TwoPhase Kernel Estimation for Robust Motion Deblurring Li Xu and Jiaya Jia Department - PDF document

Two-PhaseKernelEstimationforRobustMotionDeblurringLiXuandJiayaJiaDepartmentofComputerScienceandEngineeringTheChineseUniversityofHongKong@cse.cuhk.edu.hkAbstract.Wediscussafewnewmotiondeblurringproblemsthatare 158L.XuandJ.Jiaincreasetheestimationambiguity.Wewillanalyzethisproblemandproposeanautomaticgradientselectionalgorithmtoexcludethedetrimentalstructures.Ourmethodalsomakesseveralothercontributions.1)First,weproposeanoveltwo-phasekernelestimationalgorithmtoseparatecomputationallyexpen-sivenon-convexoptimizationfromquickkernelinitialization,givingrisetoanecientandrobustkernelestimationprocess.2)Weintroduceanewspatialpriortopreservesharpedgesinquicklatentimagerestoration.3)Inthekernelre“nementstage,weemploytheIterativeSupportDetection(ISD)algorithm,whichisapowerfulnumericalschemethroughiterativesupportdetection,toadaptivelyenforcethesparsityconstraintandproperlypreservelarge-valueel-ements.Soft-threshold-likeeectisachievedinthisstep.4)Finally,torestorethelatentimage,weemployaTV-objectivefunctionthatisrobusttonoiseanddevelopanecientsolverbasedonhalf-quadraticsplitting.Weappliedourmethodtochallengingexamples,wheremanyimagesareblurredwithverylargePSFs(spanningupto100pixelsinwidthorheight)duetocamerashake.OurrobustdeblurringŽprojectwebsiteisputonlinewhichincludesthemotiondeblurringexecutableandimagedata.1.1RelatedWorkShift-invariantmotionblurcanbemodeledasimageconvolutionwithaPSF.Webrie”yreviewtheblindandnon-blinddeconvolutionmethods.BlindDeconvolution.Earlyworkonblindimagedeconvolutionfocusesones-timatingsmall-sizeblurkernels.Forexample,YouandKaveh[8]proposedavariationalframeworktoestimatesmallGaussiankernels.ChanandWong[9]appliedtheTotalVariationregularizerstobothkernelsandimages.Anothergroupofmethods[10…12]didnotcomputetheblurkernels,butstudiedthereversionofadiusionprocess.Lately,impressiveprogresshasbeenmadeinestimatingacomplexmotionblurPSFfromasingleimage[1,3,6].Thesuccessarisesinpartfromtheemploymentofsparsepriorsandthemulti-scaleframework.Fergusetal.[1]usedazero-meanMixtureofGaussianto“ttheheavy-tailednaturalimageprior.AvariationalBayesianframeworkwasemployed.Shanetal.[3]alsoexploitedthesparsepriorsforboththelatentimageandblurkernel.Deblurringisachievedthroughanalternating-minimizationscheme.Caietal.[6]introducedaframeletandcurveletsystemtoobtainthesparserepresentationforkernelsandimages.etal.[13]showedthatcommonMAPmethodsinvolvingestimatingboththeimageandkernellikelyfailbecausetheyfavorthetrivialsolution.Specialattentionsuchasedgere-weightingisprobablytheremedy.Itisnotablethatusingsparsepriorsusuallyresultinnon-convexobjectivefunctions,encumberingecientoptimization.Anothergroupofmethods[4,5,7]donotusesparsepriors,butinsteademployanexplicitedgepredictionstepforthePSFestimation.Speci“cally,Joshi[4]predictedsharpedgesby“rstlocatingstepedgesandthenpropagating leojia/projects/robust_deblur/index.html Two-PhaseKernelEstimationforRobustMotionDeblurring159thelocalintensityextrematowardstheedge.ThismethodwasusedtohandlecomplexPSFswithamulti-scalescheme[7].ChoandLee[5]adoptedbilateral“lteringtogetherwithshock“lteringtopredictsharpedges.ThesemethodsimposesimpleGaussianpriors,whichavailtoconstructquicksolvers.ThesepriorshowevercannotcapturethesparsenatureofthePSFandimagestructures,whichoccasionallymaketheestimatesnoisyanddense.Non-blinddeconvolution.GivenaknownblurPSF,theprocessofrestoringanunblurredimageisreferredtoasnon-blinddeconvolution.EarlyworksuchasRichardson-Lucy(RL)orWeiner“lteringisknownassensitivetonoise.Yuan[14]proposedaprogressivemulti-scalere“nementschemebasedonanedge-preservingbilateralRichardson-Lucy(BRL)method.TotalVariationregularizer(alsoreferredtoasLaplacianprior)[9],heavy-tailednaturalimagepriors[1,3]andHyper-Laplacianpriors[15…18]werealsoextensivelystudied.Tosuppressnoise,Baretal.