Robust Classification of Blurred Imagery

RobustClassificationofBlurredImagery

DeepaKundur,Member,IEEE,DimitriosHatzinakos,SeniorMember,IEEE,andHenryLeung,Member,IEEE

Abstract—Inthispaper,wepresenttwonovelapproachesfortheclassificationofblurryimages.Itisassumedthattheblurislinearandspaceinvariant,butthattheexactblurringfunctionisunknown.Theproposedfusion-basedapproachesattempttoper-formthesimultaneoustasksofblindimagerestorationandclas-sification.Wecallsuchaproblemblindimagefusion.Thetech-niquesareimplementedusingthenonnegativityandsupportcon-straintsrecursiveinversefiltering(NAS-RIF)algorithmforblindimagerestorationandtheMarkovrandomfield(MRF)-basedfu-sionmethodforclassificationbySchistad-Solbergetal..Simula-tionresultsonsyntheticandrealphotographicdatademonstratethepotentialoftheapproaches.Thealgorithmsarecomparedwithoneanotherandtosituationsinwhichblindblurremovalisnotat-tempted.

IndexTerms—Blindimagerestoration,classification,multispec-tralimagefusion.

I.INTRODUCTION

HEinaccuracyofmanyimageclassificationstrategiesoftenresultsfromattemptingtofusedatathatexhibitsmotion-inducedblurringordefocusingeffects.Compensationforsuchblurringisinherentlysensor-dependentandisnon-trivialastheexactblurisoftentime-varyingandunknown[1].Insuchasituation,restorationisfrequentlyperformedonthedegradeddatapriortoclassification.Amajorobstacleariseswhentheexactblurringfunctionisunknown.Thismaybeover-comebyusingblindimagerestorationalgorithms.Blindimagerestorationreferstothedualprocessofbluridentificationandimagerestorationandisusedonlywhenpartialinformationabouttheimagedegradationprocessisavailable.Itissuitedforsituationsinwhichtheblurringandnoisecharacteristicsoftheimagingsystemmaybeunknownduetotheirtime-varyingnature.Arecentsurveyofsuchalgorithmscanbefoundin[2].Theweaknessofmostblindrestorationtechniquesstemsfromnumericalinstability;thereisofteninsufficientinforma-tiontoprovideanaccurateregularizedsolutiontotheproblemandnoiseamplificationmayresult[3].Inaddition,itmaybeimpracticalforahumanobservertosupervisetherestorationstopreventinstability.Thismayresultinanunreliableimageestimate,whichinturncaneffecttheaccuracyofsubsequenthigher-levelprocessingtaskssuchasclassification.

Inthispaper,weconsidertheclassificationofblurredandnoisyimagesusingdatafusionstrategies.Itisimportantthatwe

ManuscriptreceivedMay4,1998;revisedApril28,1999.Theassociateed-itorcoordinatingthereviewofthismanuscriptandapprovingitforpublicationwasProf.ScottT.Acton.

D.KundurandD.HatzinakosarewiththeDepartmentofElectricalandCom-puterEngineering,UniversityofToronto,Toronto,Ont.,Canada,M5S3G4(e-mail:dimitris@comm.toronto.edu).

H.LeungiswiththeDepartmentofElectricalandComputerEngineering,UniversityofCalgary,Calgary,Alta.,Canada,T2N1N4.PublisherItemIdentifierS1057-7149(00)01158-1.

T

distinguishbetweenouruseoftheterms“fusion”and“classi-fication.”Multisensordatafusionreferstotheacquisition,pro-cessing,andsynergisticcombinationofinformationfromvar-iousknowledgesourcestoprovideabetterunderstandingofthesituationunderconsideration[4].Classificationisaninforma-tionprocessingtaskinwhichspecificentitiesaremappedtogeneralcategories.Fortheclassificationofmultispectralim-ages,thespecificgoalistoassigneachvector-valuedpixelofthecombinedmultispectralimagetoitsappropriatecategoryusingtonaland/ortexturaldata;theresultisasinglecolor-codedimageshowingtheseveraltypesofclassesinthescene.Inthispaper,imageclassificationisthespecificgoalwewishtoachieveanddatafusionistheprocessbywhichweaccomplishthetask.

