for Resolution Enhancement and Clutter Reduction
BrianKarlsen a
,Kaj B. Jakobsen b
, JanLarsen c
,and Helge B.D.Srensen a
a
rstedDTU -Electronics and SignalProcessing,
The Technical University of Denmark,
Building451, DK-2800Kongens Lyngby, Denmark.
b
rstedDTU - Electromagnetic Systems,
The Technical University of Denmark,
rstedsPlads, Building348, DK-2800 Kongens Lyngby, Denmark.
c
Informatics and Mathematical Modelling - Sectionfor DigitalSignal Processing
Technical University of Denmark,
Richard Petersens Plads, Building321, DK-2800 Kongens Lyngby, Denmark.
ABSTRACT
Proper clutter reduction is essential for Ground Penetrating Radar data since low signal-to-clutter ratio prevent
correct detectionof mine objects. A signalprocessing approach forresolution enhancementand clutter reduction
used on Stepped-Frequency Ground PenetratingRadar (SF-GPR) data is presented, and the eects of combining
clutterreductionwithresolutionenhancementareexaminedusingsimulatedSF-GPRdataexamples. Theresolution
enhancementmethod isbasedonmethodsfrom opticalsignalprocessingandislargelycarriedoutin thefrequency
domaintoreducethecomputationalburden. Theclutterreductionmethodisbasedonbasisfunctiondecomposition
oftheSF-GPRtime-seriesfromwhichtheclutterandthesignalareseparated.
Keywords: Anti-personalminedetection,stepped-frequencyGPR,resolutionenhancement,opticalsignalprocess-
ing,clutterreduction,PCAsubspacedecomposition.
1. INTRODUCTION
Minesandotherexplosiveordnancesburiedbelowthegroundsurfaceareanincreasingthreattociviliansandmilitary
forcesinmanywar-tornanddevelopingcountries. Theoverallobjectiveoftheapproachespresentedinthispaperis
toidentifysmallmine-likemetallicandnon-metallicobjectsburiedinthegroundusingaStepped-FrequencyGround
PenetratingRadar(SF-GPR),whichisoneofthemostpromisingminedetectors.
Mines,especiallyanti-personalmines,areingeneralburiedclosetothesurfaceoftheground. Smallminesburied
closeto thegroundsurfacearediÆcultto detectusingaGPRdue to thefact thattheGPR signalsare hampered
byalowsignal-to-clutterratioandalowsignal-to-noiseratio 2
.
Toincreasethedetectionprobabilityofmines,thesignal-to-noiseratiomustbeimproved. Whenusingamonos-
taticSF-GPR,theenergyreectedfromtheobjectsburiedinthegroundarespatiallysmeared. Thesmearedenergy
canbefocususingvariousimagingtechniquesandtherebyincreasingthesignal-to-noiseratio. Severalimagingme-
thodshavebeendiscussedintheliterature. Themajorityofthemethodsarederivedfromtheinversetimemigration
method 3
andthe Stolt! k migration method 10
,which arewidely usedexamplesof time-domain andfrequency-
domainapproaches,respectively. Inthis paperwesuggestanapproachinspiredbyopticalsignalprocessing,which
mainlyiscarriedoutinthefrequencydomain.
Theclutter that eects a SF-GPR can be dened as those signals that are unrelated to the target scattering
characteristics but occupy thesame frequencyband as thetargets. Clutter canbecaused by multiple reections,
Author information on BK: brk@oersted.dtu.dk,www.oersted.dtu.dk; KBJ: kbj@oersted.dtu.dk, www.oersted.dtu.dk;
JL:jl@imm.dtu.dk,www.imm.dtu.dk/jl;HBDS:hbs@oersted.dtu.dk,www.oersted.dtu.dk
Theclutterhampertheimprovementsthatcanbeobtainedusingimagingprocessingandtherebypreventanincrease
in thesignal-to-noiseratio. Ingeneral,clutter is moresignicantat closerangesand reduces whenthe rangegets
larger,primarilybecauseofthelongerdistancesbetweenthereectionsurfacesandthelossesintheground 2
. Thisis
thereasonwhyclutterismostseverefornearthesurfaceplacedlandmines,whichcallsforclutterreduction. Several
clutterreductiontechniqueshavebeendeployedonGPRsignals 2
,butnonedoprovidesuÆcientsuppressiondueto
thestochasticnatureofthegroundsurface. Aclassicalmethodisthewellknownmean-subtractionmethod 2
,where
theaveragevalueoftheensembleofone-ortwo-dimensionalscanareaissubtractedfromeachoftheconsideredone-
dimensionalscans. Recently 7
wesuggestedasubspacedecomposingtechniquebasedonsubspacedecomposingusing
Principal Component Analysis (PCA) in which highly correlated spatial clutter is removed. PCA haspreviously
beenapplied toGPRdatabothforthedetectionofmines 13
andforclutterreduction 4
. Ourapproachtakenhereis
dierentandinspiredbyexplorativeanalysisoffunctional neuroimages 5
.