[19]usedthe“delitytermtogetherwithaMumford-Shahregularizertorejectimpulsenoise.Joshietal.[20]incorpo-ratedalocaltwo-colorpriortosuppressnoise.Thesemethodsusedtheiterativere-weightedleastsquaretosolvethenonlinearoptimizationproblem,whichin-evitablyinvolvesintensivecomputation.Inthispaper,wedevelopedafastTV-deconvolutionmethodbasedonhalf-quadraticsplitting[16,18],toecientlyre-jectoutliersandpreservestructures.2Two-PhaseSparseKernelEstimationByconvention,theblurprocessismodeledasB=IwhereIisthelatentimage,istheblurkernel,istheimagenoise,denotesconvolutionandBistheobservedblurimage.Inthissection,weintroduceatwo-phasemethodforPSFestimation.The“rststageaimstoecientlycomputeacoarseversionofthekernelwithoutenforcingmuchsparsity.Inthesecondphase,althoughnon-convexoptimizationisemployed,withtheinitialkernelestimatepropagatedfromstageone,nosigni“cantcomputationisrequiredtoproducethe“nalresult.2.1PhaseOne:KernelInitializationInthe“rststep,weestimatetheblurkernelinamulti-scalesetting.Highe-ciencycanbeyieldedasweusetheGaussianpriorswhereclosed-formsolutionsexist.ThealgorithmissketchedinAlg.1.withthreemainsteps…thatis,sharpedgeconstruction,kernelestimation,andcoarseimagerestoration.Inthe“rstplace,likeothermotiondeblurringmethods,we“ltertheim-ageandpredictsalientedgestoguidethekernelinitialization.WeuseGaussian 160L.XuandJ.Jia Algorithm1.KernelInitialization INPUT:BlurimageBandanall-zerokernel(sizehBuildanimagepyramidwithlevelindex=1toComputegradientcon“denceforallpixels(Eq.(2)).=1toisthenumberofiterations)(a)Selectedgesforkernelestimationbasedoncon“dence(Eq.(4)).(b)EstimatekernelwiththeGaussianprior(Eq.(6)).(c)EstimatethelatentimageIwiththespatialprior(Eq.(8)),andupdateendforUpscaleimageIendforOUTPUT:Kernelestimateandsharpedgegradientmap (a)(b) Fig.1.Ambiguityinmotiondeblurring.Twolatentsignals(greendashedlines)in(a)and(b)areblurred(showninblue)withthesameGaussiankernel.In(a),theblurredsignalisnottotal-variationpreserving,makingthekernelestimationambiguous.Infact,theredcurveismorelikelythelatentsignalthanthegreenoneinacommonoptimizationprocess.Thebottomorangelinesindicatetheinputkernelwidth.“lteringtopre-smooththeimageandthensolvethefollowingshock“lteringPDEproblem[10]toconstructsigni“cantstepedges:/tsign(input(1)whereI=(IandI=I+2Iarethe“rst-andsecond-orderspatialderivativesrespectively.IdenotestheGaussiansmoothedinputimage,whichservesasaninitialinputforiterativelyupdating/tSelectiveEdgeMapforKernelEstimation.Insigni“cantedgesmakePSFestimationvulnerabletonoise,asdiscussedin[3…5,13].Wehoweverobserveadierentconnectionbetweenimageedgesandthequalityofkernelestimation…thatis,salientedgesdonotalwaysimprovekernelestimation;onthecontrary,thescaleofanobjectissmallerthanthatoftheblurkernel,theedgeinformationcoulddamagekernelestimation.WegiveanexampleinFigure1.Twostepsignals(thegreendashedlines)in(a)and(b)areblurredwithalargePSF.Theobservedblursignalsareshown Two-PhaseKernelEstimationforRobustMotionDeblurring161 (a)Blurredinput(b)Fergus[1]etal.(c)Shan[3]etal.(d)map(e)(f)(g)(h)(k)(l) Fig.2.Imagestructurein”uenceinkernelestimation.(a)Blurredimage.(b)ResultofFergusetal.[1].(c)ResultofShanetal.[3].(d)map(byEq.(2)).