Theaccuracyofimageclassificationisoftenhighlyde-pendentonthequalityoftherestoredimages1.Wearguethatperformingblindimagerestorationpriortoandseparatelyfromclassificationresultsinsuboptimalsolutions.Weattempttocombinebothprocessesusingmultisensordatafusionstrategiestoproduceamoreregularizedsolution;wecallthisprocessblindimagefusionforclassification.Theproblemhasappli-cationstomanyareasofimageanalysis,suchasrobotvision,remotesensingforland-useclassificationandmedicalimaging,amongothers.Theimagerymaybemultisensor/multispectralinnatureorcanconsistofasinglesensorimageband.Themaincontributionsofthispaperareasfollows.

1)Theintegrationofblindimagerestorationwithtraditionaldatafusionconceptstoprovideamoreoptimalimageclassification.Twonovelapproachesbasedondifferentphilosophiesareproposedtoaddresstheproblemofblindimagefusion.

a)Inourfirsttechniquewetakeanewperspectiveontheimageestimatesateachiterationofarecursiverestorationalgorithm.Eachestimateistreatedasadifferentreadingofanimagesensorandtheesti-matesaresimultaneouslyfusedtoproduceamoreregularizedclassifiedimage.

b)Inthesecondapproachwedefineanerrormetricwhichusestheresultsfromintermediate-levelimagefusionandclassificationtoproduceanappropriate2terminationpointfortherestorationalgorithm.

2)Theimplementationofthetwoarchitecturestoassessthepracticalfeasibilityofblindimagefusion.Theauthorsareunawareofotheradvancedresearchintocombining

isespeciallytrueiftheclassificationtechniqueistrainedonoruses

modelsfofnonblurredimagery.

2Bythetermappropriatewemeanthattheimageestimateatterminationresultsinanaccurateclassification.Thisterminationpointisnotalwaysthebestimageestimatevisuallyorinthemeansquaresense.

1This

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Fig.1.Theblindimagerestorationandclassificationproblem.Thesensorimagesareassumedtobedegradedaccordingtothelineardegradationmodel.Theseimagesareusedtoproduceaclassificationofthesceneusingpartialinformationabouttheundistortedimagedscene,andtheblurringprocess.

restorationandfusionandassessthepotentialofthetech-nology.

3)Acomparativestudyoftheeffectsofblurremovalforimageclassification.Inthenextsectionwedefinethespecificproblemtoaddressanddiscussourassumptions.InSectionIIIweproposethetwonovelapproachesforblindimagefusion.ImplementationissuesarediscussedinSectionIV.SimulationresultsandcomparisonswithexistingtechniquesaregiveninSectionV,andfinalre-marksareconveyedinSectionVI.

AssumptionSet1(GeneralAssumptionsfortheBlindImageFusionProblem)

1)Multisensorimagesofthesamesceneareregistered.Iftheimagesare,forexample,thedifferentcolorbandsofacolorimage,thenitissafetoassumethattheimagesareregistered.Otherwise,aregistrationalgorithmmustbeappliedtotheimagespriortoprocessing.

2)Theblurringprocessobeysthelineardegradationmodelof(1).Thismodelissuccessfullyusedinimagingapplicationsinwhichtheblurringprocessisisoplantic(i.e.,theblurringoperationislinearandshiftinvariant).Themodelmakesthesolutiontotheimagerestorationproblemtractable[10].

3)Partialinformationabouttheimagedsceneisavailabletoperformblindimagerestoration.Thisinformationisspe-cifictothealgorithmemployed.SectionIV-A1providesthespecificassumptionsfortheNAS-RIFalgorithm.4)Statisticalinformationabouttheundistortedimagesofthesceneisavailableforclassification.Thisinformationisalsospecifictotheparticularclassificationapproachimplemented.SectionIV-A2providesthespecificsfortheMRFclassificationalgorithm.

