• Ingen resultater fundet

(1)for Resolution Enhancement and Clutter Reduction BrianKarlsen a ,Kaj B

N/A
N/A
Info
Hent
Protected

Academic year: 2023

Del "(1)for Resolution Enhancement and Clutter Reduction BrianKarlsen a ,Kaj B"

Copied!
11
0
0

Indlæser.... (se fuldtekst nu)

Hele teksten

(1)

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

(2)

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)$ (!)

(3)

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.

(4)

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

(5)

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.

(6)

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.

(7)

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.

(8)

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.

(9)

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.

(10)

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.

(11)

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.

Referencer

RELATEREDE DOKUMENTER

Figure 6.5 shows runtime results for test case 1 and 4, i.e., using the AS method to solve the dense Fourier, and sparse Laplace problem.. The results clearly show, that qpsub can

In this paper, we present a constraint-oriented state-based proof method- ology for concurrent software systems which exploits compositionality and abstraction for the reduction of

6 Towards this end, the State shall pursue a poverty reduction program that promotes an 7 environment conducive to the development and growth of a vibrant social

Objective: The aim of this study was to investigate a potential correlation between slip reduction and clinical improvement in patients with isthmic spondylolisthesis treated with

Figure  56  shows  that  alternatives  A  and  B  lead  to  95 th   percentile  harmonic  gain  factors  of  1.25  and 

Using examples from field research in Acholiland and an analysis of human rights relating to dispute resolution, this paper shows the linkages between (1) the chaotic factors

To overcome the common dilemma in remote sensing data between temporal coverage and spatial resolution, we combine optical USGS Landsat 8 OLI and very high-resolution

To deal with that, reconstruction-based super-resolution (SR) algorithms might be used. But, the problem with these algorithms is that they mostly require motion estimation between