New Type of Gegenbauer-Jacobi-Hermite Monogenic Polynomials and Associated Continuous Clifford Wavelet Transform Some Monogenic Clifford Polynomials and Associated Wavelets
Recently 3D image processing has interested researchers in both theoretical and applied fields and thus has constituted a challenging subject. Theoretically, this needs suitable functional bases that are easy to implement by the next. It holds that Clifford wavelets are main tools to achieve this ne...
Saved in:
| Published in | Acta applicandae mathematicae Vol. 170; no. 1; pp. 1 - 35 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.12.2020
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0167-8019 1572-9036 |
| DOI | 10.1007/s10440-020-00322-0 |
Cover
Loading…
| Abstract | Recently 3D image processing has interested researchers in both theoretical and applied fields and thus has constituted a challenging subject. Theoretically, this needs suitable functional bases that are easy to implement by the next. It holds that Clifford wavelets are main tools to achieve this necessity. In the present paper we intend to develop some new classes of Clifford wavelet functions. Some classes of new monogenic polynomials are developed firstly from monogenic extensions of 2-parameters Clifford weights. Such classes englobe the well known Jacobi, Gegenbauer and Hermite ones. The constructed polynomials are next applied to develop new Clifford wavelets. Reconstruction and Fourier-Plancherel formulae have been proved. Finally, computational examples are developed provided with graphical illustrations of the Clifford mother wavelets in some cases. Some graphical illustrations of the constructed wavelets have been provided and finally concrete applications in biofields have been developed dealing with EEG/ECG and Brain image processing. |
|---|---|
| AbstractList | Recently 3D image processing has interested researchers in both theoretical and applied fields and thus has constituted a challenging subject. Theoretically, this needs suitable functional bases that are easy to implement by the next. It holds that Clifford wavelets are main tools to achieve this necessity. In the present paper we intend to develop some new classes of Clifford wavelet functions. Some classes of new monogenic polynomials are developed firstly from monogenic extensions of 2-parameters Clifford weights. Such classes englobe the well known Jacobi, Gegenbauer and Hermite ones. The constructed polynomials are next applied to develop new Clifford wavelets. Reconstruction and Fourier-Plancherel formulae have been proved. Finally, computational examples are developed provided with graphical illustrations of the Clifford mother wavelets in some cases. Some graphical illustrations of the constructed wavelets have been provided and finally concrete applications in biofields have been developed dealing with EEG/ECG and Brain image processing. |
| Author | Cattani, Carlo Ben Mabrouk, Anouar Arfaoui, Sabrine |
| Author_xml | – sequence: 1 givenname: Sabrine surname: Arfaoui fullname: Arfaoui, Sabrine email: sabrine.arfaoui@issatm.rnu.tn organization: Algebra, Number Theory and Nonlinear Analysis Laboratory LR18ES15, Department of Mathematics, Faculty of Sciences, University of Monastir, Department of Mathematics, Faculty of Sciences, University of Tabuk – sequence: 2 givenname: Anouar surname: Ben Mabrouk fullname: Ben Mabrouk, Anouar organization: Algebra, Number Theory and Nonlinear Analysis Laboratory LR18ES15, Department of Mathematics, Faculty of Sciences, University of Monastir, Department of Mathematics, Higher Institute of Applied Mathematics and Computer Science, University of Kairouan, Department of Mathematics, Faculty of Sciences, University of Tabuk – sequence: 3 givenname: Carlo surname: Cattani fullname: Cattani, Carlo organization: Engineering School (DEIM), Tuscia University |
| BookMark | eNp9kMtOAzEMRSNUJNrCD7DKDwTymOeyqqAF8VoUsYwyGadKNZNUyQyof0-grFh0YVmy77F17wxNnHeA0DWjN4zS8jYymmWUUJ6KCs4JPUNTlpec1FQUEzSlrChJRVl9gWYx7mhS1UUxRfsX-MKbwx6wN3gFW3CNGiGQR6V9Y8kaQm8HwM_e-bSzGr_57uB8b1UXsXItXsTotVUDtHjp3WDd6MeIl501xocWf6hP6GDAm6BcTJP-Ep2bxMLVX5-j9_u7zXJNnl5XD8vFE9G8ZgMBXgquGct0UVYFmIrrhhthdA06K1vWCGaMyJOobNuCZ4bmebKk67yhWd42Yo748a4OPsYARu6D7VU4SEblT2bymJlMmcnfzCRNUPUP0nZQg03GgrLdaVQc0Zj-uC0EufNjcMniKeobxLSEOQ |
| CitedBy_id | crossref_primary_10_3390_e23070844 crossref_primary_10_3390_math9101117 crossref_primary_10_1063_5_0015989 crossref_primary_10_1007_s00500_021_06217_y crossref_primary_10_32604_cmc_2022_030954 crossref_primary_10_3390_math9212748 |