Fig.2.NAS-RIFalgorithmforblindimagedeconvolution.

paperandthataddressedinotherliteratureonimageclassifica-tion[5]–[9]isthatweexplicitlyaccountfortheblurringdegra-dationintheimagewhileotherapproachesdonot.Wefocusonthedesignoftechniquesforthesimultaneousrestorationandclassificationofblurredimageryusingfusion-basedstrategies.Weconsiderthescenarioinwhichwehave

where

thsensor,

rep-resentsthetwo-dimensional(2-D)linearconvolutionoperator.3Ifweneglectthenoisetermin(1),theprocessofrecovering

II.PROBLEMFORMULATION

Weaddresstheissueoftherobustclassificationofblurredim-agery.Thedifferencebetweentheproblemweconsiderinthis

KUNDURetal.:ROBUSTCLASSIFICATIONOFBLURREDIMAGERY245

TABLEI

STATISTICALMRFFUSIONMETHODUSINGTHEICMALGORITHM

Welistthegeneralassumptionsmadeinourproblemformu-lationbelow.Morespecificassumptionsaremadeduringimple-mentationasspecificalgorithmsareemployedforblindimagefusion.TheseassumptionsarediscussedinSectionsIV-A1andIV-A2.

A.BlurringasSignal-DependentNoise

Inthissection,wedemonstratehowarestoredimageesti-mateisconsideredtosufferfrombothsignal-dependentand-independentadditivenoiseprocesses.Weassumethatimagerestorationisperformedbytheprocessofinversefiltering(i.e.,

.4As-thefilteringof

sumingthelineardegradationmodelof(1),therestoredimage

III.BLINDIMAGEFUSION

Thetwomajorconsiderationsinthedesignofourblindimagefusionscenarioswastheportabilityofthetechniquestodif-ferentapplicationsandtheeaseofimplementation.Asare-sult,wehavedesignedourmethodssuchthattheycanincorpo-rateexistingiterativeblindimagerestorationandclassificationalgorithms.Thisallowstheflexibilitytoselectthealgorithmsmostappropriateforagivenapplication.Inaddition,theuseofwell-knownandwell-documentedmethodsmakesimplementa-tionandtestingeasier,andallowsausertopredictandassessthebehavioroftheoverallblindfusionschemetoagreaterde-gree.

Theselectionofthedatafusionapproachisbasedonexistingresearchdemonstratingthesuccessoffusionineffectivelycom-biningcomplementaryandredundantinformation(see[1],[4]andreferencestherein).Inaddition,theauthors’previousre-searchintodatafusionsuggestsitspromisefortheprocessingofdataexhibitingsignal-dependentnoise[11].Inthenextsec-tionweshowhowarestoredimagecanbeconsideredtosufferfromsignal-dependentnoise.InSectionIII-Bwediscussthegeneralscenarios.

As

wecansee,therestoredimageestimatesuffersfromtwoer-rors:

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randomprocess.The

Ideally,iftheblurredimagedoesnotcontainadditivenoise(i.e.,

forallwhere

Thedifferencebetweenand

if

andsgn

and

KUNDURetal.:ROBUSTCLASSIFICATIONOFBLURREDIMAGERYFig.3.BlindImageFusionMethod1:Thesimultaneousmergingofdistinctrestorations.

TABLEII

PERCENTAGECLASSIFICATIONACCURACIESFORTHESYNTHETICDATA.IMAGE2ISANADDITIONALREGISTEREDIMAGEOFTHESAMEISLAND-LIKESCENE

WHICHISDEGRADEDSOLELYBYADDITIVEWHITEGAUSSIANNOISEWITHASNROF20dB.THEboldfacerowsREPRESENTTHERESULTSOF

THEPROPOSEDAPPROACH

thesteepest-descentminimizationroutine,theupdatelawfor

istheupdatestep-size,

istheunitstepfunction,

attheAlternatively,theconju-gategradientroutinemayalsobeimplementedtominimize

247

denotesdatafromaparticularsensor,

arethe

sensorimages(inlexicographicalorder),

istheclassificationofthescene

andisthesamedimensionsasthesensorimagery.Eachelementof

arecalledthesensor-specific

6This

informationcanbeobtainedinastronomyandsatelliteremotesensing

applications.

