Recent Advances in Mathematics and Technology: Proceedings of the First International Conference on Technology, Engineering, and Mathematics, Kenitra, ... (Applied and Numerical Harmonic Analysis) PDF
Preview Recent Advances in Mathematics and Technology: Proceedings of the First International Conference on Technology, Engineering, and Mathematics, Kenitra, ... (Applied and Numerical Harmonic Analysis)
Applied and Numerical Harmonic Analysis Serge Dos Santos Mostafa Maslouhi Kasso A. Okoudjou Editors Recent Advances in Mathematics and Technology Proceedings of the First International Conference on Technology, Engineering, and Mathematics, Kenitra, Morocco, March 26-27, 2018 Applied and Numerical Harmonic Analysis SeriesEditor JohnJ.Benedetto UniversityofMaryland CollegePark,MD,USA AdvisoryEditors AkramAldroubi GittaKutyniok VanderbiltUniversity TechnicalUniversityofBerlin Nashville,TN,USA Berlin,Germany DouglasCochran MauroMaggioni ArizonaStateUniversity JohnsHopkinsUniversity Phoenix,AZ,USA Baltimore,MD,USA HansG.Feichtinger ZuoweiShen UniversityofVienna NationalUniversityofSingapore Vienna,Austria Singapore,Singapore ChristopherHeil ThomasStrohmer GeorgiaInstituteofTechnology UniversityofCalifornia Atlanta,GA,USA Davis,CA,USA StéphaneJaffard YangWang UniversityofParisXII HongKongUniversityof Paris,France Science&Technology Kowloon,HongKong JelenaKovacˇevic´ CarnegieMellonUniversity Pittsburgh,PA,USA Moreinformationaboutthisseriesathttp://www.springer.com/series/4968 Serge Dos Santos • Mostafa Maslouhi Kasso A. Okoudjou Editors Recent Advances in Mathematics and Technology Proceedings of the First International Conference on Technology, Engineering, and Mathematics, Kenitra, Morocco, March 26-27, 2018 Editors SergeDosSantos MostafaMaslouhi InstitutNationaldesSciencesAppliquées Informatics,LogisticsandMathematics CentreValdeLoire UniversitéIbn-Tofail Blois,France Kenitra,Morocco KassoA.Okoudjou NorbertWienerCenter DepartmentofMathematics UniversityofMaryland CollegePark,MD,USA ISSN2296-5009 ISSN2296-5017 (electronic) AppliedandNumericalHarmonicAnalysis ISBN978-3-030-35201-1 ISBN978-3-030-35202-8 (eBook) https://doi.org/10.1007/978-3-030-35202-8 MathematicsSubjectClassification:42B10,37Mxx,82-06 ©SpringerNatureSwitzerlandAG2020 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant protectivelawsandregulationsandthereforefreeforgeneraluse. Thepublisher,theauthors,andtheeditorsaresafetoassumethattheadviceandinformationinthisbook arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsor theeditorsgiveawarranty,expressedorimplied,withrespecttothematerialcontainedhereinorforany errorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictional claimsinpublishedmapsandinstitutionalaffiliations. This book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered companySpringerNatureSwitzerlandAG. Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Thisbookisdedicatedtotheauthors’ children: Youssef,Mariam,andMouadMaslouhi; Shadeh,Shola,andFemiOkoudjou; Lauryne,Maëlys,Lazare,andAlcideDos Santos. ANHA Series Preface The Applied and Numerical Harmonic Analysis (ANHA) book series aims to providetheengineering,mathematical,andscientificcommunitieswithsignificant developments in harmonic analysis, ranging from abstract harmonic analysis to basic applications. The title of the series reflects the importance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applicationsandtheircreativesymbioticevolutionisaxiomatic. Harmonicanalysisisawellspringofideasandapplicabilitythathasflourished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationshipbetweenharmonicanalysisandfieldssuchassignalprocessing,partial differentialequations(PDEs),andimageprocessingisreflectedinourstate-of-the- artANHAseries. Our vision of modern harmonic analysis includes mathematical areas such as wavelettheory,Banachalgebras,classicalFourieranalysis,time-frequencyanalysis, andfractalgeometry,aswellasthediversetopicsthatimpingeonthem. Forexample,wavelettheorycanbeconsideredanappropriatetooltodealwith some basic problems in digital signal processing, speech and image processing, geophysics, pattern recognition, biomedical engineering, and turbulence. These areas implement the latest technology from sampling methods on surfaces to fast algorithms and computer vision methods. The underlying mathematics of wavelet theorydependsnotonlyonclassicalFourieranalysis,butalsoonideasfromabstract harmonicanalysis,includingvonNeumannalgebrasandtheaffinegroup.Thisleads toastudyoftheHeisenberggroupanditsrelationshiptoGaborsystems,andofthe metaplectic group for a meaningful interaction of signal decomposition methods. Theunifyinginfluenceofwavelettheoryintheaforementionedtopicsillustratesthe justification for providing a means for centralizing and disseminating information fromthebroader,butstillfocused,areaofharmonicanalysis.Thiswillbeakeyrole of ANHA. We intend to publish with the scope and interaction that such a host of issuesdemands. vii viii ANHASeriesPreface Alongwithourcommitmenttopublishmathematicallysignificantworksatthe