Tài liệu SEC 07 docx

VII InverseProblemsand SignalReconstruction RichardJ.Mammone RutgersUniversity 25SignalRecoveryfromPartialInformation ChristinePodilchuk Introduction • FormulationoftheSignalRecoveryProblem • LeastSquaresSolutions • Signal RecoveryusingProjectionontoConvexSets(POCS) • Row-BasedMethods • Block-BasedMethods • ImageRestorationUsingPOCS 26AlgorithmsforComputedTomography GaborT.Herman Introduction • TheReconstructionProblem • TransformMethods • FilteredBackprojection(FBP) • TheLinogramMethod • SeriesExpansionMethods • AlgebraicReconstructionTechniques(ART) • ExpectationMaximization(EM) • ComparisonofthePerformanceofAlgorithms 27RobustSpeechProcessingasanInverseProblem RichardJ.MammoneandXiaoyu Zhang Introduction • SpeechProductionandSpectrum-RelatedParameterization • Template-Based SpeechProcessing • RobustSpeechProcessing • AffineTransform • TransformationofPredic- torCoefficients • AffineTransformofCepstralCoefficients • ParametersofAffineTransform • CorrespondenceofCepstralVectors 28InverseProblems,StatisticalMechanicsandSimulatedAnnealing K.Venkatesh Prasad Background • InverseProblemsinDSP • AnalogieswithStatisticalMechanics • TheSimulated AnnealingProcedure 29ImageRecoveryUsingtheEMAlgorithm JunZhangandAggelosK.Katsaggelos Introduction • TheEMAlgorithm • SomeFundamentalProblems • Applications • Experimental Results • SummaryandConclusion 30InverseProblemsinArrayProcessing KevinR.Farrell Introduction • BackgroundTheory • NarrowbandArrays • BroadbandArrays • InverseFormula- tionsforArrayProcessing • SimulationResults • Summary 31ChannelEqualizationasaRegularizedInverseProblem JohnF.Doherty Introduction • Discrete-TimeIntersymbolInterferenceChannelModel • ChannelEqualization Filtering • Regularization • Discrete-TimeAdaptiveFiltering • NumericalResults • Conclusion 32InverseProblemsinMicrophoneArrays A.C.Surendran Introduction:DereverberationUsingMicrophoneArrays • SimpleDelay-and-SumBeamformers • MatchedFiltering • DiophantineInverseFilteringUsingtheMultipleInput-Output(MINT) Model • Results • Summary c  1999byCRCPressLLC 33SyntheticApertureRadarAlgorithms ClayStewartandVicLarson Introduction • ImageFormation • SARImageEnhancement • AutomaticObjectDetectionand ClassificationinSARImagery 34IterativeImageRestorationAlgorithms AggelosK.Katsaggelos Introduction • IterativeRecoveryAlgorithms • SpatiallyInvariantDegradation • Matrix-Vector Formulation • Matrix-VectorandDiscreteFrequencyRepresentations • Convergence • Useof Constraints • ClassofHigherOrderIterativeAlgorithms • OtherFormsof(x) • Discussion T HEREAREMANYSITUATIONSwhereadesiredsignalcannotbemeasureddirectly.The measurementmightbedegradedbyphysicallimitationsofthesignalsourceand/orbythe measurementdeviceitself.Theacquiredsignalisthusatransformationofthedesiredsignal. Theinversionofsuchtransformationsisthesubjectofthepresentchapter.Inthefollowingsections wewillreviewseveralinverseproblemsandvariousmethodsofimplementationoftheinversionor recoveryprocess.Themethodsdifferintheabilitytodealwiththespecificlimitationspresentineach application.Forexample,theaprioriconstraintofnon-negativityisimportantforimagerecovery, butnotsoforadaptivearrayprocessing.Thegoalofthefollowingsectionsistopresentthebasic approachesofinversionandsignalrecovery.Eachsectionfocusesonaparticularapplicationarea anddescribestheappropriatemethodsforthatarea. Thefirstchapter,25,isentitled“SignalRecoveryfromPartialInformation”byChristinePodilchuk. Thissectionreviewsthebasicproblemofsignalrecovery.Theideaofprojectionontoconvexsets (POCs)isintroducedasanelegantsolutiontothesignalrecoveryproblem.Theinclusionoflinear andnon-linearconstraintsareaddressed.ThePOCsmethodisshowntobeasubsetoftheset theoreticapproachtosignalestimation.Theapplicationofimageofrestorationisdescribedin detail. Chapter26isentitled“AlgorithmsforComputedTomography”byGaborT.Herman.Thissection presentsmethodstoreconstructtheinteriorsofobjectsfromdatacollectedbasedontransmittedor emittedradiation.Theproblemoccursinawiderangeofapplicationareas.Thecomputeralgorithms usedforachievingthereconstructionsarediscussed.Thebasictechniquesofimagereconstruction fromprojectionsareclassifiedinto“TransformMethods”(includingFilteredBackprojectionandthe LinogramMethods)and“SeriesExpansionMethods”(including,inparticular,theAlgebraicRecon- structionTechniquesandthemethodofExpectationMaximization).Inaddition,aperformance comparisonofthevariousalgorithmsforcomputedtomographyisgiven. Chapter27isentitled“RobustSpeechProcessingasanInverseProblem”byRichardJ.Mammone andXiaoyuZhang.Theperformanceofspeechandspeakerrecognitionsystemsissignificantly affectedbytheacousticenvironment.Thebackgroundnoiselevel,thefilteringeffectsintroducedby themicrophoneandthecommunicationchanneldramaticallyaffecttheperformanceofrecognition systems.Itisthereforecriticalthatthesespeechrecognitionsystemsbecapableofdetectingthe ambientacousticenvironmentcontinueandinversetheireffectsfromthespeechsignal.Thisis theinverseprobleminrobustspeechprocessingthatwillbeaddressedinthissection.Ageneral approachtosolvingthisinverseproblemispresentedbasedonanaffinetransformmodelinthe cepstrumdomain. Chapter28isentitled“InverseProblems,StatisticalMechanicsandSimulatedAnnealing”byK. VenkateshPrasad.Inthissection,acomputationalapproachto3-Dcoordinaterestorationispre- sented.Theproblemistoobtainhigh-resolutioncoordinatesof3-Dvolume-elements(voxels)from