construction and optimization of discrete wavelets

《construction and optimization of discrete wavelets》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、CONSTRUCTIONANDOPTIMIZATIONOFDISCRETEWAVELETSPetkoFaberHerbertSusseFriedrich-Schiller-UniversitatJenaDepartmentofMathematicsandInformatics,DigitalImageProcessingGroupD-07740Jena,Germanypetko.faber@uni-jena.detopics:discretewavelets,construction,optimiza-2

2、.DISCRETELOCAL1DWAVELETStion,entropy2.1.GeneralapproachThefundamentaloftheinthispaperusedapproachtothediscretewavelet-transform(DWT)isahierarchicalappli-ABSTRACTcationofatransformationmatrixforanysignalf(x).Therebythedimensionofthetransformationmatrixde-T

3、hispaperpresentsthedescriptionandconstructionofdiscretewaveletswithonlyusingthedescriptionbymatri-pendsonthedimensionofthesignalf(x).cesincontrasttothemethodsknownfromtheliterature.23hhh::::::hItispossibletodenemoreclearlythecharacteristicsof012N?1ggg:::

4、:::gdiscretewavelets.Furthermore,thepossibilitiesofusing012N?16767:::hhhh:::thewavelet-transforminimage-processingarestudied.TheN?101267:::gggg:::advantagesanddisadvantagesareworkedoutandthecon-N?101267=67structionof"optimal"discretewaveletsindicationsati

5、ts.6.7.constructionaregiven.Forbetterunderstandingthefol-45hh::::::hh12N?10lowingexaminationsarejustfortheone-dimensionalcase.gg::::::gg12N?10Theextensiontothetwo-andhigher-dimensionalorderscanberealizedeasilybyformingtheCartesianproduct.Itcanbeseenfromth

6、estructureofthetransforma-Thefeatureoftheseparationoftheusedwaveletltersistionmatrixthattherstrowgeneratestherstcom-hereassumedascondition.ponentoftheresultbylteringviatheanalysislterH=(h;h;h;:::;h).Analogouslythethird,fth,012N?1andsoonrowscanbeunde

7、rstood.Theevenrowsof1.INTRODUCTIONthematrixarecalculatedbylteringviatheanalysisl-terG=(g;g;g;:::;g).012N?1IntheareaoftheimageprocessingtheanalysisofsignalsisThetransformationcorrespondstoapyramidalalgo-oneofthemostimportantprocesses.Goingoutfromtheserit

8、hm.TheresultoftheDWTisasetofsocalleddetailaregularsearchfornewprocedureswhicharearealalter-signalsd,[1jJ]withjasthelevelofdecomposi-jknativetoknownmethodsandwhichcompensateifpossibletionandktheshiftterm,andthesoca