Least squares generalized B-spline signal and image processing

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1、SignalProcessing81(2001)2005}2017LeastsquaresgeneralizedB-splinesignalandimageprocessingRutuparnaPanda
,B.N.Chatterji*DepartmentofElectronicsandElectricalCommunicationEngineering,IndianInstituteofTechnology,Kharagpur721302,IndiaReceived20February1997;receivedinrevisedform11January2001Abst

2、ractThispaperpresentsgeneralizedB-splineinterpolationandapproximationtechniques.The"rstpartofthispaperdescribesatechniqueforthecontinuousrepresentationofdiscretesignalsintermsofgeneralizedB-splines(directB-splinetransform)andforinterpolativesignalreconstruction(indirectB-splinetransform)w

3、ithanexpansionfactorm.ThekeytoourapproachistouseafamilyofgeneralizedB-spline"lters.Ithasbeenshownthatthescalefactorcanbemodi"edtotunetheapproximated"lterbandwidths.Thesecondpartofthispapermakesuseoftheseresultstodescribeanequivalent"lteringinterpretation(low-pass"lteringfollowedbyageneral

4、izedB-splineinterpolator)ofgeneralizedB-splinestogetherwithleastsquaresgeneralizedB-splinesignalapproximationmethods.Thispartalsoconcernwithnewtheoreticalresultsshowingfactorizationofthetransferfunctionsofthehigherdegree(n'3)generalizedB-spline"lters.Experimentally,itisseenthatdatacompres

5、sionwithreducedamountoferrorcanbeachievedusingtheseleastsquaresgeneralizedB-spline"lteringtechniques.
2001ElsevierScienceB.V.Allrightsreserved.Keywords:GeneralizedB-spline"ltering;LeastsquaresgeneralizedB-splines;Signalprocessing;Imageprocessing;Recursive"ltering1.Introductionevaluatethed

6、irectorindirectB-splinetransforms[1,8}11].Unseretal.havealsopresentedtheB-splinesignalrepresentationandinterpolationtheoryofleastsquarescubicB-splinesignalap-methodsarefoundincreasinglypopularduetotheproximationtechniquewhichisanextensionoftheadventofmultiresolutiontechniques[4,5].Unserst

7、andardleastsquaresapproximationtechniqueetal.havedescribedthegeneralcaseofB-splineproposedbyCarldeBoor[3],andtheyhaveusedinterpolationofanyorderandhaveprovidedthistechniquefordi!erentimageprocessingap-mechanismsforthee$cientdesignof"lterstoplications[9,10].Wehavebee