Thispapercomparessimplemean-subtractionversusPCAbasedclutterreductionincombinationwithresolution
enhancement. Theresults arebased onsimulated SF-GPRdata in the S-band(2.65GHz- 3.95GHz). Intypical
practicalsettingsthis bandwidthisrealisticandhasbeenusedin previouswork 7
.
In Section 2theclutter reductionapproach is discussed. Theresolution enhancementapproachis presented in
Section3. InSection4thedeployedSF-GPRsystemandsimulatedSF-GPRsignalsaredescribed. Finally,examples
andresultsof theclutter reductionandtheresolutionenhancementapproachesarepresentedinSection 5.
2. CLUTTER REDUCTION BASED ON SUBSPACE DECOMPOSING
Due to the stochastic nature of the SF-GPR signalsand the fact that the ground surfacein general is roughand
notperfectly at,near surfaceburied mines arediÆcult to detect. Toreduce these problems we suggestaclutter
reductionapproachbasedonsubspacedecomposingusingPCA 7
.
ToemploythePCAsubspacedecomposition ontheSF-GPR signalsavectorspacemustbedened. Thespace
observedisspanned bythemulti-channelSF-GPRtime-signalgivenbythesignalmatrixS2R MN
expressedby
S=fS
m;n g=fs
m
(n)g=[s(1);s(2);;s(N)]; (1)
whereM isthenumberofone-dimensionalscansconsideredandN isthenumberofsamplesineachoftheconsidered
one-dimensionalscaninthesignalmatrixS, ands
m
(n)is givenbythemeanvalue
s
m (n)=s
ij (n)=s
ij (n)
1
IJ I
X
i=1 J
X
j=1 s
ij
(n); m=i+(j 1)I; i2[1;I]; j2[1;J]; m2[i;JI]; (2)
where s
i;j
(n) denotes the SF-GPR time-signal y
one-dimensional scan received at the antenna located at
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
locationstepsizeinthex-andy-direction,respectively. Thatis,inthesignalmatrixS,i.e.,s
m
(n),n=1;2;;N
isthem'thsignal,or in practice,them'th one-dimensionalscanin thetime-domain subtractedbythemeanvalue
oftheensembleofconsidered one-dimensionalscans.
The PCAsubspacedecomposition of thetime-signalsin S is basedonalineartransformation, which produces
uncorrelatedsequenceshavingdecreasingvarianceofinformationfortime-seriesinS. Inpractice,itistheSVDthat
isusedto performthePCAsubspacedecomposition. ForagivenchoiceofP M,theSVDofS canbeexpressed
as 5
X =UDV T
= P
X
i=1 u
i D
i;i v
T
i
; P =min fM;Ng; (3)
where the M N matrixU =fU
m;i g=[u
1
;u
2
;;u
N
] and NN matrix V =fV
n;i g=[v
1
;v
2
; ;v
N
] repre-
sentstheorthogonalbasisvectors,i.e.,eigenvectorsofthesymmetricmatricesSS T
andS T
S,respectively. Disan
N N diagonalmatrixofsingularvaluesrankedindecreasingorder,as expressedbyD
i 1;i 1 D
i;i
;8i 2[2;N].
TheSVDidentiesaset ofuncorrelatedtimesequencesgivenbythePC's: y
i
=D
i;i v
i
,enumeratedbythecompo-
nentindexi =1;2;:::;N. Thatis,wecanwritetheobservedsignalmatrixasaweightedsumofxedeigenvectors,
y
TheFouriertransformgivenbysij(n)$ (!)
i
varianceundertheconstraintthatitisorthogonaltoalltheotherPC's,i.e.,y T
i y
k
=0;8k6=i.
It is possible to remove uninteresting subspaces in S, e.g., the air-to-groundreection, by projectiononto an
M-dimensionalsubspacespannedbyanumberofPC's,asshownby,
Y =
~
U T
S;
~
U =[u
i1
;u
i2
;;u
iM ]; i
j
2[1;N]; j=1;2;;M (4)
whereY isanM N matrix,i.e.,Y =[y
1
;y
2
;;y
M ]
T
. ByidentifyingtimepeaklocationsofthepowerofthePC
signals,y
i
that correspondtotheair-to-groundreectionandexcludesuchcomponents,theair-to-groundreection
issuppressed. Thescansarereconstructedas
^
S=
~
UY: (5)
Examplesandresultsofthisapproachareshownin Section5.
3. FOCUSING OF THE SF-GPR SIGNALS: A SF-SAR APPROACH
ImagingtechniquescanbedeployedontheSF-GPRsignalstofocusthereectedsignalsfromthetargetsandthereby
increasethesignal-to-noiseratio. Theapproachconsidered in this paperis inspiredbyoptical signalprocessingof
aninputinthefrontfocalplaneofaplano-convexlens 8
.
