201001-Best Basis Compressed Sensing

《201001-Best Basis Compressed Sensing》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、Authormanuscript,publishedin"IEEETransactionsonSignalProcessing(2010)?"DOI:10.1109/TSP.2010.20424901BestBasisCompressedSensingGabrielPeyre,´Member,IEEEAbstract—Thispaperproposesabestbasisextensionofcom-strategycanbeusedinMRIimaging[6]toreducethepressedsensingrecovery.Insteadofregularizingthecompre

2、ssedacquisitiontimeandincreasethespatialresolution.sensinginverseproblemwithasparsitypriorinafixedbasis,ourframeworkmakesuseofsparsityinatree-structureddictionaryoforthogonalbases.AnewiterativethresholdingB.BestBasisRepresentationsalgorithmperformsboththerecoveryofthesignalandtheestimationofthebest

3、basis.TheresultingreconstructionfromSparseapproximationinorthogonalbasesisattheheartofcompressivemeasurementsoptimizesthebasistothestructureofmanyefficientcompressionanddenoisingalgorithms.Fixedthesensedsignal.Adaptivityiscrucialtocapturetheregularityorthogonalbasesarehowevernotflexibleenoughtocaptu

4、reofcomplexnaturalsignals.Numericalexperimentsonsoundsthecomplexregularityofsoundsornaturalimages.Forandgeometricalimagesindeedshowthatthisbestbasissearchinstancetheorthogonalwavelettransformdoesnotcompressimprovestherecoverywithrespecttofixedsparsitypriors.efficientlyregularedges[7],[8]andafixedloca

5、lcosinebasisIndexTerms—Compressedsensing,bestbasis,sparsity,waveletfailstocapturetransientpartsofmusicalsounds[9].packets,cosinepackets,bandlets.Toimprovethesparsityofcomplicatedsoundsorimages,onecanconsiderseveralorthogonalbasesthatcomposealargeI.INTRODUCTIONdictionaryofatoms.Inthisframework,oneh

6、astochooseOMPRESSEDsensingisanewsamplingstrategythatabestbasisadaptedtothesignaltoprocess.ToenablefastCusesafixedsetoflinearmeasurementstogetherwithcomputation,thisdictionaryisrequiredtohaveatreestructure,anon-linearrecoveryprocess.Inorderforthisschemetosothatthebestbasiscanbeoptimizedusingafastdyn

7、amicworkwithalownumberofmeasurements,compressedsensingprogrammingalgorithm.theoryrequiresthesensedsignaltobesparseinagivenLocalcosinebases[9]dividethetimeaxisinsegmentsthatorthogonalbasisandthesensingvectorstobei