太赫兹图像高分辨重构 论文

HighrsolutionrconstructionfortrahrtzimagingLiMinXu,1,2WnHuiFan,1,andJiaLiu1,21StatKyLaboratoryofTransintOpticsandPhotonics,Xi’anInstitutofOpticsandPrcisionMchanics,ChinsAcadmyofScincs,Xi’an710119,China2UnirsityofChinsAcadmyofScincs,Bijing100049,ChinaCorrspondingauthor:fanwh@optaccnRcid26May2014;risd25August2014;accptd15Octobr2014;postd16Octobr2014(DocID212774);publishd14Nombr2014Wprsntahighrsolution(HR)rconstructionmodlandalgorithmsfortrahrtzimaging,takingadantagofsuprrsolutionmthodologyandalgorithmsThalgorithmsusdincludprojctionontoaconxstsapproach,itratibackprojctionapproach,Lucy–Richardsonitration,and2DwaltdcompositionrconstructionUsingthfirsttwoHRrconstructionmthods,wsuccssfullyobtainHRtrahrtzimagswithimproddfinitionandlowrnoisfromfourlowrsolution(LR)22×24trahrtzimagstaknfromourhommadTHz–TDSsystmatthsamxprimntalconditionswith10mmpixlUsingthlasttwoHRrconstructionmthods,wtransformonrlatilyLRtrahrtzimagtoaHRtrahrtzimagwithdcrasdnoisThisindicatspotntialapplicationofHRrconstructionmthodsintrahrtzimagingwithpulsdandcontinuouswatrahrtzsourcs©2014OpticalSocityofAmricaOCIScods:(1106795)Trahrtzimaging;(1003020)Imagrconstructionrstoration;(1002960)Imaganalysishttp:dxdoiorg101364AO530078911IntroductionSincthpionringworks[1]oftrahrtzimagingbasdontrahrtztimdomainspctroscopy(THz–TDS),rapiddlopmntshabnwitnssdbcausoftrahrtzwas’uniqucharactristics[2]Trahrtzimaginghaspotntialapplicationsinthfildssuchasbiomdicalimaging,nondstructialuationforscuritydtction,andindustrialprocsscontrol[3]Howr,trahrtzimagingalsohasbnconfrontdwithmanyobstacls[4];forxampl,lowrsolutionanddfinitionInthispapr,wfocusonthhighrsolution(HR)rconstructionfortrahrtzimagingutilizingthidologyandmthodologyofsuprrsolution(SR)rstorationinimagprocssingSRrstorationalgorithmsarfirstusdinisiblimagingtoorcomthspatialrsolutionlimitofimagingsnsors(CCDandCMOS)withoutsuffringthffctsofshotnoisandcanalsodcrasthmanufacturingcost[5,6]SRrstorationhasbnutilizdsosuccssfullythatithasbnapplidinHRrconstructionformicrowaimaging[7]andinfrardimaging[8],nthoughthrarstillsomfundamntalthorticalproblms[9]Hr,tothbstofourknowldg,wusHRrconstructionfortrahrtzimagingtoobtainHRtrahrtzimagsfrompulsdandcontinuouswa(CW)trahrtzimagingsystmsforthfirsttimWfirstanalyzthobsrationmodlofHRrconstructionformultiframlowrsolution(LR)imagsandillustratthncssityofsubpixlshiftandintrpolationforrconstructionThn,projctionontoaconxstsapproach(POCS)andanitratibackprojctionapproach(IBP)arutilizdtorconstructthHRtrahrtzimagfromfourLRtrahrtzimagsobtaindfromourhommadTHz–TDSsystmatthsamxprimntalconditionsWalsoattmpttousLucy–Richardson(LR)itrationandwaltdcompositionrconstructiontorconstructthtrahrtzimagfrom1559128X1433789107$15000©2014OpticalSocityofAmrica20Nombr2014Vol53,No33APPLIEDOPTICS7891anLRtrahrtzimagThdiffrntffctsforthdiffrntparamtrsofanLRalgorithmaranalyzdThfalscolorimagalsohasbnusdtocratcontrastbtwnthoriginalLRimagandHRrconstructdimagbasdonawaltalgorithmThrsultsindicatapromisingprospctforHRtrahrtzimagingrconstruction2HighRsolutionRconstructionModlforMultiframLowRsolutionImagsThopticalimagingsystmcanbiwdasalowpassfiltrforthcontinuousscnthatallowsonlylowfrquncycomponntstopassthroughGnralimagrstorationmthodscanonlyrcorthcutofffrquncyatmost,thuslosinghighfrquncycomponntsbyondthcutoffpoint,andthdtaildinformationattachdSRrconstructiontchniqussktorstorthinformationbyondthcutofffrquncyandthusincludmordtailsofthimagInordrtorconstructanHRimagfromsralLRimags,wfirstinstigatthrlationshipbtwnthHRimagandthsLRimagsFigur1illustratsthgnralobsrationmodlthatcombinsthLRimagstothHRimagThcontinuousscn,assumdtobbandlimitd,isadquatlysampldatorabothNyquistratThrsultisanHRimag,dnotdasx,withoutanydistortionandnoisThHRimagxprincsthprocssofwarping,blur,downsampling,andaddingnoistoobtainanLRimag,dnotdasykEachprocssisrprsntdbyamatrixoprator,namly,M,B,D,andn,rspctilyThobsrationmodl[6]thatdscribsthrlationshipbtwnthHRimagxandthkthLRimagcanbxprssdasEq(1):yk�DBkMkx�nk;1≤k≤p:(1)ThdiffrntprocsssthatruinthHRimagarnormallymixdandcannotbsparatdsodistinctilyundrthpracticalconditionsThisobsrationmodlisasimplifidtypthatignorsthmixdffctofdiffrntruiningprocsssThprmisforHRrconstructionfrommultiframLRimagsisasubpixlshift[6,10,11],asillustratdinFig2BcausthsubpixlshiftdLRimagsdonotblongtoachothr,achLRimagcontainsnwinformationThwaytorcombinnwinformationfromdiffrntLRimagstorconstructanHRimagisthultimattargtThus,thHRrconstructionfromsralLRimagsisaninrsproblmofthobsrationmodl,namly,rcoringthoptimalsolutionforxfromyk,1≤k≤pGnrally,thpointspradfunction(PSF)thatrlatsthLRandHRsnsorscanbdscribdasanaragoprator,asshowninFig3(a)Blurringcanbcausdbythopticalsystm,rlatimotionbtwnimagingsystmandscn,andthPSForlappingofthLRsnsorsFigur3(b)illustratsthoriginofblurringcausdbyPSForlapping[12]ThHRsnsorpointcisorlappdbyfourLRsnsorpixls,maningthgrayllinpointcisaffctdbythsurroundingLRpixlsThbasicflowtoimplmntHRrconstructionisshowninFig4Thwholprocsscanbsparatdintothrstps:rgistration,intrpolation,anddblurring[6,13,14]Usually,thsthrstpsndtobitratdtoobtainthbstrsult3HighRsolutionRconstructionforTrahrtzImagingThispartfocussonthHRrconstructionfortrahrtzimagingxprimntallyByusingPOCSandIBPalgorithms,firstwattmpttorconstructanHRtrahrtzimagfromfoursubpixlshiftdLRtrahrtzimagsacquirdundrthsamxprimntalconditioniathTHz–TDSsystmThPSFadoptdhrisanaragingopratorasdiscussdaboThnwtrytorconstructanHRtrahrtzimagforonLRtrahrtzimagusingthLRFig1GnralobsrationmodlcombiningLRimagstoHRimagFig2BasicprconditionforSRrconstructionsubpixlshift7892APPLIEDOPTICSVol53,No3320Nombr2014algorithmandwaltdcompositionrconstructionmthodThPSFadoptdinthLRalgorithmcanbdscribdasaGaussianoprator,whichisbttrrlatdtothnrgydistributionofthtrahrtzbam[15,16]AHRRconstructionfromSralLRImags1ProjctionOntoConxStsApproachFigur5illustratsfourLRtrahrtzimagswithsubpixlshiftsThsizofLRtrahrtzimagsis22×24,with1mmpixlThsfoursubpixlshiftdLRtrahrtzimagswracquirdundrthsamxprimntalconditioniathgnralTHz–TDStransmissionimagingsystmThsourcusdhrisatrahrtzphotoconductiantnnawithLTGaAsasitssubstratThradiationspctrumiswithinthrangof01–30THzwith03THzatthhighstpointThEOdtctorusdhrisanlctroopticcrystalZnTwithawidrsponsspctrumandhighsnsitiity[17,18]Thrastrscanningstplngthwasstat1mmThwaformofachstpisrcorddandthpakpakamplitudistransformdtograyscaldistributionBcausthrlatisubpixlshiftsarnotknownbforthPOCSalgorithmisxcutd,thsubpixlshiftsndtobstimatdPOCSalgorithmisawaytofindthoptimalsolutionthatsatisfisthrstrictions,whichcanbdscribdasasrisofconxstsAccordingtothmthodofPOCS,incorporatingaprioriknowldgofthfourLRimagscanbachidbyrstrictingthsolutiontobammbrofaclosdconxstCi,whichisdfindasastofctorsthatsatisfyaspcificproprtyIfthconxstshaanonmptyintrsction,thnasolutionthatblongstothintrsctionstCs�mi�1CicanbfoundbyaltrnatingprojctionsontothsconxstsThmthodofPOCScanbimplmntdbyfindingactorthatblongsinthintrsctionbythrcursionxn�1�PmPm−1P2P1xn,whichisschmaticallyshowninFig6Figur7illustratsthHRrconstructionrsultsfordiffrntitrationtimsusingaPOCSalgorithmTabl1illustratsthrrorcomputationfordiffrntitrationtimsThrroraludcrasswithincrasingitrationtims,butthconrgncratslowsdown,alidatingthatthPOCSalgorithmFig3OriginofblurringrprsntdbyPSFFig4Basicrconstructionflow:rgistrationintrpolationdblurringFig5FourLRtrahrtzimagstaknfromthTHz–TDSsystmundrthsamxprimntalcondition20Nombr2014Vol53,No33APPLIEDOPTICS7893hasaryslowconrgncspd,andthalgorithmfficincyisrylow[19]WhatostaconrgnccritriaforPOCSitrations,xprssdinanrrorthrsholdalu(0001)Thmansquarrror(MSE)inFig7dcrasswithitrationtims,butthblurringffctbcomsmorsriousFigurs7(a),7(b),and7(c)arbadlyruindbythlatticpattrnnois,whichcanbdcrasdbynonlocal(NL)mansfiltring[20,21],whichprformsmuchbttrthanthgnralspatialfiltringmthodforsupprssingpriodicnoisFigur7(d)hasthminimumMSE,butthblurringffctisthworstFigur6()showsthnonlocalfiltringforFig7(b)Figur7(f)showsthfiltrdrsidualsfromFig7(b)ThlatticpattrnnoisaftrthlnthPOCSitrationisgratlysuprssdThbladdgsbcommuchclarandrsolutionimprosobiously2ItratiBackprojctionApproachInthIBPapproach,thHRimagisstimatdbybackprojctingthrror(thdiffrnc)btwnthcalculatdLRimagsiaimagblurandthobsrdLRimagsThisprocssisrpatditratilytominimizthnrgyofrror;thrfor,thoptimalsolutiontothHRimagmatrixx�n1;n2�isachidThstopcritriaforthitrationprocsscanbstwhnthmaximumdiffrncofthlmntsbtwnxn�1�n1;n2�andxn�n1;n2�issmallrthanacrtainthrshold;forxampl,0001ThIBPitrationschmcanbxprssdasxˆn�1�n1;n2��xˆn�n1;n2��Xm1;m2γm1;n1k�yˆk�m1;m2�−yˆnk�m1;m2��×hBP�m1;m2;n1;n2�;(2)whryˆnk�WkxˆnarthcalculatdLRimagsfromthapproximationofxnaftrnitrations;γm1;n1krprsntsthst{m1,m2ykjm1,m2isinfluncdbyn1,n2,whrn1,n2xn};andhBPisthbackprojctionkrnlthatcontrolsthcontributionsofrror(yˆk�m1;m2�−yˆnk�m1;m2�)toxˆn�n1;n2�ThmatrixWkrprsntsthblurringanddtriorationffctsthatrlatthcalculatdHRimagxˆandLRimagsyˆkWithonlytharagingffcttaknintoconsidration,wchoosthmatrixWktobthPSF,whichcontainsonlytharagingopratorThchoicofthbackprojctionkrnl(hBP)affctsthcharactristicsofthoptimalsolutionwhnthrarpossiblsolutionsandusuallyisrprsntdbya3×3or5×5sharpnmatrixwithzroorrysmalllmntsatthcornrandlargrlmntsinthcntrFigur8illustratsthHRrconstructionrsultsfromfourLRtrahrtzimagsusingIBP[6]ThlatticnoisinFig8(a)isobiousdutothsmallLRimagnumbrsandrlatimotionstimationrrorToorcomthlatticnoiswithrgularapparanc,thffctiwayistoadoptnonlocalmansfiltring[20,21]Figur8(b)illustratsthnonlocalmansfiltrdrsult,withthlatticnoissupprssdBHRRconstructionfromOnLRImag1Lucy–RichardsonHRAlgorithmUndrmanycircumstancs,thgraylldistributionofimagscouldbmodldbyaPoissonrandomFig7HRrconstructionfromfourLRtrahrtzimagsusingprojctionontoconxstsapproach(a)Onitration(b)11itrations(c)21itrations(d)31itrations()Nonlocalmansfiltring(withsarchwindowt�11,filtringdpthh�100,diffrntsimilaritywindowf�5)for(b)(f)Filtrdrsidualsfrom(b)Fig6POCSalgorithmtofindthoptimalsolution7894APPLIEDOPTICSVol53,No3320Nombr2014fildWhnthimagingtargtsarscanndbytrahrtzwas,thtrahrtznrgyonrypixlcanbiwdasthintractionbtwnplntyoftrahrtzphotonsandthimagingdotinatransinttimscal,andachpixlisindpndntThus,graylldistributionofthtrahrtzimagcouldbapproximatdbyPoissonfild[22]ThLRrstorationalgorithmprformswllwhnthaprioriknowldgofimagnoisisnotknown,andthgraylldistributioncouldbapproximatdbyaPoissonfild[23]ThLRitrationcanbxprssdasfollows:fˆk�1�x;y��fˆk�x;y��h�−x;−y��g�x;y�h�x;y��fˆk�x;y��;(3)inwhichfˆisthstimatdaluofthdgraddimag,gisthdgraddimag,andhisthPSFThcoordinatxrprsntsthhorizontaldirction,andthpositidirctionisright,whilthcoordinatyrprsntsthrticaldirction,andthpositidirctionisupwardThappropriatPSFisthkytoachigoodrstorationrsultsThrhabnpaprsanalyzingthchoosingofPSFfortrahrtzimagrstoration[24]AsthtrahrtzbamsargnrallyiwdasGaussiandistribution[15,16],wchoosthGaussianopratorforPSFintrahrtzimaging,asshowinEq(4):h�x;y��8<:kxp�−2�x−x0�22xΔx2−−2�y−y0�22yΔy2�;�x;y�C;0;othrwis;(4)inwhichkisconstantfornormalization,isthradiusofthscanningtrahrtzbam,ΔxandΔyarthscanningstps,�x0;y0�isthoriginalcoordinat,andCdscribsthsupportingdomainofhFigur9illustratsthrstorationffctofchssboardblurringadopingthLRitrationWcanconcludthatthdgsandtxturofthchssboardarstillblurrdaftronLRitration;thtxturbcomsclarr,butthdgsarstillblurrdwhnthitrationtimrachs20,withdtaillosscontroladdd;thtxturanddgsallbcomclarrwhnthitrationtimrachs20,withdtaillosscontrolandpixlwightcontroladddFigur10illustratsthrstorationffctofthcointrahrtzrflctionimagadoptingthLRitration(O)isthrawtrahrtzrflctionimagusingthCWsourc[23]Thoprationfrquncyofatrhrtzlasrusdhris252THz(11883μm),andtharagoutputpowrisabout50mWThscanningstplngthisstto02mmThrawimagsizis110×142Ittookabout500mstoscanachpixl,soittookabout2htoscanthwholcoinSuchalongtimmantthscanningrsultwasbadlyinfluncdbythsourpowrfluctation(I)isthfluctuationsupprssdrsultusinghomomorphicfiltring[25](a)–(d)arthLRrstorationffctfor(I)Equation(3)ischosnasthPSFxprssionfortrahrtzimagrstorationFromFig10(a),wcanconcludthatthLRalgorithmwillproduclowfrquncynoiswhilrstoringthdgs;fromFig10(b),incrasditrationswillsupprsslowfrquncynois;fromFig10(c),dtaillosscontrolwillprsrthtxtur;fromFig10(d),dtaillosscontrolandpixlwightcontrolcanprsrthtxturanddgswhilnhancingthimagingtargtbackgroundcontrast2WaltDcompositionRconstructionMthodInthispart,wdmonstratHRtrahrtzimagrconstructionusingthwaltdcompositionrconstructionmthodThmthodusdhrcanTabl1ErrorCalculatdbyDiffrntItrationTimsUsingPOCSforFourLRTrahrtzImagsItrations1112131Error033182001618400014364000013447Fig8HRrconstructionfromfourLRtrahrtzimagsusingIBPalgorithm(a)IBPrconstructionrsult(b)Nonlocalmansfiltring(withthfiltrparamtrst�11,f�5,h�10)for(a)Fig9RstorationofchssboardblurringadopingthLRitration(a)Blurrdandnoisdimag(b)OnitrationusingthLRalgorithm(c)20itrationsusingthLRalgorithmwithdtaillosscontrol(d)20itrationsusingthLRalgorithmwithdtailcontrolandpixlwightcontrol20Nombr2014Vol53,No33APPLIEDOPTICS7895bdscribdasfollows,thoughthrarmanyothrkindsofHRrconstructionbasdonwaltdcompositionrconstruction[26]First,intrpolatthLRtrahrtzimag(bilinarintrpolationisusdhr);thnprocssthintrpolatdLRtrahrtzimagby2Dwaltdcomposition;slctthfirstlayrwaltcofficintsforrconstruction(biorthogonalwaltbassarusdhr);andthHRimagisachidThwholprocssofHRrconstructiondscribdabocanbshownasFig11schmaticallyFigur12illustratsHRrconstructionforonLRtrahrtzimagusingthwaltdcompositionrconstructionmthodRsolutionimpromntcanbobsrdobiouslyinthHRrconstructdimagThfalscolorimag(b)ismadaccordingtothgrayscalasshownasidtonhanccontrast4DiscussionandConclusionTorconstructHRtrahrtzimags,fourdiffrntalgorithmsardiscussdinthispaprThsalgorithmscanbdiiddintotwoclasss,namly,rconstructingaHRtrahrtzimagfrommultiframLRimagsandrconstructingaHRtrahrtzimagfromanLRdgraddtrahrtzimagThobsrationmodlforthfirstclassisillustratd,withthHRrconstructionprmis:subpixlshiftmphasizdThPSFcanbdidintotwotyps:aragingopratorandGaussianopratorWhnthsnsitiityofachpixlisnotuniform,tharagFig10RstorationofcointrahrtzrflctionimagadoptingthLRitration(O)Rawtrahrtzrflctionimag[23