ConsideramonostaticSF-GPRthat collectsthedata inthe xy-planeat z=0. Thecollecteddata isdescribed
bythereectioncoeÆcient 6
(x;y;!)
z=0
. Sincethecollectedfrequencydatacanbeapproximatedbythediracted
eldfromanapertureilluminatedbyaplanewaveandthenusingHuygen'sPrinciple 8
,wecanexpressthecollected
eldby
(x;y;!)
z=0
= 1
j Z
1
1 Z
1
1 Z
1
1 g(x
t
;y
t
;z
t )
e jk r
jrj dx
t dy
t dz
t
; (6)
whereg(x
t
;y
t
;z
t
)isagivensourcedistributionintheground,kisthewavenumbervectorgivenbyk=k
x
^ x+k
y
^ y+k
z
^ z,
risthepositionvectorgivenbyr=(x x
t
)^x+(y y
t
)^y+(z z
t
)^z,andisthewavelength.
The objective of the focusing procedure is to reconstruct the source distribution given by g(x
t
;y
t
;z
t
), which
describesthereectingsurfacesof thetargets. Thefocusing canbeobtainedthroughtheopticalsignalprocessing,
byusingthesignalprocessingpropertiesoftheplano-convexlens 8
and Huygen'sPrinciple.
From the optical signal processing given by the signal processing describing the plano-convexlens we can, if
we assume homogeneous ground and at ground surface, reconstruct the reection surface from the 3-D Fourier
transformgivenby
g(x;y;z)
t=0
= Z
1
1 Z
1
1 Z
1
1 G(k
x
;k
y
;!)e j
p
(k 2
k 2
x k
2
y )z
e jk
x x
e jk
y y
e j!t
dk
x dk
y d!
t=0
(7)
where
G(k
x
;k
y
;!)= Z
1
1 Z
1
1
(x;y;!)
z=0 e
jk
x x
e jk
y y
dxdy (8)
Bysteppingwithsmallstepsin thez-directionanimagecanbeconstructedusing (7). FocusingtheSF-GPRdata
in thiswayprovidesthat thepropagationvelocitykanbechanged. Intheresults,shown inSection 5,theSF-GPR
dataisfocusedintwodimensionsonly,i.e.,k
y
=0. Thisapproachcanlargelybecarriedoutinthefrequencydomain
byusingFFT's.
The clutter reduction and resolution enhancement approaches presented in this paper are evaluated on simulated
data. ThedataincludesanM56dummynon-metallicminesandanM56shapedironminesburiedinsand. Thesim-
ulateddataareobtainedbysimulatingaeld-testsetupusingthenite-dierencetime-domain(FD-TD)numerical
method 12
.
The SF-GPR Data
Figure 1showsthecoordinatesin a(x,y,z) cartesiancoordinate systemused foreach simulationsetup. The used
minesareametallicM-56shapedAPlandmineandanon-metallicM-56dummyAPlandmine. All theobjectshave
thesameirregularshapewithadiameter of5.4cmandaheightof4.0cm.
Object M-56dummy iron
x-position(cm) 25 25
y-position(cm) 25 25
z-position,depth fromthesurface(cm) 5 5
Permeability,
r
1 2000
Permittivity,"
r
2.6 1
Conductivity, (S=m) 0.03 1:0310
7
Figure 1. Theminesconsideredin thisstudyisanon-metallicM56dummyminelled withbeeswaxand anM56
shaped minemade of iron. Theblackmarkin thecoordinatesystem indicates amine and the corner-coordinates
indicate the numberof measurementpoints in the x- and x-direction,respectively. Each measurement pointwere
located1cm1cmfromeachother. Thetabletotherightgivesthepositionanddielectricandmagneticproperties
oftheobjects.
Inoursimulations,theinterfacebetweenthegroundandtheairismodeledroughsurface. Thesurfaceroughness
is assumed to havea Gaussian spectrum 9
. Thespatial correlationfunction forthe roughsurface asa function of
positionx isexpressedas
p(x)=h 2
e x
2
=l
; (9)
whereh isthermssurfaceheightandl thecorrelationlength. Thesurfaceprolevariesrandomlybetweensurfaces
ofdierentrmsroughness. Inthesimulationsthefollowingrms-roughnessandcorrelationlengthvalueswere used:
h
1
=0:5cm,h
2
=1:0cm,h
3
=2:0cm,l
1
=0:5cm,l
2
=1:0cm,andl
3
=2:0cm.
