英语翻译4.THEWAVELETTRANSFORMInthispaper,thewavelettransformisutilizedtodeterminethelocationofejectorpinsafterexecutingtheoptimizationThus,abriefdescriptionwillbegivenofthebasicsofthewavelettransforminrelationto

　　英语翻译

　　4.THEWAVELETTRANSFORM

　　Inthispaper,thewavelettransformisutilizedtodeterminethelocationofejectorpinsafterexecutingtheoptimizationThus,abriefdescriptionwillbegivenofthebasicsofthewavelettransforminrelationtotheproposedproblemWavelets[11.lg]aremathematicaltoolsforhierarchicallydecomposingfunctions.WaveletsareclassifiedintotheHaarwavelet.splinewavelet.Daubechieswavelet,etc..dependinguponthebasisfunctionThesimplestformofwavelet.theHaarbasis,wasused.One-dimensionalwavelettransformswillbeexplainedfirst,anditwillbeshownhowthesetoolscanbeusedtocompresstherepresentalionofapiecewise-constantfunction.

　　4.1one-dimensionalHaarwavelettransform

　　TheHaarbasisisthesimplestwaveletbasisTobeginwith.anexaminationwillbemadeofhowaonedimensionalfunctioncanbedecomposedusingHaarwavelets.Thealgorithmwillbedescribedlater.Togiveabriefideaofhowthewaveletworks,asimpleexamplewillbeexamined.Takeaone-dimensionalimagewitharesolutionof4pixels[9735]ThisimagecanberepresentedintheHautbasisbycomputingthewavelettransformasfollowsStartbyaveraging,andthenanewtower-resolutionimageisobtainedwiththepixelvalues[84].Clearly.someinformationhasbeenlostinthisaveraginganddown-samplingprocessInordertorecovertheoriginalBurpixelvaluesfromthetwoaveragedpixels,itisnecessarytostoresomedetailcoefficientsthatcapturethatmissinginformation.Inthepresentexample,Iwillbechosenforthefirstdetailcoefficient,sincetheaveragegthatwascomputedis1

　　lessthan9andImorethan7.Thissinglenumbermakesitpossibleedrecoverthefirsttwopixelsofouroriginalfour-pixelimageSimilarly.theseconddetailcoefficientis-1,since4+(-1)-3and4-(-1)=5.

　　Summarizing.theoriginalimagehassofarbeendecomposedintoalower-resolutionversionanddetailcoefficientsasshowninFig4Thus.usingtheonedimensionalHaarbasis,thewavelettransformoftheoriginalfour-pixelimageisgivenasinFig4.

　　Giventhetransform,itispossibletoreconstructtheimagetoanyresolutionbyrecursivelyaddingendsubtractingthedetailcoefficientsfromthelower-resolutionver