observationsoftheircorresponding2-Dpicture-elements(pixels).Theproblemisposedasacom- binatorialoptimizationproblemandborrowingfromourunderstandingofstatisticalmechanics, weshowhowtoadaptthetoolofsimulatedannealingtosolvethisproblem.Thismethodishighly amenabletoparallelanddistributedprocessing. Chapter29isentitled“ImageRecoveryUsingtheEMAlgorithm”byJunZhangandAggelosK. c  1999byCRCPressLLC Katsaggelos. Inthissection, theimagerecovery/reconstruction problemisformulatedasamaximum- likelihood (ML) problem in which the image is recovered by maximizing an appropriately defined likelihood function. These likelihood functions are often highly non-linear and when some of the variables involved are not directly observable, they can only be specified in integral form (i.e., aver- aging over the “hidden variables”). The EM (expectation-maximization) algorithm is revised and applied to some typical image recovery problems. Examples include image restoration using the Markov random field model and single and multiple channel image restoration with blur identifica- tion. Chapter 30 is entitled “InverseProblems In Array Processing” by Kevin R. Farrell. Array processing uses multiple sensors to improve signal reception by reducing the effects of interfering signals that originate from different spatial locations. Array processing algorithms are generally implemented via narrowband and broadband arrays, both of which are discussed in this chapter. Two classical approaches, namely sidelobe canceler and Frost beam formers, are reviewed. These algorithms are formulated as an inverse problem and an iterative approach for solving the resulting inverse problem is provided. Chapter 31 is entitled “Channel Equalization as a RegularizedInverse Problem” by JohnF. Doherty. In this section, the relationship between communication channel equalization and the inversion of a linear system of equations is examined. A regularized method of inversion is an inversion process in which the noise dominated modes of the restored signal are attenuated. Channel equalization is the process that reduces the effects of a band-limited channel at the receiver of a communication system. A regularized method of channel equalization is presented in this section. Although there are many ways to accomplish this, the method presented uses linear and adaptive filters, which makes the transition to matrix inversion possible. Chapter 32 is entitled “Inverse Problems in Microphone Arrays” by A.C. Surendran. The response of an acoustic enclosure is, in general, a non-minimum phase function and hence not invertible. In this section, we discuss techniques using microphone arrays that attempt to recover speech signals degraded by the filtering effect of acoustic enclosures by either approximately or exactly “inverting” the room response. The aim of such systems is to force the impulse response of the overall system, after de-reverberation, to be an impulse function. Beamforming and matched-filtering techniques (that approximate this ideal case) and the Diophantine inverse filtering method (a technique that provides an exact inverse) are discussed in detail. Chapter 33 is entitled “Synthetic Aperture Radar Algorithms” by Clay Stewart and Vic Larson. A synthetic aperture radar (SAR) is a radar sensor that provides azimuth resolution superior to that achievable with its real beam by synthesizing a long aperture by platform motion. This section presents an overview of the basics of SAR phenomenology and the associated algorithms that are used to form the radar image and to enhance it. The section begins with an overview of SAR applications, historical development, fundamental phenomenology, and a survey of modern SAR systems. It also presents examples of SAR imagery. This is followed by a discussion of the basic principles of SAR image formation that begins with side looking radar, progresses to unfocused SAR, and finishes with focused SAR.A discussion ofSAR image enhancement techniques, such as thepolarimetric whitening filters, follows. Finally, a brief discussion of automatic target detection and classification techniques is offered. Chapter 34 is entitled “Iterative Image Restoration Algorithms” by Aggelos K. Katsaggelos. In this section, a class of iterative restoration algorithms is presented. Such algorithms provide solutions to the problem of recovering an original signal or image from a noisy and blurred observation of it. This situation is encountered in a number of important applications, ranging from the restoration c  1999 by CRC Press LLC of images obtained by the Hubble space telescope, to the restoration of compressed images. The successive approximation methods form the basis of the material presented in this section. The sample of applications and methods described in this chapter are meant to be representative of the large volume of work performed in this field. There is no claim of completeness, any omissions of significant contributors or other errors are solely the responsibility of the section editor, and all praiseworthy contributions are due solely to the chapter authors. c  1999 by CRC Press LLC . butnotsoforadaptivearrayprocessing.Thegoalofthefollowingsectionsistopresentthebasic approachesofinversionandsignalrecovery.Eachsectionfocusesonaparticularapplicationarea. Theinversionofsuchtransformationsisthesubjectofthepresentchapter.Inthefollowingsections wewillreviewseveralinverseproblemsandvariousmethodsofimplementationoftheinversionor