SF-GPR Data Simulation
Byconvenienceweconneto atwo-dimensional SF-GPRdatasimulatation (x;z)usingthe FD-TDmethod 12
and
imposearotationalsymmetry,althoughafull3Dsimulationisfeasible. Themethodincorporatesalossyhalfspace,
aroughsurface,burieddielectricobjectsandgoodconductingobjects. Thesimulationsareusingtransverseelectric
magnetic(TEM)elds. Fora2-Dmedium, theTEMeld fromaline sourcecanbeexpressedas 11
E=yE^
0 e
j(!t+k r)
: (10)
Thewavepropagationthroughthemedium(air,ground,andtargets)canbeexpressed bythewaveequationgiven
by 1
@ 2
E
@x 2
+
@ 2
E
@z 2
="
@ 2
E
@t 2
+
@E
@t
; (11)
where=
0
r
istheabsolutpermeability,
0
=1:2610 6
H=mistheabsolutemagneticpermeabilityoffreespace,
r
istherelativemagneticpermeability,"="
0
"
r
istheabsoluteelectricpermittivity,"
0
=8:854210 12
F=m,and
"
r
istherelativepermittivity.
Using (10) and (11) and absorbing boundary conditions given by Engquist-Majda, 12
the FD-TD simulations
RESOLUTION ENHANCEMENT
Theimagingapproachforresolution enhancement, thePCAapproach, andtheclassicalmean-subtraction method
forclutterreductionweredeployedonthesimulateddataforevaluatingtheproperclutterreductioncombinedwith
resolutionenhancement. Theresultsofourapproachesarebestillustratedbythefollowingexamples,whicharethe
simulatedexamplesdescribedin Section4.
The results are shown in Figure 2 to 11. Figure 2 to 5 shows examples of the choice of PC's in the PCA
based reconstruction method, and Figure 6 to 11 showsresults of the clutter reduction combined with resolution
enhancement. Theresultsarevisualizedusingtwo-dimensionalscansacrossthemine.
The PCAbased Reconstruction
The PCA method were deployedon the signal matrixS asdescribed in Section 2. Each eigenimagesummarizes
thereection associatedwith thetime signature givenbythe correspondingPC time signal. Figures2to 5shows
examples of the power of the PC signals and associate eigenimages. The power is calculated using a non-causal
Kaiserwindowofsize3withacharacteristicparameterof2. IfthePCtimeisratherpeaked,thentheeigenimage
corresponds to thereection from thedepth related to that peaklocation. Furthermore,the varianceof thePC's
decreaseswith thePCnumber, indicatingthestrengthof thereectionsfrom variousdepth. Figure6to 11shows
comparison between the previous mentioned mean-subtraction method and the PCA based reconstruction of the
signal matrix. The third rowin the gures are the example resultsfrom the PCA based reconstruction method.
From the resultsit is clearthat the minesignalis morepronounced, and thesuppression of the groundreection
seemssatisfactory. However,when the groundsurface roughness getsto high it also seemsthat the PCA method
fails. Butforsmalluctuationsin thegroundsurfacethePCAworkssatisfactory.
The Mean-Subtraction Clutter Reduction
The PCA based reconstruction approach is compared to the classic mean-subtraction method. Results on mean-
subtractionisgiveninthesecondrowin theFigures6to11. Fromtheresultsitisclearthatthemean-subtraction
method fails. Evenat a small rms-roughness(0.5 cm)there still exist alot of surfacereection in thesignal. As
expected theM56 dummy mine(non-metallic) ismuch harderto detect thanthe ironM56 mine-liketarget, since
thereectionsareverysmall.
The Focusing of the SF-GPR signals
IntherightpanelofFigure6to11thefocusedSF-GPRdataoftheresultsaregivenintheleftpanelofFigure6to
11. Fromtheresultsit isclearthat thefocusedmine reection ismorepronouncedwhen properclutterreduction
hasbeendeployedontheSF-GPRdata.
EI 1
0.01 0.02 0.03
EI 2
0.02 0.04 0.06 0.08
EI 3
0.01 0.02 0.03 0.04 0.05
EI 4
0.02 0.04 0.06
EI 5
0.01 0.02 0.03 0.04
EI 6
0.02 0.04 0.06 0.08
EI 7
0.05 0.1 0.15
EI 8
0.02 0.04 0.06
EI 9
0.01 0.02 0.03 0.04
20 40 60 80
0 2 4 6
x 10 −5 PC 1
20 40 60 80
0 1 2
x 10 −5 PC 2
20 40 60 80
0 0.5 1
x 10 −5 PC 3
20 40 60 80
0 0.5 1
x 10 −6 PC 4
20 40 60 80
0 2 4 6 8
x 10 −7 PC 5
20 40 60 80
0 2 4 6 8
x 10 −8 PC 6
20 40 60 80
0 2 4 6
x 10 −8 PC 7
20 40 60 80
0 0.5 1 1.5
x 10 −8 PC 8
20 40 60 80
0 0.5 1
1.5 x 10 −9 PC 9
Figure 2. Iron M56 Mine-like Target, Example 1: The left panel shows the eigenimages (in xy-plane) and the
rightpanelshowstheassociatedprincipalcomponents(PC's),forthesimulatedexamplewithrms-roughnessof0.5
cm and correlationlengthof 50 cm. Fromthe PC's itis clearthat PC1showsapeakclose to theground surface
(the ground surfaceis located near sample 20 and the iron M56 mine-like target is located near sample 25), and
theassociateeigenimageprovides theuctuationsin thegroundsurface. PC2 peaks muchlater and theassociate
eigenimageclearlyhasastrongminesignature. SubsequentPC'sbecomeslessfocusedin timeandtheeigenimages
show aclutter liketexture. Alsonotice that thepower ofthe PC'sdecrease with thenumber, indicatingthat the
surfacereectionhasthestrongestpower,theminesignalhasasmallerpower,andclutterhaslowestpower. Much
ofthegroundreectioncanberemovedbyremovingPC1.
EI 1
0.01 0.02 0.03 0.04
EI 2
0.01 0.02 0.03 0.04
EI 3
0.02 0.04 0.06 0.08 0.1
EI 4
0.02 0.04 0.06 0.08 0.1 0.12
EI 5
0.02 0.04 0.06
EI 6
0.02 0.04 0.06
EI 7
0.01 0.02 0.03 0.04
EI 8
0.02 0.04 0.06
EI 9
0.02 0.04 0.06 0.08 0.1
20 40 60 80
0 0.5 1
x 10 −4 PC 1
20 40 60 80
0 2 4
x 10 −5 PC 2
20 40 60 80
0 0.5 1 1.5
x 10 −5 PC 3
20 40 60 80
0 2 4 6
x 10 −6 PC 4
20 40 60 80
0 1 2
3 x 10 −6 PC 5
20 40 60 80
0 0.5 1 1.5 2
x 10 −6 PC 6
20 40 60 80
0 1 2
x 10 −7 PC 7
20 40 60 80
0 0.5 1
x 10 −7 PC 8
20 40 60 80
0 2 4 6
x 10 −8 PC 9
Figure3. IronM56Mine-likeTarget,Example2: Theleftpanelshowstheeigenimages(inxy-plane)andtheright
panelshowstheassociatedprincipalcomponents(PC's),forthesimulatedexamplewithrms-roughnessof2cmand
correlationlength of10 cm. From thePC's itis clearthat PC1, PC2,and PC3showsapeak closeto theground
surface(the groundsurfaceislocatednearsample20andtheironM56mine-liketargetislocatednearsample25),
andtheassociateeigenimageprovidestheuctuationsinthegroundsurface. PC4peaksmuchlaterandtheassociate
eigenimageclearly has astrong minesignature. In this examplewe canremovemuch of the groundreection by
removingPC1,PC2andPC3.
EI 1
0.005 0.01 0.015 0.02 0.025
EI 2
0.01 0.02 0.03 0.04 0.05
EI 3
0.02 0.04 0.06
EI 4
0.02 0.04 0.06
EI 5
0.02 0.04 0.06
EI 6
0.01 0.02 0.03 0.04
EI 7
0.02 0.04 0.06 0.08 0.1 0.12
20 40 60 80
0 2 4 6
x 10 −5 PC 1
20 40 60 80
0 1 2 3
x 10 −6 PC 2
20 40 60 80
0 0.5 1 1.5
2 x 10 −7 PC 3
20 40 60 80
0 2 4
6 x 10 −8 PC 4
20 40 60 80
0 1 2
x 10 −8 PC 5
20 40 60 80
0 1 2 3
4 x 10 −9 PC 6
20 40 60 80
0 1 2 3
x 10 −9 PC 7
Figure 4. M56DummyMine,Example 1: Theleftpanel showstheeigenimages(inxy-plane)andtherightpanel
shows the associated principal components (PC's), for the simulated example with rms-roughness of 0.5 cm and
correlationlength of50cm. Similarto thetwopreviousexamplesbyremovingPC1and PC2much oftheground
reectioncanberemoved.
EI 1
0.01 0.02 0.03 0.04
EI 2
0.01 0.02 0.03 0.04
EI 3
0.02 0.04 0.06 0.08
EI 4
0.02 0.04 0.06
EI 5
0.02 0.04 0.06
EI 6
0.01 0.02 0.03 0.04
EI 7
0.01 0.02 0.03 0.04 0.05
EI 8
0.02 0.04 0.06 0.08
EI 9
0.01 0.02 0.03 0.04 0.05
20 40 60 80
0 0.5 1
x 10 −4 PC 1
20 40 60 80
0 2 4
x 10 −5 PC 2
20 40 60 80
0 1
2 x 10 −5 PC 3
20 40 60 80
0 1 2
x 10 −6 PC 4
20 40 60 80
0 0.5 1
x 10 −6 PC 5
20 40 60 80
0 0.5
1 x 10 −6 PC 6
20 40 60 80
0 1 2 3 4
x 10 −7 PC 7
20 40 60 80
0 0.5 1
x 10 −7 PC 8
20 40 60 80
0 1 2
3 x 10 −8 PC 9
Figure 5. M56 Dummy Mine, Example 2: The left panel shows the eigenimages (in xy-plane) and the right
panelshowstheassociatedprincipalcomponents(PC's),forthesimulatedexamplewithrms-roughnessof2cmand
correlationlengthof 10cm. Again,removingPC1,PC2andPC3will reducethegroundreection. Noticethatthe
morethesurfaceuctuatesthehigheristhenumberofPC'sthat mustberemoved.
