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1、6958IEEETRANSACTIONSONINFORMATIONTHEORY,VOL.57,NO.10,OCTOBER2011BlindCompressedSensingSivanGleichmanandYoninaC.Eldar,SeniorMember,IEEEAbstract—ThefundamentalprincipleunderlyingcompressedInprinciple,recoveryfromcompressedmeasurementsissensingisthatasignal,whichissparseund
2、ersomebasisrep-NP-hard.Nonetheless,manysuboptimalmethodshavebeenresentation,canberecoveredfromasmallnumberoflinearproposedtoapproximateitssolution[1],[2],[4][6].Thesemeasurements.However,priorknowledgeofthesparsitybasisalgorithmsrecoverthetruevalueofwhenissufficientlyises
3、sentialfortherecoveryprocess.Thisworkintroducesthesparseandthecolumnsofareincoherent[3],[5],[12],conceptofblindcompressedsensing,whichavoidstheneedtoknowthesparsitybasisinboththesamplingandtherecovery[13].However,allknownrecoveryapproachesusethepriorprocess.Wesuggestthre
4、epossibleconstraintsonthesparsitybasisknowledgeofthesparsitybasis.thatcanbeaddedtotheprobleminordertoguaranteeauniqueDictionarylearning(DL)[15][18]isanotherapplicationofsolution.Foreachconstraint,weproveconditionsforuniqueness,sparserepresentations.InDL,wearegivenasetoft
5、rainingsig-andsuggestasimplemethodtoretrievethesolution.Wedemon-nals,formallythecolumnsofamatrix.Thegoalistofindstratethroughsimulationsthatourmethodscanachieveresultsadictionary,suchthatthecolumnsofaresparselyrepre-similartothoseofstandardcompressedsensing,whichrelyonsen
6、tedaslinearcombinationsofthecolumnsof.In[15],thepriorknowledgeofthesparsitybasis,aslongasthesignalsaresparseenough.ThisoffersageneralsamplingandreconstructionauthorsstudyconditionsunderwhichtheDLproblemyieldsasystemthatfitsallsparsesignals,regardlessofthesparsitybasis,uni
7、quesolutionforagiventrainingset.undertheconditionsandconstraintspresentedinthiswork.Inthisworkweintroducetheconceptofblindcompressedsensing(BCS),inwhichthegoalistorecoverahigh-dimen-IndexTerms—Blindreconstruction,compressedsensing,dictio-sionalvectorfromasmallnumberofmea
8、surements,wherenarylearning,sparserepresentation.theonlyprioristhatthereexistssomebasisinwhichissparse.