](I)Fluctuationsuprssionusinghomomorphicfiltring[25](a)OnitrationusingthLRalgorithmfor(I)(b)SixitrationsusingthLRalgorithmfor(I)(c)SixitrationsusingthLRalgorithmfor(I)withdtaillosscontrol(d)SixitrationsusingthLRalgorithmfor(I)withdtaillosscontrolandpixlwightcontrolFig11SchmaticflowofHRrconstructionfromonLRimagusingwaltdcompositionrconstructionFig12HRrconstructionforonLRtrahrtzimagusingthwaltdcompositionrconstructionmthod(O)LRtrahrtzimag(a)HRrconstructiontrahrtzimag(b)Falscolorimagfor(a)tonhancthcontrast7896APPLIEDOPTICSVol53,No3320Nombr2014opratorwillbringasriousblurringffctAGaussianopratorprformswllconsidringthGaussiancharactristicsoftrahrtzbamsActually,thffctofHRrconstructiondpndsonthnumbrofLRimagsslctd,thsubpixlshiftstimation,andthrconstructionalgorithmchosnThabilityofthrsolutionimpromntisalsolimitdbysomothrfactors,asdiscussdinpriouslitratur[5]AccordingtothHRrconstructionxprimntsdiscussdabo,thPOCSmthodhasthdisadantagoflowconrgingspdandsriouspattrnnoisifthsubpixlshiftisstimatdinaccuratly;thrconstructionffctofIBPalgorithmislarglydpndntonthchoicofthbackprojctionkrnl(hBP),whichissomtimsdifficulttoslct;thLRitrationmodlrflctsthphysicalfactorsthatdtrioratthtrahrtzimagingrsolutionbutismorcomplxanddifficulttobuild;thschmaticflowofthwaltdcompositionrconstructionmthodisapparnt,andthrconstructionffctdpndsonthchoicofthintrpolationmthodandwaltdcompositionrconstructionbassThfurthrquantitaticomparisonandanalysisforthaluationofrconstructionffctandspdisbyondthscopofthispapr,butisalsoimportantasforthslctionofthHRrconstructionmthodfortrahrtzimags,sowwouldliktoinstmornrgytowardthisobjctiinthfuturThrarstillmanyothrSRrconstructionmthodsthatmaybadaptdforHRrconstructionoftrahrtzimags,suchasBaysmthods[27,28],thnonuniformintrpolationapproach,rgularizdSRrconstructionapproach,hybridrstorationapproach,motionfrSRapproach,andthfrquncydomainapproach[6,13,14]Inconclusion,HRrconstructionfortrahrtzimagingshowsanncouragingprospcttoimprothrsolutionoftrahrtzimagstaknfromapulsdandCWsourcimagingsystmThoughthHRrconstructionffctdmandsfurthranalysisquantitatily,thispaprproidsonpossibloptionforHRtrahrtzimaginginthnarfuturThisworkwassupportdbythInnoatiProjctofthChinsAcadmyofScincs(grantnoYYYJ11234),th“HundrdsofTalntsPrograms”ofthChinsAcadmyofScincs(grantnoJ08029),andthCASSAFEAIntrnationalPartnrshipProgramforCratiRsarchTamsRfrncs1BBHuandMCNuss,“Imagingwithtrahrtzwas,”OptLtt20,1716–1718(1995)2DMMittlman,RHJacobsn,andMCNuss,“Trayimaging,”IEEEJSlTopQuantumElctron2,679–692(1996)3JFFdrici,BSchulkin,FHuang,DGary,RBarat,FOliira,andDZimdars,“THzimagingandsnsingforscurityapplications—xplosis,waponsanddrugs,”SmicondSciTchnol20,S266–S280(2005)4XCZhang,“Trahrtzwaimaging:horizonsandhurdls,”PhysMdBiol47,3667–3677(2002)5BRHunt,“Suprrsolutionofimagry:undrstandingthbasisforrcoryofspatialfrquncisbyondthdiffractionlimit,”ProcIEEE99,243–248(1999)6SCPark,MKPark,andMGKang,“Suprrsolutionimagrconstruction:atchnicaloriw,”IEEESignalProcssMag20,21–36(2003)7TJCui,WCChw,XXYin,andWHong,“Studyofrsolutionandsuprrsolutioninlctromagnticimagingforhalfspacproblms,”IEEETransAntnnPropag52,1398–1411(2004)8RCHardi,KJBarnard,JGBognar,EEArmstrong,andEAWatson,“Highrsolutionimagrconstructionfromasquncofrotatdandtranslatdframsanditsapplicationtoaninfrardimagingsystm,”OptEng37,247–260(1998)9SBakrandTKanad,“Limitsonsuprrsolutionandhowtobrakthm,”IEEETransPattrnAnal24,1167–1183(2002)10DKrn,SPlg,andRBrada,“Imagsquncnhancmntusingsubpixldisplacmnts,”inProcdingsofComputrVisionandPattrnRcognition(CVPR)(IEEE,1988),pp742–74611HUrandDGross,“Improdrsolutionfromsubpixlshiftdpicturs,”CVGIP:GraphModlsImagProcss54,181–186(1992)12MKNgandNKBos,“Mathmaticalanalysisofsuprrsolutionmthodology,”IEEESignalProcssMag20,62–74(2003)13MEladandAFur,“Rstorationofasinglsuprrsolutionimagfromsralblurrd,noisy,andundrsampldmasurdimags,”IEEETransImagProcss6,1646–1658(1997)14SBormanandRLStnson,“Suprrsolutionfromimagsquncsariw,”inProcdingsofMidwstSymposiumonCircuitsandSystms(IEEE,1998)15MVanExtrandDRGrischkowsky,“Charactrizationofanoptolctronictrahrtzbamsystm,”IEEETransMicrowThoryTch38,1684–1691(1990)16PUhdJpsn,RHJacobsn,andSRKiding,“Gnrationanddtctionoftrahrtzpulssfrombiasdsmiconductorantnnas,”JOptSocAmB13,2424–2436(1996)17GGallotandDGrischkowsky,“Elctroopticdtctionoftrahrtzradiation,”JOptSocAmB16,1204–1212(1999)18PCMPlankn,HKNinhuys,HJBakkr,andTWnckbach,“MasurmntandcalculationofthorintationdpndncoftrahrtzpulsdtctioninZnT,”JOptSocAmB18,313–317(2001)19HStarkandPOskoui,“Highrsolutionimagrcoryfromimagplanarrays,usingconxprojctions,”JOptSocAmA6,1715–1726(1989)20ABuads,BColl,andJMMorl,“Anonlocalalgorithmforimagdnoising,”inProcdingsofComputrVisionandPattrnRcognition(IEEE,2005)ol2,pp60–6521ABuads,BColl,andJMMorl,“Ariwofimagdnoisingalgorithms,withanwon,”MultiscalModlSimul4,490–530(2005)22YLi,LLi,AHllicar,andYJGuo,“Suprrsolutionrconstructionoftrahrtzimags,”ProcSPIE6949,69490J(2008)23SHDing,QLi,RYao,andQWang,“Highrsolutiontrahrtzrflctiimagingandimagrstoration,”ApplOpt49,6834–6839(2010)24QLi,QYin,RYao,SDing,andQWang,“Continuouswatrahrtzscanningimagrsolutionanalysisandrstoration,”OptEng49,037007(2010)25LXu,WFan,andJLiu,“Supprssionoffluctuationffctintrahrtzimagingusinghomomorphicfiltring,”ChinOptLtt11,081201(2013)26SMallat,AWaTourofSignalProcssingThSparsWay,3rdd(Elsir,2009)27LCPickup,DPCapl,SJRobrts,andAZissrman,“Baysianmthodsforimagsuprrsolution,”ComputJ52,101–113(2009)28HShn,LPZhang,BHuang,andPLi,“AMAPapproachforjointmotionstimation,sgmntation,andsuprrsolution,”IEEETransImagProcss16,479–490(2007)20Nombr2014Vol53,No33APPLIEDOPTICS7897