248IEEETRANSACTIONSONIMAGEPROCESSING,VOL.09,NO.2,FEBRUARY2000

Fig.4.BlindImageFusionMethod2:Theuseofafusion-basedstoppingcriterionforblindimagerestoration.

whereand

and

isauser-specifiednonnegativescalarparameter,isgivenby

(11)

TheoverallalgorithmweimplementedisshowninTableI.Thevalueof

9

Fig.5.SyntheticImageDatatoTestApproach1.Thegrey-levelsrepresenttheactualsimulatedradianceofthescene.(a)Original,(b)degradedimagewithBSNRof40dB,(c)restorationatsixthiteration,and(d)restorationatseventhiteration.

andin-

termediate-levelfusionfor

Thetermimpliesthattheclassificationofa

pixelatlocation

imagestatisticfunctionandthespatialcontextenergyfunction,respectively.

Inthesimulationsperformedweassumedthattheimagenoisestatisticscanbemodeledbyanormaldistributionandthatthenoiseprocessesareindependentfromoneanother.7

Asaresult,isgivenby

(9)

wassuccessfullydonebySchistad-Solbergetal.fornon-Gaussiannoisein[5].

7This

bandsfortheimagesensor,eachpixelcanbeconsid-eredtohaveanassociatedvectorwhoseelementsconsistoftheradiancevaluesfromeachofthebands.9If󰀌=0;thenU=U:Therefore,itcanbeseenfrom(9)thatthe

withrespecttoC(i;j)onlydependsonthecorrespondingminimumofU

pixelvalueofeachofthesensorimagesand,hence,theclassificationprocedureinvolvespixel-levelfusion.

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Fig.6.ClassificationresultsforApproach1onsyntheticdata.Thefourdifferentgrey-levelsrepresenteachofthedifferentclassesintheimage.Thewhite,black,lightgreyanddarkgreycolorsdenoteclasses1,2,3,and4,respectively.

Fig.7.Photographiccolorimagedata.Theimagesrepresenttheredbandofacolorphotographofchalk.(a)Original,(b)degradedimagewithBSNRof40dB,(c)restorationatfirstiteration,and(d)restorationateleventhiteration.

Thespecificassumptionsmadebythealgorithmareprovidedbelow.

AssumptionSet3(AssumptionsSpecifictotheMRFClassificationMethod)

1)Themeanand(co-)variancesoftheradianceofthedif-ferentclassesinthesceneareknownorestimatedfromsimilar(nonblurred)data.Thetonalandtexturalinforma-tionabouteachclassisusedbytheMRFmethodtoseg-menttheimageintodifferentregions.Thisinformationcanbegatheredfromtheuseofimagedatacontainingsimilartypesofregions[5].

2)Themultispectralimagesareofthesamedimensions.In-terpolationmethodsmaybeusedtoresizetheimagestoonesize.Theclassifiedimageresultisthedimensionsastheinterpolatedimages.

3)Theindividualsensorreliabilityfactorsforeachimageareknownpriortoblindimagefusion.Thismaybepro-videdbythesensormanufacturerorcanbeapproximatedbytheindividualsensorimageclassificationaccuracy[5].B.TheTwoApproaches

1)Approach1:SimultaneousFusionofDistinctRestora-tions:Weconsiderforsimplicitytheclassificationofasinglenoisyblurredimage,althoughthemethodcaneasilybeextendedtothesituationsinwhichothersensorimagesareavailable.Thetechniqueiscomprisedoftwostages.ThefirststageofthetechniqueinvolvestheblindrestorationoftheimageusingtheNAS-RIFalgorithm.Wehypothesizethatifwetreateachrestorationataselectedsetofiterationsastheoutputofadifferentimagesensorbandandfusetheresultsfor

Fig.8.ClassificationresultsforApproach1onphotographicdata.Thefivedifferentgrey-levelsrepresenteachofthedifferentclassesintheimage.Thewhite,lightgrey,mediumgrey,darkgreyandblackcolorsdenoteclasses1,2,3,4,and5,respectively.

classification,thentherewillbeanoverallregularizingeffectontheoutput.