time [nsec]
1 25 51
0 1 2
1 25 51
0 1 2
1 25 51
0 1 2
time [nsec]
1 25 51
0 1 2
1 25 51
0 1 2
1 25 51
0 1 2
x [cm]
time [nsec]
1 25 51
0 1 2
x [cm]
1 25 51
0 1 2
x [cm]
1 25 51
0 1 2
− z [cm]
1 25 51
0 20 40
1 25 51
0 20 40
1 25 51
0 20 40
− z [cm]
1 25 51
0 20 40
1 25 51
0 20 40
1 25 51
0 20 40
x [cm]
− z [cm]
1 25 51
0 20 40
x [cm]
1 25 51
0 20 40
x [cm]
1 25 51
0 20 40
Figure 6. Iron M56Mine-likeTarget: Theimages showstwo-dimensionalscans acrossthe mine foracorrelation
lengthof 50 cm. Left panel: Fromleft to right andtop to downwehave 1) rms =0.5 cm, rawSF-GPR data 2)
rms=1.0 cm,rawSF-GPRdata3) rms=2.0cm, rawSF-GPRdata4)rms =0.5cm,mean-subtracted 5)rms=
1.0cm, mean-subtracted6) rms=2.0cm,mean-subtracted7)rms =0.5cm, PCAreconstructed8) rms=1.0cm,
PCAreconstructed9)rms=2.0cm,PCAreconstructed. Rightpanel: Thefocusedtwo-dimensionalscansfromleft
panel.
time [nsec]
1 25 51
0 1 2
1 25 51
0 1 2
1 25 51
0 1 2
time [nsec]
1 25 51
0 1 2
1 25 51
0 1 2
1 25 51
0 1 2
x [cm]
time [nsec]
1 25 51
0 1 2
x [cm]
1 25 51
0 1 2
x [cm]
1 25 51
0 1 2
− z [cm]
1 25 51
0 20 40
1 25 51
0 20 40
1 25 51
0 20 40
− z [cm]
1 25 51
0 20 40
1 25 51
0 20 40
1 25 51
0 20 40
x [cm]
− z [cm]
1 25 51
0 20 40
x [cm]
1 25 51
0 20 40
x [cm]
1 25 51
0 20 40
Figure 7. Iron M56Mine-likeTarget: Theimages showstwo-dimensionalscans acrossthe mine foracorrelation
lengthof 30 cm. Left panel: Fromleft to right andtop to downwehave 1) rms =0.5 cm, rawSF-GPR data 2)
rms=1.0 cm,rawSF-GPRdata3) rms=2.0cm, rawSF-GPRdata4)rms =0.5cm,mean-subtracted 5)rms=
1.0cm, mean-subtracted6) rms=2.0cm,mean-subtracted7)rms =0.5cm, PCAreconstructed8) rms=1.0cm,
PCAreconstructed9)rms=2.0cm,PCAreconstructed. Rightpanel: Thefocusedtwo-dimensionalscansfromleft
panel.
time [nsec]
1 25 51
0 1 2
1 25 51
0 1 2
1 25 51
0 1 2
time [nsec]
1 25 51
0 1 2
1 25 51
0 1 2
1 25 51
0 1 2
x [cm]
time [nsec]
1 25 51
0 1 2
x [cm]
1 25 51
0 1 2
x [cm]
1 25 51
0 1 2
− z [cm]
1 25 51
0 20 40
1 25 51
0 20 40
1 25 51
0 20 40
− z [cm]
1 25 51
0 20 40
1 25 51
0 20 40
x [cm]
1 25 51
0 20 40
x [cm]
− z [cm]
1 25 51
0 20 40
x [cm]
1 25 51
0 20 40
x [cm]
1 25 51
0 20 40
Figure 8. Iron M56Mine-likeTarget: Theimages showstwo-dimensionalscans acrossthe mine foracorrelation
lengthof 10 cm. Left panel: Fromleft to right andtop to downwehave 1) rms =0.5 cm, rawSF-GPR data 2)
rms=1.0 cm,rawSF-GPRdata3) rms=2.0cm, rawSF-GPRdata4)rms =0.5cm,mean-subtracted 5)rms=
1.0cm, mean-subtracted6) rms=2.0cm,mean-subtracted7)rms =0.5cm, PCAreconstructed8) rms=1.0cm,
PCAreconstructed9)rms=2.0cm,PCAreconstructed. Rightpanel: Thefocusedtwo-dimensionalscansfromleft
panel.
