提高超声成像的分辨率

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552IEEETRANSACTIONSONIMAGEPROCESSING,VOL.18,NO.3,MARCH2009

LowBit-RateImageCompressionviaAdaptive

Down-SamplingandConstrainedLeast

SquaresUpconversion

XiaolinWu,SeniorMember,IEEE,XiangjunZhang,andXiaohanWang

Abstract—Recently,manyresearchersstartedtochallengealong-standingpracticeofdigitalphotography:oversamplingfollowedbycompressionandpursuingmoreintelligentsparsesamplingtechniques.Inthispaper,weproposeapracticalap-proachofuniformdownsamplinginimagespaceandyetmakingthesamplingadaptivebyspatiallyvarying,directionallow-passpreﬁltering.Theresultingdown-sampledpreﬁlteredimagere-mainsaconventionalsquaresamplegrid,and,thus,itcanbecompressedandtransmittedwithoutanychangetocurrentimagecodingstandardsandsystems.Thedecoderﬁrstdecompressesthelow-resolutionimageandthenupconvertsittotheoriginalresolu-tioninaconstrainedleastsquaresrestorationprocess,usinga2-Dpiecewiseautoregressivemodelandtheknowledgeofdirectionallow-passpreﬁltering.Theproposedcompressionapproachofcollaborativeadaptivedown-samplingandupconversion(CADU)outperformsJPEG2000inPSNRmeasureatlowtomediumbitratesandachievessuperiorvisualquality,aswell.Thesuperiorlowbit-rateperformanceoftheCADUapproachseemstosuggestthatoversamplingnotonlywasteshardwareresourcesandenergy,anditcouldbecounterproductivetoimagequalitygivenatightbitbudget.

IndexTerms—Autoregressivemodeling,compressionstandards,imagerestoration,imageupconversion,lowbit-rateimagecom-pression,sampling,subjectiveimagequality.

I.INTRODUCTIONOVERthepasthalfcentury,theprevailingengineering

practiceofimage/videocompression,asexempliﬁedby

allexistingimageandvideocompressionstandards,istostart

withadense2-Dsamplegridofpixels.Compressionisdoneby

transformingthespatialimagesignalintoaspace(e.g.,spaces

ofFourierorwaveletbases)inwhichtheimagehasasparserep-

resentationandbyentropycodingoftransformcoefﬁcients.Re-

cently,researchersintheemergingﬁeldofcompressivesensing

challengedthewisdomofwhattheycalled“oversamplingfol-

lowedmassivedumping”approach.Theyshowed,quitesur-

prisingly,itispossible,atleasttheoretically,toobtaincompact

signalrepresentationbyagreatlyreducednumberofrandom

samples[1].

ManuscriptreceivedMarch12,2008;revisedNovember05,2008.CurrentversionpublishedFebruary11,2009.Theassociateeditorcoordinatingthere-viewofthismanuscriptandapprovingitforpublicationwasProf.BrunoCar-pentieri.TheauthorsarewiththeDepartmentofElectricalandComputerEngineering,McMasterUniversity,Hamilton,ONL8S4K1Canada(e-mail:xwu@ece.mc-master.ca;zhangxj@grads.ece.mcmaster.ca;wangx28@mcmaster.ca).Colorversionsofoneormoreoftheﬁguresinthispaperareavailableonlineathttp://ieeexplore.ieee.org.DigitalObjectIdentiﬁer10.1109/TIP.2008.2010638Inthispaper,weinvestigatetheproblemofcompactimage

representationinanapproachofsparsesamplinginthespa-

tialdomain.Thefactthatmostnaturalimageshaveanexpo-

nentiallydecayingpowerspectrumsuggeststhepossibilityof

interpolation-basedcompactrepresentationofimages.Atyp-

icalscenecontainspredominantlysmoothregionsthatcanbe

satisfactorilyinterpolatedfromasparselysampledlow-resolu-

tionimage.Thedifﬁcultyiswiththereconstructionofhighfre-

quencycontents.Ofparticularimportanceisfaithfulreconstruc-

tionofedgeswithoutlargephaseerrors,whichisdetrimentalto

perceptualqualityofadecodedimage.

Toanswertheabovechallenge,wedevelopanewimagecom-

pressionmethodologyofcollaborativeadaptivedown-sampling

andupconversion(CADU).TheCADUapproachputsanem-

phasisonedgereconstructionfortheperceptualimportanceof

edgesandalsotoexploittheanisotropyofedgespectrum.In

theCADUencoderdesign,wechoosenottoperformuneven

irregulardownsamplingofaninputimageaccordingtolocal

spatialorfrequencycharacteristics.Instead,westicktocon-

ventionalsquarepixelgridbyuniformspatialdownsampling

oftheimage.Consequently,theresultinglow-resolutionimage

canbereadilycompressedbyanyofexistingimagecompres-

siontechniques,suchasDCT-basedJPEGandJPEG2000.Yet

thesimpleuniformdown-samplingschemeismadeadaptiveby

adirectionallow-passpreﬁlteringsteppriortodown-sampling.

Theotherpurposeofthispreprocessingistoinduceamecha-

nismofcollaborationbetweenthespatialuniformdown-sam-

plingprocessattheencoderandoptimalupconversionprocess

atthedecoder.

TheCADUdecoderﬁrstdecompressesthelow-resolution

imageandthenupconvertsittotheoriginalresolutionincon-

strainedleastsquaresrestorationprocess,usinga2-Dpiece-

wiseautoregressivemodel(PAR)andbyreversingthedirec-

tionallow-passpreﬁlteringoperationoftheencoder.Two-di-

mensionalautoregressivemodelingwasaknowneffectivetech-

niqueofpredictiveimagecoding[2],[3].FortheCADUde-

coder,thePARmodelplaysaroleofadaptivenoncausalpre-

dictor.WhatisnovelanduniqueoftheCADUapproachisthat

thepredictorisonlyusedatthedecoderside,andthenoncausal

predictivedecodingisperformedincollaborationwiththepre-

ﬁlteringoftheencoder.

Fig.1presentsablockdiagramoftheproposedCADU

imagecompressionsystem,summarizingtheaboveideasand

depictingthecollaborationbetweentheencoderanddecoder.

TheCADUimagecompressiontechnique,althoughoper-

atingondown-sampledimages,obtainssomeofthebestPSNR

提高超声成像的分辨率

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