ThesecondstagefusesthevariousimageestimatesintoaclassifiedimageusingtheMRFclassificationmethod.Thefu-sionprocesstakesintoaccountthecorrelationinnoiseamongthevariousimageestimates.Fig.3givesanoverviewofthepro-posedarchitecture.Wefuseseveralimageestimates,whichex-hibitvariousdegreesofblurremovalandnoiseamplification,

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TABLEIII

PERCENTAGECLASSIFICATIONACCURACIESFORTHEPHOTOGRAPHICDATA.THEboldfacerowREPRESENTTHERESULTSOFTHEPROPOSEDAPPROACH

toproduceamorereliableclassifiedoutput.Assumingthatweusetherestorationsat

restorationssuchthatwhere

representstheEuclideannorm,wecan

neglect

for

areallfilteredversionsof

,10theassociatedco-variancematrixisgivenby

is

theexpectationoperator,and

whoseelementsaregivenby

arecalculatedusing(14).

theclassificationarefedbacktothefirststagetoenhancetherestoration.Wemakeuseofthesmoothnessproperties12oftheclassifiedimagetoprovideanestimateofthesuc-cessoftheblindimagerestorationstage.Oftenthevisualqualityoftherestoredimageisnotagoodindicatorofthereliabilityofhigher-levelprocessingtaskssuchasclassifi-cation.Therefore,toimprovethereliabilityofthefusionprocess,itisimportanttomakeuseofinformationfromthehigher-levelprocessingstagetoenhancetherestorationstage.Fig.4givesasummaryoftheproposedapproach.Forsimplicityweconsiderthefusionofablurredimage

isthecurrentiteration)is

passedthroughtheMRFclassificationmethod.Classificationof

values:

and

and

andisusedtodeterminethepossibilityof

noiseamplificationeffectingthefusionresults.Thismeasureisgivenby

Err

rrrrrrrrrrrrrrrrrerrrrrrrrerrererrKUNDURetal.:ROBUSTCLASSIFICATIONOFBLURREDIMAGERYFig.9.Syntheticimagedatatotestapproach2.Syntheticimagedatatotestapproach2.(a)Blurredimage,(b)noisyimagedegradedbymultiplicativechi-squarednoise,(c)trueclassificationofthescene.Theblack,darkgrey,lightgreyandwhiteshadesdenoteclasses1,2,3,and4,respectively.

Fig.10.ClassificationresultsforApproach2onsyntheticdata.(a)

ClassificationaccuracyversusiterationoftheNAS-RIFalgorithm.(b)Thestoppingcriterionerrorasafunctionofiteration.(c)Restoredimage1atthesixthiterationoftheNAS-RIFalgorithm.(d)Classificationresultforthesixthiteration(correspondstotheresultwiththehighestclassificationaccuracy).

discussedattheendofSectionIV-B1intheformulationof(13)and(14),wecanshowthatthevarianceoftheassociatedaddi-tivenoiseoftherestoredimagecanbeapproximatedas

251

NumberofcorrectlyclassifiedimagepixelsTotalnumberofpixelsintheclassifiedimage

(17)

ormoreformally

isthenumberofpixels

inisthetrueclassification,andif

and

otherwise.Thetrueclassification

Gaussian

PSF14.WhiteGaussiannoiseisaddedtotheresultingimagetoproduceablurredsignal-to-noiseratio(BSNR)of40dB.TheoveralldegradedimageisshowninFig.5(b).TheNAS-RIFal-gorithmisappliedtotheblurredandnoisyimageusinganFIR

filtersizeof

15andassuminganaccuratesupportsizeof252IEEETRANSACTIONSONIMAGEPROCESSING,VOL.09,NO.2,FEBRUARY2000