time [nsec]
1 25 51
0 1 2
1 25 51
0 1 2
1 25 51
0 1 2
time [nsec]
1 25 51
0 1 2
1 25 51
0 1 2
1 25 51
0 1 2
x [cm]
time [nsec]
1 25 51
0 1 2
x [cm]
1 25 51
0 1 2
x [cm]
1 25 51
0 1 2
− z [cm]
1 25 51
0 20 40
1 25 51
0 20 40
1 25 51
0 20 40
− z [cm]
1 25 51
0 20 40
1 25 51
0 20 40
1 25 51
0 20 40
x [cm]
− z [cm]
1 25 51
0 20 40
x [cm]
1 25 51
0 20 40
x [cm]
1 25 51
0 20 40
Figure9. M56Dummymine: Theimagesshowstwo-dimensionalscans acrossthemineforacorrelationlengthof
50 cm. Left panel: From leftto rightand topto down wehave1) rms =0.5 cm, rawSF-GPRdata 2) rms =1.0
cm, rawSF-GPR data 3) rms =2.0 cm, rawSF-GPR data 4) rms =0.5 cm, mean-subtracted 5) rms = 1.0 cm,
mean-subtracted 6) rms =2.0 cm, mean-subtracted 7) rms = 0.5 cm, PCA reconstructed 8) rms = 1.0 cm, PCA
reconstructed9)rms=2.0cm,PCAreconstructed.Rightpanel: Thefocusedtwo-dimensionalscansfromleftpanel.
time [nsec]
1 25 51
0 1 2
1 25 51
0 1 2
1 25 51
0 1 2
time [nsec]
1 25 51
0 1 2
1 25 51
0 1 2
1 25 51
0 1 2
x [cm]
time [nsec]
1 25 51
0 1 2
x [cm]
1 25 51
0 1 2
x [cm]
1 25 51
0 1 2
− z [cm]
1 25 51
0 20 40
1 25 51
0 20 40
1 25 51
0 20 40
− z [cm]
1 25 51
0 20 40
1 25 51
0 20 40
1 25 51
0 20 40
x [cm]
− z [cm]
1 25 51
0 20 40
x [cm]
1 25 51
0 20 40
x [cm]
1 25 51
0 20 40
Figure 10. M56Dummymine: Theimagesshowstwo-dimensionalscans acrossthemine foracorrelationlength
of 30 cm. Left panel: From left to right andtop to downwehave1) rms =0.5 cm, raw SF-GPRdata 2) rms =
1.0cm,rawSF-GPRdata3)rms=2.0 cm,rawSF-GPRdata4)rms=0.5cm,mean-subtracted5)rms=1.0cm,
mean-subtracted 6) rms =2.0 cm, mean-subtracted 7) rms = 0.5 cm, PCA reconstructed 8) rms = 1.0 cm, PCA
reconstructed9)rms=2.0cm,PCAreconstructed.Rightpanel: Thefocusedtwo-dimensionalscansfromleftpanel.
time [nsec]
1 25 51
0 1 2
1 25 51
0 1 2
1 25 51
0 1 2
time [nsec]
1 25 51
0 1 2
1 25 51
0 1 2
1 25 51
0 1 2
x [cm]
time [nsec]
1 25 51
0 1 2
x [cm]
1 25 51
0 1 2
x [cm]
1 25 51
0 1 2
− z [cm]
1 25 51
0 20 40
1 25 51
0 20 40
1 25 51
0 20 40
− z [cm]
1 25 51
0 20 40
1 25 51
0 20 40
1 25 51
0 20 40
x [cm]
− z [cm]
1 25 51
0 20 40
x [cm]
1 25 51
0 20 40
x [cm]
1 25 51
0 20 40
Figure 11. M56Dummymine: Theimagesshowstwo-dimensionalscans acrossthemine foracorrelationlength
of 10 cm. Left panel: From left to right andtop to downwehave1) rms =0.5 cm, raw SF-GPRdata 2) rms =
1.0cm,rawSF-GPRdata3)rms=2.0 cm,rawSF-GPRdata4)rms=0.5cm,mean-subtracted5)rms=1.0cm,
mean-subtracted 6) rms =2.0 cm, mean-subtracted 7) rms = 0.5 cm, PCA reconstructed 8) rms = 1.0 cm, PCA
reconstructed9)rms=2.0cm,PCAreconstructed.Rightpanel: Thefocusedtwo-dimensionalscansfromleftpanel.
