频率域Bregman自适应稀疏脉冲反褶积方法（英文）-豆柴文库

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频率域Bregman自适应稀疏脉冲反褶积方法（英文）
FrequencyDomainBregmanAdaptiveSparsePulseDeconvolutionMethod
Introduction
Pulsedeconvolutionisawidelyusedtechniqueinsignalprocessingforrecoveringtheoriginalsignalfromadistortedorconvolvedsignal.Themostcommonapproachtopulsedeconvolutionisbyusingatime-domainfilter,whichcanbesensitivetonoiseandcancreateringingartifactsintherecoveredsignal.Toovercometheseissues,afrequency-domainapproachhasbeendeveloped.Oneofthemostpromisingfrequency-domaintechniquesistheBregmanAdaptiveSparsePulseDeconvolution(BASPD)method,whichhasdemonstratedgoodresultsinsparsesignalswithlownoiselevels.
TheBASPDmethodisbasedontheBregmaniterationprocess,whichusesanauxiliaryvariabletofindthesparsestsolutiontoanoptimizationproblem.Theapproachisparticularlyeffectiveinsparsesignalrecovery,wherethesparsityconstraintisimposedonthesignal.ThispaperpresentstheFrequencyDomainBregmanAdaptiveSparsePulseDeconvolution(FD-BASPD)technique,whichextendstheBASPDmethodtothefrequencydomaintoimproveitsapplicabilityandaccuracyindeconvolvingsignals.
Methodology
ThefrequencydomainimplementationoftheBASPDmethodinvolvesthreestages.First,theFouriertransformisappliedtothesignalandtoasparsepulsefilter.TheFouriertransformisusedtoconvertthesignalandfilterfromtime-domaintofrequencydomain,whichallowstheconvolvedsignaltoberepresentedasaproductofthesignalandfilterinthefrequencydomain.Second,theresultingfrequencydomainproblemissolvedusingtheBregmaniterationprocesstofindthesparsestsolution.Anauxiliaryvariableisusedtoseparatethesignalandfilterandimposesparsityconstraints.Finally,theinverseFouriertransformisappliedtotherecoveredsignalinthefrequencydomaintoobtainthedeconvolvedsignalinthetimedomain.
TheFD-BASPDmethodhasseveraladvantagesovertraditionaltime-domain-basedtechniques.Firstly,becauseitisbasedinthefrequencydomain,itislesssensitivetonoiseandabletodealwithallthefrequencycomponentsofthesignal.Secondly,becauseitusesasparsepulsefilter,itisbetteratpreservingthehigh-frequencycontentofsignals,whichistypicallylostintra