简介：Westartfromarealistichalfspacemodelforthermalimaging,whichwethenusetodevelopamathematicalasymptoticanalysiswellsuitedforthedesignofreconstructionalgorithms.Weseektoreconstructthermalanomaliesonlythroughtheirroughfeatures.Withthiswayourproposedalgorithmsarestableagainstmeasurementnoiseandgeometryperturbations.Basedonrigorousasymptoticestimates,wefirstobtainanapproximationforthetemperatureprofilewhichwethenusetodesignnoniterativedetectionalgorithms.Weshowonnumericalsimulationsevidencethattheyareaccurateandrobust.Moreover,weprovideamathematicalmodelforultrasonictemperatureimaging,whichisanimportanttechniqueincanceroustissueablationtherapy.

简介：Itisknownfromclassicaldifferentialgeometrythatonecanreconstructacurvewith(n-1)prescribedcurvaturefunctions,ifthesefunctionscanbedifferentiatedacertainnumberoftimesintheusualsenseandifthefirst(n-2)functionsarestrictlypositive.ItisestablishedherethatthisresultstillholdsundertheassumptionthatthecurvaturefunctionsbelongtosomeSobolevspaces,byusingthenotionofderivativeinthedistributionalsense.ItisalsoshownthatthemappingwhichassociateswithsuchprescribedcurvaturefunctionsthereconstructedcurveisofclassC∞.

简介：Amodifiedpolynomialpreservinggradientrecoverytechniqueisproposed.Unlikethepolynomialpreservinggradientrecoverytechnique,thegradientrecoveredwiththemodifiedpolynomialpreservingrecovery(MPPR)isconstructedelement-wise,anditisdiscontinuousacrosstheinterioredges.OneadvantageoftheMPPRtechniqueisthattheimplementationiseasierwhenadaptivemeshesareinvolved.SuperconvergenceresultsofthegradientrecoveredwithMPPRareprovedforfiniteelementmethodsforellipticboundaryproblemsandeigenvalueproblemsunderadaptivemeshes.TheMPPRisappliedtoadaptivefiniteelementmethodstoconstructasymptoticexactaposteriorierrorestimates.Numericaltestsareprovidedtoexaminethetheoreticalresultsandtheeffectivenessoftheadaptivefiniteelementalgorithms.

简介：AconvexvariationalformulationisproposedtosolvemulticomponentsignalprocessingproblemsinHilbertspaces.Thecostfunctionconsistsofaseparableterm,inwhicheachcomponentismodeledthroughitsownpotential,andofacouplingterm,inwhichconstraintsonlineartransformationsofthecomponentsarepenalizedwithsmoothfunctionals.Analgorithmwithguaranteedweakconvergencetoasolutiontotheproblemisprovided.Variousmulticomponentsignaldecompositionandrecoveryapplicationsarediscussed.

简介：AlthoughGaussianrandommatricesplayanimportantroleofmeasurementmatricesincompressedsensing,onehopesthatthereexistotherrandommatriceswhichcanalsobeusedtoserveasthemeasurementmatrices.Hence,Weibullrandommatricesinduceextensiveinterest.Inthispaper,wefirstproposethel2,qrobustnullspacepropertythatcanweakentheD-RIP,andshowthatWeibullrandommatricessatisfythel2,qrobustnullspacepropertywithhighprobability.Besides,weprovethatWeibullrandommatricesalsopossessthelqquotientpropertywithhighprobability.Finally,withthecombinationoftheabovementionedproperties,wegivetwoimportantapproximationcharacteristicsofthesolutionstothelq-minimizationwithWeibullrandommatrices,oneisonthestabilityestimatewhenthemeasurementnoisee∈Rnneedsapriori‖e‖2≤,theotherisontherobustnessestimatewithoutneedingtoestimatetheboundof‖e‖2.TheresultsindicatethattheperformanceofWeibullrandommatricesissimilartothatofGaussianrandommatricesinsparserecovery.

简介：Inthispaper,westudyoptimalrecovery(reconstruction)offunctionsonthesphereintheaveragecasesetting.WeobtaintheasymptoticordersofaveragesamplingnumbersofaSobolevspaceonthespherewithaGaussianmeasureintheLd-1q(S)metricfor1≤q≤∞,andshowthatsomeworst-caseasymptoticallyoptimalalgorithmsarealsoasymptoticallyoptimalintheaveragecasesettingintheLdq(S-1)metricfor1≤q≤∞.

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简介：Inthispaper,wepresentatheoreticalanalysisforlinearfiniteelementsuperconvergentgradientrecoveryonPar6mesh,thedualofwhichiscentroidalVoronoitessellationswiththelowestenergyperunitvolumeandisthecongruentcellpredictedbythethree-dimensionalGersho'sconjecture.Weshowthatthelinearfiniteelementsolutionu_handthelinearinterpolationu_1havesuperclosegradientonPar6meshes.Consequently,thegradientrecoveredfromthefiniteelementsolutionbyusingthesuperconvergencepatchrecoverymethodissuperconvergentto▽u.Anumericalexampleispresentedtoverifythetheoreticalresult.