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1、IEEETRANSACTIONSONMEDICALIMAGING,VOL.30,NO.9,SEPTEMBER20111649AFastWavelet-BasedReconstructionMethodforMagneticResonanceImagingM.Guerquin-Kern*,M.Häberlin,K.P.Pruessmann,andM.UnserAbstract—Inthiswork,weexploitthefactthatwaveletscanThecommonandgenericapp
2、roachtoalleviatetherecon-representmagneticresonanceimageswell,withrelativelyfewstructionproblemistotreatthetaskasaninverseproblem[1].Incoefficients.Weusethispropertytoimprovemagneticresonancethisframework,ill-posednessduetoareducedsamplingdensityimaging(
3、MRI)reconstructionsfromundersampleddatawithisovercomebyintroducingproperregularizationconstraints.arbitraryk-spacetrajectories.ReconstructionisposedasanoptimizationproblemthatcouldbesolvedwiththeiterativeTheyassumeandexploitadditionalknowledgeabouttheob
4、-shrinkage/thresholdingalgorithm(ISTA)which,unfortunately,jectunderinvestigationtorobustifythereconstruction.convergesslowly.Tomaketheapproachmorepractical,weEarliertechniquesusedaquadraticregularizationterm,proposeavariantthatcombinesrecentimprovements
5、inconvexleadingtosolutionsthatexhibitalineardependenceupontheoptimizationandthatcanbetunedtoagivenspecifick-spacemeasurements.Unfortunately,inthecaseofsevereundersam-trajectory.Wepresentamathematicalanalysisthatexplainstheperformanceofthealgorithms.Using
6、simulatedandinvivodata,pling(i.e.,locallylowsamplingdensity)anddependingontheweshowthatournonlinearmethodisfast,asitacceleratesISTAstrengthofregularization,thereconstructedimagesstillsufferbyalmosttwoordersofmagnitude.Wealsoshowthatitremainsfromnoisepro
7、pagation,blurring,ringing,oraliasingerrors.ItcompetitivewithTVregularizationintermsofimagequality.iswellknowninsignalprocessingthattheblurringofedgesIndexTerms—Compressedsensing,fastiterativeshrinkage/canbereducedviatheuseofnonquadraticregularization.In
8、thresholdingalgorithm(FISTA),fastweightediterativeshrinkage/particular,-waveletregularizationhasbeenfoundtooutper-thresholdingalgorithm(FWISTA),iterativeshrinkage/thresh-formclassicallinearalgorithmssuchasWienerfilteringintheoldin
