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Non-local Sparse Models for Image Restoration - Département d ...

Non-local Sparse Models for Image Restoration - Département d ...

Non-local Sparse Models for Image Restoration - Département d

Non-localSparseModelsforImageRestoration JulienMairal 1,5 FrancisBach 1,5 JeanPonce 2,5 GuillermoSapiro 3 AndrewZisserman 2,4,5 1 INRIA 2 EcoleNormaleSupérieure 3 UniversityofMinnesota 4 OxfordUniversity Abstract We propose in this paper to unify two different approachestoimagerestoration:Ontheonehand,learninga basisset(dictionary)adaptedtosparsesignaldescriptions hasproventobeveryeffectiveinimagereconstructionand classificationtasks.Ontheotherhand,explicitlyexploiting theself-similaritiesofnaturalimageshasledtothesuccessfulnon-localmeansapproachtoimagerestoration.Weproposesimultaneoussparsecodingasaframeworkforcombiningthesetwoapproachesinanaturalmanner. Thisis achievedbyjointlydecomposinggroupsofsimilarsignals onsubsetsofthelearneddictionary. Experimentalresults inimagedenoisinganddemosaickingtaskswithsynthetic andrealnoiseshowthattheproposedmethodoutperforms thestateoftheart,makingitpossibletoeffectivelyrestore rawimagesfromdigitalcamerasatareasonablespeedand memorycost. 1.Introduction Thispaperaddressestheproblemofreconstructingand enhancingacolorimagegiventhenoisyobservationsgatheredbyadigitalcamerasensor. Today,withadvancesin sensordesign,thesignalisrelativelycleanfordigitalSLRs atlowsensitivities,butitremainsnoisyforconsumer-grade andmobile-phonecamerasathighsensitivities(low-light and/orhigh-speedconditions). Therestorationproblemis thusstillofacuteandinfactgrowingimportance(e.g., [3,7,11,15]),andwepresentanovellearnedimagemodel thatoutperformsthestateoftheartindenoisinganddemosaickingtasksonimageswithrealandsyntheticnoise. Thismodelshouldalsoproveofinterestindeblurringand inpaintingtasksthathavebecomethetopicofmuchrecent research(e.g.,[2,6,23])withtheemergenceofcomputationalphotography. Workingwithnoisyimagesrecorded bydigitalcamerasisdifficultsincedifferentdevicesproducedifferentkindsofnoise,andintroducedifferenttypes ofartefactsandspatialcorrelationsinthenoiseasare- 5 WILLOWproject,Laboratoired’Informatiquedel’EcoleNormale Supérieure,ENS/INRIA/CNRSUMR8548. sultofinternalpost-processing(demosaicking,whitebalance,etc.). Inthispaper,weoperatedirectlyontheraw sensoroutput,thatsuffersfromnon-homogeneousnoise, butislessspatiallycorrelatedandnotcorruptedbypostprocessingartefacts. Inturn,thisrequiresdemosaicking therawsignal—thatis,reconstructingafullcolorimage fromthesensor’sRGB(Bayer)pattern—adifficultprobleminitself.Whereasdemosaickingisusuallytackledusinginterpolation-basedmethods[13,20,32],muchofthe denoisingefforthasbeenaimedatfindingagoodmodel fornaturalimages. Earlyworkreliedonvarioussmoothnessassumptions—suchasanisotropicfiltering[21],total variation[25],orimagedecompositionsonfixedbasessuch aswavelets[17]forexample. Morerecentapproachesincludenon-localmeansfiltering[3],whichexploitsimage self-similarities,learnedsparsemodels[11,15],Gaussian scalemixtures[22],fieldsofexperts[24],andblockmatchingwith3Dfiltering(BM3D)[7].Inthispaper,weviewbothdenoisinganddemosaickingasimagereconstructionproblems,andproposeanovel imagemodelthatcombinestwonowclassicaltechniques intoasingleframework:Thenon-localmeansapproachto imagerestorationexplicitlyexploitsself-similaritiesinnaturalimages[3,10]toaverageoutthenoiseamongsimilarpatches,whereassparsecodingencodesnaturalimage statisticsbydecomposingeachimagepatchintoalinear combinationofafewelementsfromabasissetcalledadictionary. 1 Althoughfixeddictionariesbasedonvarioustypes ofwavelets[17]havebeenusedinthissetting,sparsedecompositionsbasedonlearned,possiblyovercomplete,dictionariesadaptedtospecificimageshavebeenshowntoprovidebetterresultsinpractice[11,15].Weproposetoextend andcombinethesetwoapproachesbyusingsimultaneous sparsecoding[28,29,31]toimposethatsimilarpatches sharethesamedictionaryelementsintheirsparsedecomposition.Tothebestofourknowledge,thisisthefirsttimethatthecorrespondingmodelsofimageself-similaritiesareexplicitlyusedinacommonsettingwithlearneddictionaries (theBM3Dprocedure[7]exploitsbothself-similaritiesand sparsityforthedenoisingtask,butitisbasedonclassical, 1 Theusageoftheword“basis”isslightlyabusiveheresincetheelementsofthedictionariesarenot(apriori)necessarilyindependent.

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