forallclassesandthecovariancematrixwasestimatedusing(13).Thevalueof

(aswas

usedin[5]).ThetworestorationsshowwidelyvaryingCA’s.ClassificationofrestorationIisshowntosignificantlyimproveCAoverthatofclassifyingtheblurredimage;classificationofrestorationII,however,reducestheCAoverthatoftheblurredimage.WhenwefusethetwoimagesusingourfirstapproachweseethattheclassificationaccuracyisfurtherimprovedoverthatofclassifyingrestorationIsolely.Theresultsdemonstratehowtheproposedapproachcanimprovetheclassificationofdegradedimages.TableIIalsoprovidesresultsfortheclassifi-cationofthedegradedimagewithasecondnoisy(butunblurredimage)withanSNRof20dB.16WeseethatourfusionapproachstillimprovesCA,buttheimprovementislessexaggeratedduetothepresenceofthesecondnoisyimage.

Weperformthesamesimulationsonphotographiccolordataofchalk,showninFig.7.Fivedistinctclassesaretobeiden-tified:fourcorrespondtoeachofthecoloredchalkandafifthtothebackground.TheundistortedredbandoftheimageinFig.7(a)isblurredtoproducetheeffectofanout-of-focuscamera.WhiteGaussiannoisewasaddedtotheresulttopro-duceaBSNRof40dB.Therestorationsafterthe1stand11thiterationoftheNAS-RIFalgorithmaredenoted“restorationI”[showninFig.7(c)]and“restorationII”[showninFig.7(d)],respectively.TheNAS-RIFalgorithmwasrunusingaFIRfilter

estimatedfromsizeof

anunblurredgreenbandoftheimage.TheMRFclassificationmethodwasappliedtotheblurredimage,andtheindividualandcombinedrestoredimages.Themeanandvariances(duetotexture)ofeachoftheclasseswereestimatedfromasimilar,butunblurredversionofthescene,and

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TABLEIV

SUMMARYOFCHARACTERISTICSOFTHEPROPOSEDBLINDFUSIONMETHODSFORIMAGECLASSIFICATION

scene(denotedImage2)istobefusedwiththefirsttoproduceanoverallclassificationofthescene.Thesecondimageisun-selecblurred,butsuffersfrommultiplicativechi-squarednoisewitheightdegreesoffreedom.ThetrueclassificationofthesceneisshowninFig.9(c).Thefourdifferentgreylevelsdenotethefourclassesinthescene.

Oursecondapproachwasappliedtoclassifytheimages.AnFIRfiltersizeof

accuratelyestimatedfromImage2wereusedfortheNAS-RIF

algorithmstage.Parametersettingsof

andThresholdestedromhelrredreende2IEEETRANSACTIONSONIMAGEPROCESSING,VOL.09,NO.2,FEBRUARY2000

C.Discussion

AlthoughourfirstapproachoftenimprovesCA,experiencewithsimulationresultsrevealsthatthemethodisnotalwayspre-dictableorsuccessful.Forexample,fusingarestorationwhichproducesahighCAwithonewhichproducesapoorCAcanresultinaslightreductionintheoverallfusedCA.Selectionoftheappropriaterestorationstofuseisanadhocprocedure.Asaruleofthumb,theauthorsobservedthatfusingcomplementaryrestorations(e.g.fusinganimagewhichhasmildnoiseamplifi-cationwithonewhichexhibitsresidualblurring)improvesCAovernonfusedclassification.Inaddition,wefoundthatfusingapoorrestoration(possiblyexhibitingsevereblurringand/ornoiseamplification)witha“good”restorationreducestheCAoverthatofanonfusedclassificationofthe“goodrestoration.”Theauthorsalsoobservedthatifcomplementarynonblurred,butpossiblynoisyinformationofthescenewasavailable,thenthedegreeofimprovementofourfirstapproachwasdiminished.Thecomplementaryinformation,whichcouldbeintheformofanotherimageofthescene,raisedtheoverallCA.However,theimprovementinCAbyfusingtwoormorerestorations(insteadofjustone)withtheadditionalimagerywasreduced;forex-ample,insteadofa1%improvementinCA,a0.1%improve-mentwasfound.