(e)-(g)maps,visualizedusingPoissonreconstruction,inthe1st,2ndand7thiterationswithoutconsidering.(h)Deblurringresultnotusingthemap.(i)-(k)mapscomputedaccordingtoEq.(4).(l)Our“nalresult.TheblurPSFisofsize45inblue.Becausetheleftsignalishorizontallynarrow,theblurprocesslowersitsheightin(a),yieldingambiguityinthelatentsignalrestoration.Speci“cally,motionblurmethodsimposingsparsepriorsonthegradientmapofthelatentimage[1,3]willfavorthereddashedlineincomputingtheunblurredsignalbecausethisversionpresentssmallergradientmagnitudes.Moreover,theredsignalpreservesthetotalvariationbetterthanthegreenone.Soitisalsoamoreappropriatesolutionforthegroupofmethodsusingsharpedgeprediction(includingshock“lteringandthemethodof[4]).Thisexampleshowsthatifimagestructuremagnitudesigni“cantlychangesafterblur,thecorrespondingedgeinformationcouldmistakekernelestimation.Incomparison,thelarger-scaleobjectshowninFigure1(b)canyieldsta-blekernelestimationbecauseitiswiderthanthekernel,preservingthetotalvariationofthelatentsignalalongitsedges.Figure2showsanimageexample.Theblurredinput(shownin(a))containsrichedgeinformationalongmanysmall-scaleobjects.TheresultsofFergus 162L.XuandJ.Jia[1](b)andShanetal.[3](c)arecomputedbyextensivelyhand-tuningpa-rameters.However,thecorrectkernelestimatestillcannotbefound,primarilyduetotheaforementionedsmallstructureproblem.Weproposeanewcriterionforselectinginformativeedgesforkernelestima-tion.Thenewmetrictomeasuretheusefulnessofgradientsisde“nedas (2)whereBdenotestheblurredimageand)isahhwindowcenteredatpixel5istopreventproducingalargein”atregions.Thesigned)fornarrowobjects(spikes)willmostlycanceloutinisthesumoftheabsolutegradientmagnitudesinwhichestimateshowstrongtheimagestructureisinthewindow.Asmallimpliesthateitherspikesora”atregionisinvolved,whichcausesneutralizingmanygradientcomponents.Figure2(d)showsthecomputedmap.Wethenruleoutpixelsbelongingtosmall-valuewindowsusingamask(3)where)istheHeavisidestepfunction,outputtingzerosfornegativevaluesandonesotherwise.isathreshold.The“nalselectededgesforkernelestima-tionaredeterminedas(4)whereIdenotestheshock“lteredimageandisathresholdofthegradientmagnitude.Eq.(4)excludespartofthegradients,dependingjointlyonthemagnitudeandthepriormaskM.Thisselectionprocessreducesambiguityinthefollowingkernelestimation.Figures2(e)-(g)and(i)-(k)illustratethecomputedmapsindierentit-erationswithoutandwiththeedgeselectionoperation.Thecomparisonshowsthatincludingmoreedgesdonotnecessarilybene“tkernelestimation.Opti-mizationcouldbemisledespeciallyinthe“rstafewiterations.Soanimageedgeselectionprocessisvitaltoreducetheconfusion.Toallowforinferringsubtlestructuresduringkernelre“nement,wedecreasethevaluesofandiniterations(dividedby1.1ineachpass),toincludemoreandmoreedges.Sothemapsin(g)and(k)containsimilaramountofedges.Butthequalitynotablydiers.Themethodtocomputethe“nalresultsshownin(h)and(l)isdetailedfurtherbelow.FastKernelEstimation.Withthecriticaledgeselection,initialkerneles-timationcanbeaccomplishedquickly.Wede“netheobjectivefunctionwithaGaussianregularizeras(5) Two-PhaseKernelEstimationforRobustMotionDeblurring163 (a)Blurredinput(b)map(c)Gaussianprior(d)OurspatialpriorFig.3.Comparisonofresultsusingthesparseandspatialpriors.Thespatialpriormakestheresultin(d)preservemoresharpedges.whereisaweight.BasedontheParsevalstheorem,weperformFFTsonallvariablesandsetthederivativew.r.t.tozero.Theclosed-formsolutionisgiven B)+ (yIs)F(y (6)where)and)denotetheFFTandinverseFFTrespectively. )isthecomplexconjugateoperator.CoarseImageEstimationwithaSpatialPriorWeusethepredictedsharpedgegradientasaspatialpriortoguidetherecoveryofacoarseversionofthelatentimage.TheobjectivefunctionisE(I)=(7)wherethenewspatialpriordoesnotblindlyenforcesmallgradientsnearstrongedgesandthusallowsforasharprecoveryevenwiththeGaussianregularizer.Theclosed-formsolutionexists.Withafewalgebraicoperationsinthefrequencydomain,weobtain (B)+ F(x)Fx (y)Fy (k)F(k( F(x)F(x (8)Figure3comparesthedeconvolutionresultsusingthespatialandGaussianpriorsrespectively(thelatterisusuallywrittenas).Theregularizationweight.TheimageshowninFigure3(d)containswellpreservedsharp2.2PhaseTwo:ISD-BasedKernelReÞnementToobtainsparsePSFs,previousmethods[1,3,5,21]applyhardorhysteresisthresholdingtothekernelestimates.Theseoperationshoweverignoretheinher-entblurstructure,possiblydegradingthekernelquality.Oneexampleisshown 164L.XuandJ.Jia (b) (c) g.t. 123 Fig.4.SparseKernelRe“nement.(a)Ablurredimage[13].(b)Kernels.Thetoprowshowsrespectivelythegroundtruthkernel,thekernelestimatesofFergusetal.[1],Shanetal.[3],andofourmethodinphaseone.inthebottomrowisour“nalresultafterkernelre“nement.showtheiterativelydetectedsupportregionsbytheISDmethod.(c)OurrestoredimageusinginFigure4(b),whereonlykeepingthelarge-valueelementsapparentlycannotpreservethesubtlestructureofthemotionPSF.Wesolvethisproblemusinganiterativesupportdetection(ISD)methodthatcanensurethedeblurringqualitywhileremovingnoise.TheideaistoiterativelysecurethePSFelementswithlargevaluesbyrelaxingtheregularizationpenalty.Sotheseelementswillnotbesigni“cantlyaectedbyregularizationinthenext-roundkernelre“nement.Thisstrategywasshownin[22]capableofcorrectingimperfectestimatesandconvergingquickly.ISDisaniterativemethod.Atthebeginningofeachiteration,previouslyestimatedkernelisusedtoformapartialsupport;thatis,large-valueelementsareputintoasetandallothersbelongtotheset isconstructed(9)whereindexestheelementsinandisapositivenumber,evolvinginiterations,toformthepartialsupport.Wecon“gurebyapplyingthe“rstsigni“cantjumpŽrule[22].Brie”yspeaking,wesortallelementsininanascendingorderw.r.t.theirvaluesandcomputethedierencesbetweeneachtwonearbyelements.Thenweexamthesedierencessequentiallystartingfromtheheadandsearchforthe“rstelement,forexample,thatsatis“es(2h),wherehisthekernelwidthandreturnsthelargestvaluein.Wethenassignthekernelvalueinposition.Moredetailsarepresentedin[22].ExamplesofthedetectedsupportareshowninthebottomrowofFigure4(b).Theelementswithineachwillbelesspenalizedinoptimization,resultinginanadaptivekernelre“nementprocess.Wethenminimize 2sk2+j (10) Two-PhaseKernelEstimationforRobustMotionDeblurring165 Algorithm2.ISD-basedKernelRe“nement INPUT:InitialkernelB,and(outputofAlgorithm1)Initializethepartialsupport (Eq.(9)).repeatSolveforbyminimizingEq.(10).Update (Eq.(9)).+1.until empirically)OUTPUT:Kernelestimate forPSFre“nement.Thedierencebetweenthisfunctionandthoseusedin[3,6]isonthede“nitionoftheregularizationterms.Thresholdingappliessoftlyinourfunctionthroughadaptiveregularization,whichallowstheenergytoconcentrateonsigni“cantvaluesandthusautomaticallymaintainsPSFsparsity,faithfultothedeblurringprocess.ThealgorithmisoutlinedinAlg.2..TominimizeEq.(10)withthepartialsupport,weemployedtheiterativereweighedleastsquare(IRLS)method.Bywritingconvolutionasmatrixmul-tiplication,thelatentimageI,kernel,andblurinputBarecorrespondinglyexpressedasmatrixA,vector,andvector.Eq.(10)isthenminimizedbyiterativelysolvinglinearequationsw.r.t..Inthe-thpass,thecorrespondinglinearequationisexpressedassTA+diag((11)whereAdenotesthetransposedversionofAandisthevectorformof isde“nedas=max(),whichistheweightrelatedtothekernelestimatefromthepreviousiteration.diag()producesadiagonalmatrixfromtheinputvector.Eq.