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1、MaximumEntropyDeconvolutionofInfraredSpectra:UseofaNovelEntropyExpressionWithoutSignRestrictionVIÂCTORA.LOÂRENZ-FONFRIÂA*andESTEVEPADROÂSUnitatdeBiofõÂsica.DepartamentdeBioquõÂmicaideBiologiaMolecular,FacultatdeMedicina,UniversitatAutoÁnomadeBarcelona,08193Bellaterr
2、a,Barcelona,SpainAbsorbanceanddifferenceinfraredspectraareoftenacquiredaim-plexLaplacetransform,3linearpredictionbyautoregres-ingtocharacterizeproteinstructureandstructuralchangesofpro-sivemodeling,4±6wavelet-transform,7,8anddeconvolu-teinsuponligandbinding,aswellas
3、formanyotherchemicalandtion.biochemicalstudies.Theiranalysisrequiresasa®rststeptheiden-Deconvolutionhasbecomeoneofthemostusedmeth-ti®cationofthecomponentbands(number,position,andarea)andodsfornarrowingpurposes.Deconvolutionisanunstableasasecondsteptheirassignment.Th
4、e®rststepoftheanalysisisprocessanddifferentstrategiesforthestabilizationofthechallengedbythehabituallystrongbandoverlapininfraredspec-tra.Therefore,itisusefultomakeuseofamathematicalmethoddeconvolutedsolutionhavebeenproposed,namely,theuseofasmoothing®lterinFourierde
5、convolution;1,9±12abletonarrowthecomponentbandstotheextenttoeliminate,oratleastreduce,thebandoverlap.Additionally,tobeofgeneralthecombinationofdeconvolutionandlinearprediction;13±16applicabilitythismethodshouldpermitnegativevaluesfortheso-thecombinationofFourierdeco
6、nvolutionandwaveletlution.Wepresentamaximumentropydeconvolutionapproachfortransform;17,18iterativedeconvolutionwithconstraints,theband-narrowingofabsorbanceanddifferencespectrashowingalsoknownasmaximumlikelihoodrestoration;19±21andtherequiredcharacteristics,whichuse
7、sthegeneralizednegativetheapplicationofinversiontheory,inwhichweincludeBurg-entropy(Itakura±SaõÈtodiscrepancy)generalizedfordiffer-19,22relatedmethodslikeregularizationandprobabilisticencespectra.Wepresentresultsonsyntheticnoisyabsorbanceand(Bayesian)methods.23diffe
8、rencespectra,aswellasonexperimentalinfraredspectrafromthemembraneproteinbacteriorhodopsin.Regularizedandprobabilisticmethodsconsiderthede-