OursecondapproachallowsalgorithmterminationatapointoftheNAS-RIFalgorithmwhichproducesagoodclassificationaccuracy,however,thisisnotalwaysthemostoptimalresult.Inoursimulations,wefoundthatinclusionofcomplementarynonblurredimageryimprovedtheperformanceofthealgorithm(i.e.,amoreoptimalclassificationwasobtained).

Theterminationcriteriaisuser-definedanddependsonthekindsofimagesfusedforclassification.WefoundthroughsimulationsthatthresholdvaluesofErr

KUNDURetal.:ROBUSTCLASSIFICATIONOFBLURREDIMAGERYDimitriosHatzinakos(S’87–M’90–SM’98)receivedtheDiplomadegreefromtheUniversityofThessaloniki,Greece,in1983,theM.A.ScdegreefromtheUniversityofOttawa,Ottawa,Ont.,Canada,in1986andthePh.D.degreefromNortheasternUniversity,Boston,MA,in1990,allinelectricalengineering.

In1990,hejoinedtheDepartmentofElectricalandComputerEngineering,UniversityofToronto,Toronto,Ont.,Canada,whereheisnowatenuredAssociateProfessor.Hisresearchinterestsareinthe

areaofdigitalsignalprocessingwithapplicationstowirelesscommunications,imageprocessing,andmultimedia.Hehasorganizedandtaughtmanyshortcoursesonmodernsignalprocessingframeworksandapplicationsdevotedtocontinuingengineeringeducationandgivennumerousseminarsintheareaofblindsignaldeconvolution.Heisauthor/coauthorofmorethan90papersintechnicaljournalsandconferenceproceedingsandhehascontributedtofourbooksinhisareasofinterest.HisexperienceincludesconsultingtoElectricalEngineeringConsociatesLtd.andcontractswithUnitedSignalsandSystems,Inc.,BurnsandFryLtd.,PipetronixLtd.,DefenseResearchEstablishmentOttawa,andVaytek,Inc.

Dr.HatzinakoshasbeenanAssociateEditorfortheIEEETRANSACTIONSONSIGNALPROCESSINGsince1998andtheGuestEditorforthespecialissueofSignalProcessingonsignalprocessingtechnologiesforshortburstwirelesscommunications.HewasamemberoftheIEEEStatisticalSignalandArrayProcessingTechnicalCommitteefrom1992until1995andTechnicalProgramCo-Chairofthe5thWorkshoponHigher-OrderStatisticsinJuly1997.HeisamemberofEURASIP,theProfessionalEngineersofOntario)andtheTechnicalChamberofGreece.

255

HenryLeung(S’88–M’90)receivedtheB.Math.degreeinappliedmathematicsfromtheUniversityofWaterloo,Waterloo,Ont.,Canada,in1984,theM.Sc.degreeinmathematicsfromtheUniversityofToronto,Toronto,Ont.,Canada,in1985,andtheM.Eng.andPh.D.degreesinengineeringphysicsandelectricalengineeringfromMcMasterUniver-sity,Hamilton,Ont.,in1986and1991,respectively.From1990to1991,hewasaResearchEngineerwiththeCommunicationsResearchLaboratory,Mc-MasterUniversity.In1991,hejoinedtheDefense

ResearchEstablishmentOttawa,wherehewasinvolvedinthedesignofau-tomatedsystemsforairandmaritimemultisensorsurveillance.Since1998,hehasbeenwiththeDepartmentofElectricalandComputerEngineering,Univer-sityofCalgary,Calgary,Alta.,Canada,whereheisnowanAssociateProfessor.HeisalsoanAdjunctProfessorwiththeDepartmentofElectricalEngineering,McMasterUniversity.Hisresearchinterestsincludechaos,computationalin-telligence,datafusion,nonlinearsignalandimageprocessing,multimedia,andwirelesscommunications.