BLIND SEPARATION AND DECONVOLUTION FOR REAL CONVOLUTIVE MIXTURE OF TEMPORALL Y CORRELATED ACOUSTIC

Weproposeanew novel two-stageblindseparationanddeconvolution (BSD) algorithmfor a realconvolutivemixtureof temporally correlatedsignals,in which a new Single-InputMultiple-Output (SIMO)-model-basedICA (SIMO-ICA) and blind multichannel inversefiltering are combined. SIMO-ICA consistsof multiple ICAs anda fidelity controller, andeachICA runsin parallelunder fidelity control of the entire separationsystem. SIMO-ICA canseparatethe mixed signals,not into monauralsourcesignals but into SIMO-model-basedsignalsfrom independent sourcesas they areat themicrophones.Thus,theseparatedsignalsof SIMOICA canmaintainthespatialqualitiesof eachsoundsource.After theseparationby SIMO-ICA, a simpleblind deconvolution techniquebasedon multichannelinversefiltering for theSIMO model canbeappliedevenwhenthemixing systemis thenonminimum phasesystemandeachsourcesignalis temporallycorrelated.The experimentalresultsobtainedunderthe reverberantconditionrevealthatthesoundqualityof theseparatedsignalsin theproposed methodis superiorto thatin theconventionalICA-basedBSD. 1. INTR ODUCTION Blind separationand deconvolution (BSD) of sourcesis an approachtakento estimateoriginal sourcesignalsusingonly theinformationof mixed signalsobserved in eachinput channel.The differencebetweentheBSD andblind sourceseparation(BSS)of the convolutive mixture [1, 2] is that not only the sourceseparation but alsothe deconvolution of the transmissionchannelcharacteristicsareconsideredin the BSD framework. Therefore,the BSD techniqueis highly applicableto robust hands-freespeech recognitionsystems,wherethedistortiondueto theroomtransfer function shouldbe reduced.For the BSD basedon independent componentanalysis(ICA), variousmethodshave beenproposed to dealwith theseparationanddeconvolution for theconvolutive mixtureof independently , identicallydistributed(i.i.d.) sourcesignals[3, 4]. TheseBSD methodsrequirethespecificassumptions that thesourcesignalsaremutually independent andeachsource signalis alsotemporallyindependent. However, thelatterassumption doesnot hold, particularly in many practicalacousticmixturesof soundsignalswhich often correspondto the temporally correlatedsignals.Theapplicationof theconventionalICA-based BSDto speechoftenyieldsthenegativeresults,e.g.,theseparated speechis adverselydecorrelatedandwhitened[5]. In order to solve the problem,we proposea novel BSD approachthatcombinesinformation-geometrytheoryandmultichannelsignalprocessing. In thisapproach, theseparation-decon volution problemis resolved into two stages:the Single-InputMultipleOutput(SIMO)-model-basedseparationandthedeconvolution in the SIMO-modelframework. Here the term “SIMO” represents the specific transmissionsystemin which the input is a single sourcesignalandtheoutputsareits transmittedsignalsobservedat multiple sensors.First,we proposea new blind separationframework usinga SIMO-model-basedICA algorithm,SIMO-ICA. In the SIMO-ICA scenario,unknown multiple sourcesignalswhich aremixed throughunknown acousticaltransmissionchannelsare detectedat the microphones,andthesesignalscanbe separated, not into monauralsourcesignalsbut into SIMO-model-basedsignals from independentsourcesas they are at the microphones. Thus,theseparatedsignalsof SIMO-ICA canmaintainthespatial qualitiesof eachsoundsource.After theseparationby theSIMOICA, a simpleblind deconvolution techniquebasedon themultichannelinversefiltering for theSIMO modelcanbeapplied.In the proposedmethod,the separation/decon volution problemscanbe solved efficiently usingthe following reasonableassumptionand properties.(1) Theassumptionof themutualindependence among the acousticsoundsourcesusuallyholds,andconsequently , this canbeusedin theSIMO-ICA-basedseparation. (2) Thetemporalcorrelationpropertyof the sourcesignalsand the nonminimum phasepropertyof themixing systemcanbetaken into accountin theblind multichannelinversefiltering. Thus,theproposedalgorithm canprovide a morefeasibleperformancefor theseparation anddeconvolutionof realacousticsignals,comparedwith theconventionalICA-basedBSD.This canbeconfirmedfrom theexperimentalresultsobtainedundertherealreverberantcondition. 2. MIXING PROCESSAND CONVENTION AL BSD 2.1. Mixing process In this study, the numberof arrayelements(microphones)is andthenumberof multiplesoundsourcesis . In general,theobservedsignalsin which multiple sourcesignalsaremixedlinearly areexpressedas ! " $#% & (' (1) where is thesourcesignalvector, is theobservedsignal vector, is themixing filter matrix with the lengthof ) , and " $#* is thez-transformof ; thesearegivenas + , ('(./.0. '1-324 6587 ' (2) 9 + , : ('/./.;. ' :&<= 65 7 ' (3) > , ?A@;BC 65 @;B ' (4) D $#* + , EF@;BC $#* 65 @;B HG ?A@;BC I# *J @;B ' (5)