Efficient Minimization Method for a Generalized

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1、322IEEETRANSACTIONSONIMAGEPROCESSING,VOL.18,NO.2,FEBRUARY2009EfficientMinimizationMethodforaGeneralizedTotalVariationFunctionalPaulRodríguezandBrendtWohlbergAbstract—ReplacingthedatafidelitytermofthestandardAsignificantrecentdevelopmenthasbeentousethenormTotalVariation(TV)functionalwithand

2、atafidelitytermhasforthefidelityterm,correspondingtochoosinginbeenfoundtoofferanumberoftheoreticalandpracticalbene-(1).This-TVfunctional[7]–[10]hasattractedattentionduefits.Efficientalgorithmsforminimizingthis-TVfunctionalhavetoanumberofadvantages,includingsuperiorperformancewithonlyrecently

3、beguntobedeveloped,thefastestofwhichexploitgraphrepresentations,andarerestrictedtothedenoisingproblem.impulsenoise[11].WedescribeanalternativeapproachthatminimizesageneralizedTheIterativelyReweightedNorm(IRN)algorithmpresentedTVfunctional,includingboth-TVand-TVasspecialcases,hereminimiz

4、esthegeneralizedTVfunctional(1),whichin-andiscapableofsolvingmoregeneralinverseproblemsthande-cludesthe-TVand-TVasspecialcases,byrepresentingthenoising(e.g.,deconvolution).Thisalgorithmiscompetitivewiththeandnormsbytheequivalentweightednorms.Thisal-graph-basedmethodsinthedenoisingcase,and

5、isthefastestalgo-rithmofwhichweareawareforgeneralinverseproblemsinvolvinggorithmiscomputationallyefficientaswellassimpletounder-anontrivialforwardlinearoperator.standandimplement.InthispaperweexpandonourpreviousIndexTerms—Imagerestoration,inverseproblem,regulariza-results[12],[13]andprovid

6、eadetailedanalysisoftheIRNal-tion,totalvariation.gorithm,includingproofofconvergence,thedevelopmentofanInexactNewton(IN)method[14]–[16],andstrategiesforset-tingalgorithm-specificparameters.I.INTRODUCTIONII.ALGORITHMSFOR-TVAND-TVOTALVARIATION(TV)regularizationhasevolvedfromInthissection,wep

7、rovideasummaryofthemostimportantTanimagedenoisingmethod[1]intoamoregeneraltech-algorithmsforminimizingthe-TVand-TVfunctionals.Inniqueforinverseproblems[2],includingdeblurring[3],[4],general,thereareseveraltypesofnumericalalgorithms,basedblinddeconvolution[5],andinpa