This paperpresentsacombinedclutter reductionandresolution enhancementapproachbasedon PCAand know-
ledgefromopticalsignalprocessing. Inordertoevaluatetheclutterreductioncombinedwithresolutionenhancement
in SF-GPR data, dataare simulated using the Finite-DierenceTime-Domain numerical method. Ingeneral, the
simulateddataaretwo-dimensional,butbyassumingthattheantennaisrotationalsymmetricthethree-dimensional
dataareconstructedbyrotatingthetwo-dimensionaldata. Fromtheresultsitisclearthatproperclutterreduction
before focusing is valuable. The resolution enhancementmethod givessatisfactory results. From the focused SF-
GPR data it is clear that the data are indeed focused. However, the method only concerns focusing using the
time-dependence e j!t
. The results may be improvedby also including the losses in the ground. The PCA based
reconstruction method gives satisfactory results only, when we use the knowledge about the depth in which the
mine is located which is not a priori knowledge in mine clearance. The air-to-ground reection and clutter are
mainlyrepresentedinfewprincipalcomponents. Omittingthesecomponentsinthesubsequentreconstructionofthe
signalsenablespromisingsuppressionoftheair-to-groundreectionandtheclutter. However,someofthevaluable
informationintheminesignalsmaybelost,whichisunsatisfactory. Futurestudieswill involveautomaticselection
of theprincipal componentsto beretrained, aswellas related techniques,e.g., independentcomponentsanalysis 5
(ICA). Ourbelief is that ICA would produce morepeaked components,providingfor abetterseparationbetween
the air-to-groundreections, thereections from the mines, andfrom theclutter. In additionweplan to use the
PCAbasedfeaturesastheinputto anonlinearstatistical superviseddetectionalgorithm.Onefeaturethatmaybe
usedadvantageouslyisthat thePCAidentiesreectionsurfaces thataresymmetric.
7. ACKNOWLEDGEMENTS
TheauthorswouldliketothankStaanAbrahamson,DanAxelson,AndersFriedmannandAndersGustafsonfrom
theDivision of SensorTechnology, National Defense ResearchEstablishment(FOA),Linkoping, Sweden, fortheir
supportduring datacollectionsatFOA.OleNymannisacknowledgedforstimulatingdiscussions.
REFERENCES
1. H.W.Chen&T.M.Huang: \Finite-dierencetime-domain simulationofGPRdata",JournalofAppliedGeo-
physics40,pp.139{163,1998.
2. D.J.Daniels: SurfaceGroundPenetratingRadar,London: IEE,1996.
3. E.Fisher&G.A.Mcmechan: \Examplesfroreverse-timemigrationofsingle-channelgroundpenetratingradar
proles",Geophysics,vol.57,no.4,pp.577{586,1992.
4. A. Gynatilaka & B.A. Beartlein: \A subspace decomposition technique to improve GPR imaging of anti-
personnel mines",Detection and Remediation Technologies for Mines and Minelike Targets V,Proceedings of
SPIE,vol.4039,pp.1008{1018,2000.
5. L.K. Hansen, J.Larsen &T. Kolenda: \OnIndependetComponenet Analysisfor Multimedia Signals",in L.
Guan,S.Y.Kung&J.Larsen(eds.)MultimediaImageandVideoProcessing,CRCPress,Ch.7,pp.175{199,
2000.
6. K.B.Jakobsen,H.B.D.Srensen&O.Nymann: \Stepped-FrequencyGround-Penetrating-RadarforDetection
ofSmallNon-metallicBuriedObjects",DetectionandRemediationTechnologiesforMinesandMinelikeTargets
II,vol.3079,pp.538{542,1997.
7. B. Karlsen, J. Larsen, K.B.Jakobsen, H.B.D. Srensen: \Antenna Characteristicsand Air-Ground Interface
Deembedding Methods for Stepped-Frequency Ground PenetratingRadar Measurements", Detection andRe-
mediationTechnologiesforMinesandMinelikeTargetsV, vol.4039,pp.1420{1430,2000.
8. K.Lizuka: EngineeringOptics,BerlinHeidelberg: Springer-Verlag,2ndedition,1987.
9. A.v.dMerwe,I.J.Gupta&L.Peters: \AClutterReductionTechniqueforGPRDatafromMineLikeTargets",
DetectionandRemediationTechnologiesforMinesandMinelikeTargetsIV,vol.3710,pp.1094{1101,1999.
10. R.H.Stolt: \MigrationbyFourierTransform",: Geophysics,vol.43,no.1,pp.23{48,1978.
11. D.M.Pozar: MicrowaveEnginering,2.nded.,Singapore: Mcgraw-HillInc.,1980.
12. A. Taove: Computational Electrodynamics: the nite-dierence time- domain method, Artech House Inc.,
1995.
13. S.H. Yu & T.R. Witten: \Automatic Mine Detection based on Ground Penetrating Radar", Detection and
RemediationTechnologiesforMinesandMinelikeTargetsIV,vol.3710,pp.961{972,1999.