frontiersofharmonicanalysis,wehaveacomparablystrongcommitmenttopublish majoradvancesinthefollowingapplicabletopicsinwhichharmonicanalysisplays asubstantialrole: Antennatheory Predictiontheory Biomedicalsignalprocessing Radarapplications Digitalsignalprocessing Samplingtheory Fastalgorithms Spectralestimation Gabortheoryandapplications Speechprocessing Imageprocessing Time-frequencyand Numericalpartialdifferentialequations time-scaleanalysis Wavelettheory TheabovepointofviewfortheANHAbookseriesisinspiredbythehistoryof Fourieranalysisitself,whosetentaclesreachintosomanyfields. In the last two centuries Fourier analysis has had a major impact on the development of mathematics, on the understanding of many engineering and scientificphenomena,andonthesolutionofsomeofthemostimportantproblems in mathematics and the sciences. Historically, Fourier series were developed in the analysis of some of the classical PDEs of mathematical physics; these series were used to solve such equations. In order to understand Fourier series and the kindsofsolutionstheycouldrepresent,someofthemostbasicnotionsofanalysis were defined, e.g., the concept of “function.” Since the coefficients of Fourier seriesareintegrals,itisnosurprisethatRiemannintegralswereconceivedtodeal with uniqueness properties of trigonometric series. Cantor’s set theory was also developedbecauseofsuchuniquenessquestions. A basic problem in Fourier analysis is to show how complicated phenomena, suchassoundwaves,canbedescribedintermsofelementaryharmonics.Thereare twoaspectsofthisproblem:first,tofind,orevendefineproperly,theharmonicsor spectrumofagivenphenomenon,e.g.,thespectroscopyprobleminoptics;second, todeterminewhichphenomenacanbeconstructedfromgivenclassesofharmonics, asdone,forexample,bythemechanicalsynthesizersintidalanalysis. Fourieranalysisisalsothenaturalsettingformanyotherproblemsinengineer- ing, mathematics, and the sciences. For example, Wiener’s Tauberian theorem in Fourieranalysisnotonlycharacterizesthebehavioroftheprimenumbers,butalso provides the proper notion of spectrum for phenomena such as white light; this latter process leads tothe Fourier analysis associated withcorrelation functions in filtering and prediction problems, and these problems, in turn, deal naturally with Hardyspacesinthetheoryofcomplexvariables. Nowadays, some of the theory of PDEs has given way to the study of Fourier integral operators. Problems in antenna theory are studied in terms of unimodular trigonometric polynomials. Applications of Fourier analysis abound in signal processing, whether with the fast Fourier transform (FFT), or filter design, or the ANHASeriesPreface ix adaptivemodelinginherentintime-frequency-scalemethodssuchaswavelettheory. The coherent states of mathematical physics are translated and modulated Fourier transforms, and these are used, in conjunction with the uncertainty principle, for dealing with signal reconstruction in communications theory. We are back to the raisond’êtreoftheANHAseries! UniversityofMaryland JohnJ.Benedetto CollegePark SeriesEditor Preface One of the impacts of the trifecta Technology, Engineering, and Mathematics (TEM)onourdailylifeistheenormousamountofdatawegenerate.Forexample, Technology and Engineering are increasingly becoming the main source of “big data”production.Toanalyze,organize,process,andactuponthesedata,researchers inbothacademiaandindustryaredevisingnewparadigms.Theseincludepowerful machinelearningalgorithms,especiallydeeplearningmodelssuchasconvolutional neural networks (CNNs), which have recently achieved outstanding predictive performance in a wide range of multimedia applications, including visual object classification, scene understanding, speech recognition, and activity prediction. Many of these new applications are generally based on advances in mathematics, and particularly, mathematical modeling, optimization, numerical analysis and simulations,mathematicalsignalprocessing,andcomputersciences. From the modern engineering point of view, the forthcoming digital trans- formation also triggers opportunities in new and growing fields including big dataanalytics,artificialintelligence,automation,andimaging.Advancesindigital technologiesforindustrieslikeaugmentedreality,virtualreality,andmixedreality willalsoseevaluablechangesanddevelopmentsineducationandtrainingdelivery usingmodernmathematics. Toofferaforumforresearchersworkinginthesefieldstodiscusstheadvances and the challenges created by these new paradigms, the first edition of the Technology, Engineering and Mathematics Conference (TEM18) was organized, March26and27,2018,inKenitra,Morocco(seehttp://ensa.uit.ac.ma/tem2018/for moredetails).Itbroughttogetheragroupofrenownedresearchersandprofessionals both from academia and industries who presented their work on topics that were thematicallydividedasfollows: (cid:129) BigDataAnalyticsandApplications (cid:129) Biomathematics (cid:129) ComputerEngineeringandApplications (cid:129) EconomicsandFinancialEngineering (cid:129) HarmonicAnalysis xi
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