(11)canbesolvedbytheconjugategradientmethodineachpass(wealternativelyapplythematrixdivisionoperationinMatlab).AsPSFshavesmallsizecomparedtoimages,thecomputationisveryfast.Our“nalkernelresultisshowninFigure4(b).Itmaintainsmanysmall-valueelements;meanwhile,thestructureisappropriatelysparse.Optimizationinthisphaseconvergesinonlyafewiterations.Figure4(c)showsourrestoredimageusingthecomputedPSF.Itcontainscorrectlyreconstructedtexturesandsmalledges,verifyingthequalityofthekernelestimate.3FastTV-DeconvolutionAssumingthedata“ttingcostsfollowingaGaussiandistributionisnotagoodwaytogoinmanycases.Itpossiblymakesresultsvulnerabletooutliers,asdemonstratedinmanyliteratures.Toachievehighrobustness,weproposeamodelindeconvolution,whichiswrittenasE(I)=(12) 166L.XuandJ.Jia Algorithm3.RobustDeconvolution INPUT:BlurredimageBandtheestimatedkernelEdgetapinginMatlabrepeatSolveforusingEq.(18)repeatSolveforusingEq.(17)SolveforIinthefrequencydomainusingEq.(15)untilminuntilminOUTPUT:DeblurredimageI Itcontainsnon-linearpenaltiesforboththedataandregularizationterms.Weproposesolvingitusinganecientalternatingminimizationmethod,basedonahalf-quadraticsplittingforminimization[16,18].Foreachpixel,weintroduceavariabletoequalthemeasureIB.Wealsodenoteby)imagegradientsintwodirections.Theuseoftheseauxiliaryvariablesleadstoamodi“edobjectivefunctionE(I,w,v 2IkŠBŠv2+1 (13)wherethe“rsttwotermsareusedtoensurethesimilaritybetweenthemeasuresandthecorrespondingauxiliaryvariables.When0and0,thesolutionofEq.(13)approachesthatofEq.(12).Withtheadjustedformulation,Eq.(13)cannowbesolvedbyanecientAlternatingMinimization(AM)method,wherethesolveriteratesamongsolving,andindependentlyby“xingothervariables.andareinitializedtoIneachiteration,we“rstcomputeIgiventheinitialorestimatedandE(I;w,v (14)Eq.(14)isequivalenttoEq.(13)afterremovingconstants.Asaquadraticfunc-tion,Eq.(14)bearsaclosedformsolutioninminimizationaccordingtotheParsevalstheoremaftertheFouriertransform.TheoptimalIiswrittenas(I)= / F(x)F(wx (y)F(wy / F(x)F(x (15)ThenotationsarethesameasthoseinEq.(6). Two-PhaseKernelEstimationforRobustMotionDeblurring167 (a)Noisyinput(b)[15](c)[17](d)OursFig.5.Deconvolutionresultcomparison.TheblurredimagesinthetopandbottomrowsarewithGaussianandimpulsenoiserespectively.InsolvingforandgiventheIestimate,becauseandarenotcoupledwitheachotherintheobjectivefunction(theybelongtodierentterms),theiroptimizationisindependent.Twoseparateobjectivefunctionsarethusyielded:E(w;I)= E(v;I)= (16)EachobjectivefunctioninEq.(16)categorizestoasingle-variableoptimizationproblembecausethevariablesfordierentpixelsarenotspatiallycoupled.Theoptimalsolutionsforallscanbederivedaccordingtotheshrinkageformula: max(,(17)Here,isotropicTVregularizerisused…thatis, canbecomputedsimilarlyusingtheabovemethod.Computingcanbeevensimplerbecauseitisanone-dimensionalshrinkage:=sign(IB)max((18)whereandaretwosmallpositivevaluestoenforcethesimilaritybetweentheauxiliaryvariablesandtherespectiveterms.Tofurtherspeeduptheoptimiza-tion,weemploythewarm-startscheme[3,16].It“rstsetslargepenalties(andinouralgorithm)andgraduallydecreasestheminiterations.ThedetailsareshowninAlg.3..Weempiricallyset=1,,andFigure5showsexampleswheretheblurredimagesarewithGaussianandimpulsenoiserespectively.TheTV-modelperformscomparablytootherstate-of-the-artdeconvolutionmethodsundertheGaussiannoise.Whensigni“cantimpulse-likesensornoiseexists,itworksevenbetter.Intermsofthecomputationtime,themethodsof[15]and[17]spend3minutesand1.5secondsrespectivelytoproducetheresultsinFigure5withtheprovidedimplementationwhileourdeconvolutionalgorithm,albeitusingthehighlynon-linearfunction,uses6sinMatlab.Allmethodsdeconvolvethreecolorchannelsindependently. 