
2 4 6 8 10 12
x 10 −9
S 5
1 2 3
2 4 6 8
x 10 −10
S 6
1 2 3
2 4 6
x 10 −10 S 7
1 2 3
1 2 3 4
x 10 −10 S 8
1 2 3
0.5 1 1.5 2
x 10 −9 S 9
1 2 3
1 2 3 4
x 10 −10 S 10
1 2 3
2 4 6 8 10 12 14
x 10 −10 S 11
1 2 3
0.5 1 1.5 2
x 10 −9 S 12
Figure 4. Eigenimages (xy-plane) and associated timesignals for thet-ICA and the s-ICA havingthe rst M =15
PC's,y
i
,andeigenimages,ui,asinput,respectively. Onlythersteigenimagesandtimesignalsareshown. Fromthe
eigenimagesandtimesignalsitisclearthatthet-ICAprovidesagoodtimeseparation,andthes-ICAprovidesagood
spatialseparation.
SelectionofTemporal Features
IronDummy PlasticDummy
Raw Mean PCA, 15 PC’s t−ICA, 15 PC’s s−ICA, 15 EI’s
Raw Mean PCA, 10 PC’s t−ICA, 10 PC’s s−ICA, 10 EI’s
Raw Mean PCA, 5 PC’s t−ICA, 5 PC’s s−ICA, 5 EI’s
Raw Mean PCA, 15 PC’s t−ICA, 15 PC’s s−ICA, 15 EI’s
Raw Mean PCA, 10 PC’s t−ICA, 10 PC’s s−ICA, 10 EI’s
Raw Mean PCA, 5 PC’s t−ICA, 5 PC’s s−ICA, 5 EI’s
Selection ofSpatial Features
Raw Mean PCA, 15 PC’s t−ICA, 15 PC’s s−ICA, 15 EI’s
Raw Mean PCA, 10 PC’s t−ICA, 10 PC’s s−ICA, 10 EI’s
Raw Mean PCA, 5 PC’s t−ICA, 5 PC’s s−ICA, 5 EI’s
Raw Mean PCA, 15 PC’s t−ICA, 15 PC’s s−ICA, 15 EI’s
Raw Mean PCA, 10 PC’s t−ICA, 10 PC’s s−ICA, 10 EI’s
Raw Mean PCA, 5 PC’s t−ICA, 5 PC’s s−ICA, 5 EI’s
Selectionof Spatial and TemporalFeatures
Raw Mean PCA, 15 PC’s t−ICA, 15 PC’s s−ICA, 15 EI’s
Raw Mean PCA, 10 PC’s t−ICA, 10 PC’s s−ICA, 10 EI’s
Raw Mean PCA, 5 PC’s t−ICA, 5 PC’s s−ICA, 5 EI’s
Raw Mean PCA, 15 PC’s t−ICA, 15 PC’s s−ICA, 15 EI’s
Raw Mean PCA, 10 PC’s t−ICA, 10 PC’s s−ICA, 10 EI’s
Raw Mean PCA, 5 PC’s t−ICA, 5 PC’s s−ICA, 5 EI’s
Figure 5. Reconstructed powerimages. Ingeneral, it is clear that the component selection methodbased on com-
bined spatialand temporal features shows thebest performance. Thet-ICA and s-ICA are comparedwiththe PCA
method 11,12
. Thet-ICAand inparticular thes-ICAshowbothbetter performance thanthe PCAand themeansub-
tractionmethod.Itshouldbenoticedwhenusingthecomponentselectionmethodbasedontemporalfeaturesthet-ICA
showsbestperformance,andforthecomponentselectionmethodbasedonspatialfeaturesthes-ICAshowsbestperfor-
mance. Inoverall, thes-ICAcombinedwiththecomponentselectionmethodbasedoncombinedspatialand temporal
featuresshowthebestperformance. Thelandminedummyislocatedinthecenterofeachimage.
a) Mean b)t-ICA, 15 PC's,Temp.
20 40 60 80 100 120 20
40 60 80 2 3 4 5 6 7 8 9
x 10
−3x [cm]
y [cm]
20 40 60 80 100 120 20
40 60 80 1 2 3 4 5 6
x 10
−3x [cm]
y [cm]
c) s-ICA,15 EI's, Spa. d) s-ICA, 15 EI's, Spa./Temp.
20 40 60 80 100 120 20
40 60 80 1 2 3 4 5
x 10
−3x [cm]
y [cm]
20 40 60 80 100 120 20
40 60 80 0.5
1 1.5 2 2.5
x 10
−3x [cm]
y [cm]
Figure 6. a): mesh plot of mean-image. b): mesh plot of the t-ICA using 15PC's as input and temporal feature
component selection. c): meshplotof the s-ICA using15EI'sas input andspatial featurecomponent selection. d):
meshplotofthes-ICAusing15EI'sasinputandspatial/temporalfeaturecomponentselection.
Plastic Dummy (Bees Wax) Clutter Reduction Results
a) Mean b) t-ICA, 15 PC's,Temp
20 40 60 80 100 120 20
40 60 80 1 2 3 4 5 6 7 8
x 10
−3x [cm]
y [cm]
20 40 60 80 100 120 20
40 60 80 0.5
1 1.5 2 2.5 3 3.5 4 4.5
x 10
−3x [cm]
y [cm]
c) s-ICA, 15 EI's, Spa. d) s-ICA,5 EI's, Spa./Temp.
20 40 60 80 100 120 20
40 60 80 1 2 3 4 5 6 7 8
x 10
−3x [cm]
y [cm]
20 40 60 80 100 120 20
40 60 80 0.5
1 1.5 2 2.5 3 3.5 4 4.5
x 10
−3x [cm]
y [cm]
Figure 7. a): mesh plot of mean-image. b): mesh plot of the t-ICA using 15PC's as input and temporal feature
component selection. c): meshplotof the s-ICA using15EI'sas input andspatial featurecomponent selection. d):
meshplotofthes-ICAusing5EI'sasinputandspatial/temporalfeaturecomponentselection.