168L.XuandJ.Jia (a)Input(b)[1](c)[3](d)noM(e)withMFig.6.Smallobjectssuchasthecharactersandthinframesarecontainedintheimage.Theygreatlyincreasethedicultyofmotiondeblurring.(d)-(e)showourresultsusingandnotusingtheMmap.Theblurkernelisofsize51 (a)Input(b)[1](c)[3](d)[5](e)OursFig.7.Comparisonofstate-of-the-artdeblurringmethods4MoreExperimentalResultsWeexperimentedwithseveralchallengingexampleswheretheimagesareblurredwithlargekernels.Ourmethodgenerallyallowsusingthedefaultorautomati-callyadaptedparametervalues.Inthekernelestimation,weadaptivelysettheinitialvaluesofand,usingthemethodof[5].Speci“cally,thedirectionsofimagegradientareinitiallyquantizedintofourgroups.issettoguaranteethatatleast2 pixelsparticipateinkernelestimationineachgroup,wherethetotalnumberofpixelsinkernelissimilarlydeterminedbyallowingatleast0 pixelstobeselectedineachgroup.isthetotalnumberofpixelsintheinputimage.Inthecoarsekernelestimationphase,wesetand=10toresistnoise.Inthekernelre“nement,weset=1.inthe“nalimagedeconvolutionissetto2Ourtwo-phasekernelestimationisecientbecauseweputthenon-convexoptimizationintothesecondphase.OurMatlabimplementationspendsabout25secondstoestimatea2525kernelfroman800600imagewithanIntelCore2QuadCPU@2.40G.Thecoarsekernelestimationuses12sinthemulti-scaleframeworkwhilethekernelre“nementspends13sasitisperformedonlyinthe“nestimagescale.InFigure6(a),weshowanexamplethatcontainsmanysmallbutstructurally-salientobjects,suchasthecharacters,whichmakehighqualitykernelestimation Two-PhaseKernelEstimationforRobustMotionDeblurring169 (a)(b)(c) Fig.8.Onemoreexample.(a)Blurredimage.(b)Ourresult.(c)Close-ups.verychallenging.Theresults(shownin(b)and(c))oftwoothermethodscontainseveralvisualartifactsduetoimperfectkernelestimation.(d)showsourresultwithoutperformingedgeselection.Comparedtotheimageshownin(e),itsqualityislower,indicatingtheimportanceofincorporatingthegradientmaskMinde“ningtheobjectivefunction.Figure7showsanotherexamplewithcomparisonswiththreeotherblinddeconvolutionmethods.ThekernelestimatesofFergusetal.[1]andShan[3]areseeminglytoosparse,duetothe“nalhardthresholdingoperation.Therestoredimageisthereforenotverysharp.ThedeblurringresultofChoandLee[5]containssomenoise.OurrestoredimageusingAlg.3.isshownin(e).Wehavealsoexperimentedwithseveralothernaturalimageexamples.Figure8showsonetakenunderdimlight.Moreofthemareincludedinoursupplementary“ledownloadablefromtheprojectwebsite.5ConcludingRemarksWehavepresentedanovelmotiondeblurringmethodandhavemadeanumberofcontributions.Weobservedthatmotiondeblurringcouldfailwhenconsiderablestrongandyetnarrowstructuresexistinthelatentimageandproposedaneectivemaskcomputationalgorithmtoadaptivelyselectusefuledgesforkernelestimation.TheISD-basedkernelre“nementfurtherimprovestheresultqualitywithadaptiveregularization.The“naldeconvolutionstepusesadatatermthatisrobusttonoise.Itissolvedwithanewiterativeoptimizationscheme.Wehaveextensivelytestedouralgorithm,andfoundthatitisabletodeblurimageswithverylargeblurkernels,thankstotheuseoftheselectiveedgemap.AcknowledgementsTheworkdescribedinthispaperwassupportedbyagrantfromtheResearchGrantsCounciloftheHongKongSpecialAdministrativeRegion(ProjectNo.413110)andCUHKDirectGrant(No.2050450). 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