| Cites_doi | 10.1023/A:1022843426320 10.1063/1.3060000 10.1007/978-0-8176-8403-7 10.1007/BF03320981 10.1080/10652460410001727536 10.1007/BF02511157 10.1002/(SICI)1098-1098(199623)7:3<152::AID-IMA1>3.0.CO;2-7 10.1007/s00006-017-0788-9 10.1007/978-0-8176-8166-1 10.1016/j.camwa.2012.10.011 10.1007/s10851-012-0352-0 10.1007/s10851-013-0430-y 10.1007/978-3-7643-7778-6_16 10.1016/j.jat.2005.02.006 10.1007/s00006-009-0152-9 10.1007/s10851-006-3605-y 10.1155/2010/513186 10.1155/2013/161030 10.1007/BF03042219 10.1007/s10474-013-0338-4 10.1016/S1076-5670(08)01402-X 10.1007/978-1-4419-6190-7_6 10.1201/b18273-5 10.1093/imrn/rnq288 10.1007/s11071-016-2753-x 10.1007/s10440-017-0150-1 |
| ContentType | Journal Article |
| Copyright | Springer Nature B.V. 2020 |
| Copyright_xml | – notice: Springer Nature B.V. 2020 |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s10440-020-00322-0 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1572-9036 |
| EndPage | 35 |
| ExternalDocumentID | 10_1007_s10440_020_00322_0 |
| GroupedDBID | -52 -5D -5G -BR -EM -Y2 -~C -~X .86 .VR 06D 0R~ 0VY 199 1N0 1SB 2.D 203 23M 28- 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 3V. 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 7WY 88I 8AO 8FE 8FG 8FL 8FW 8G5 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYZH ABAKF ABBBX ABBXA ABDBF ABDZT ABECU ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABUWG ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACGOD ACHSB ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACUHS ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFEXP AFFNX AFGCZ AFKRA AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN AZQEC B-. BA0 BAPOH BBWZM BDATZ BENPR BEZIV BGLVJ BGNMA BPHCQ BSONS CAG CCPQU COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DWQXO EBLON EBS EIOEI EJD ESBYG ESX F5P FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRNLG FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNUQQ GNWQR GQ6 GQ7 GQ8 GROUPED_ABI_INFORM_COMPLETE GROUPED_ABI_INFORM_RESEARCH GUQSH GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IXE IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K60 K6V K6~ K7- KDC KOV KOW L6V LAK LLZTM M0C M0N M2O M2P M4Y M7S MA- N2Q NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P62 P9R PF0 PQBIZ PQBZA PQQKQ PROAC PT4 PT5 PTHSS Q2X QOK QOS R4E R89 R9I RHV RNI ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TSG TSK TSV TUC TUS U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WK8 YLTOR Z45 Z7X Z81 Z83 Z88 Z8R Z8U Z8W ZMTXR ZWQNP ~8M ~A9 ~EX AAPKM AAYXX ABBRH ABDBE ABFSG ACSTC ADHKG AEZWR AFDZB AFHIU AFOHR AGQPQ AHPBZ AHWEU AIXLP AMVHM ATHPR AYFIA CITATION PHGZM PHGZT |
| ID | FETCH-LOGICAL-c291t-e2732c114c6786ef82cb2f3fc9ec47d1b31ff357327dd624f055039c95b045db3 |
| IEDL.DBID | U2A |
| ISSN | 0167-8019 |
| IngestDate | Tue Jul 01 00:58:43 EDT 2025 Thu Apr 24 23:03:45 EDT 2025 Fri Feb 21 02:38:01 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Keywords | Fourier-Plancherel, monogenic polynomials, EEG/ECG, Brain images 44A15 Continuous wavelet transform Clifford analysis 42B10 30G35 Clifford Fourier transform |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c291t-e2732c114c6786ef82cb2f3fc9ec47d1b31ff357327dd624f055039c95b045db3 |
| PageCount | 35 |
| ParticipantIDs | crossref_primary_10_1007_s10440_020_00322_0 crossref_citationtrail_10_1007_s10440_020_00322_0 springer_journals_10_1007_s10440_020_00322_0 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 20201200 2020-12-00 |
| PublicationDateYYYYMMDD | 2020-12-01 |
| PublicationDate_xml | – month: 12 year: 2020 text: 20201200 |
| PublicationDecade | 2020 |
| PublicationPlace | Dordrecht |
| PublicationPlace_xml | – name: Dordrecht |
| PublicationTitle | Acta applicandae mathematicae |
| PublicationTitleAbbrev | Acta Appl Math |
| PublicationYear | 2020 |
| Publisher | Springer Netherlands |
| Publisher_xml | – name: Springer Netherlands |
| References | Saillard, J., Bunel, G.: Apport des fonctions sphéroidales pour l’estimation des paramètres d’une cible radar. 12ème Colloque Gretsi-Juan-Les-Pins, 12-19 Juin 1989, 4 pages De Bie, H.: Clifford algebras, Fourier transforms and quantum mechanics. arXiv:1209.6434v1, September 2012, 39 pages BrackxF.SommenF.Clifford-Hermite wavelets in Euclidean spaceJ. Fourier Anal. Appl.200063299310175514510.1007/BF02511157 ArfaouiS.Ben MabroukA.Some old orthogonal polynomials revisited and associated wavelets: two-parameters Clifford-Jacobi polynomials and associated spheroidal waveletsActa Appl. Math.201710.1007/s10440-017-0150-11407.42028 BrackxF.De SchepperN.SommenF.Clifford-Jacobi polynomials and the associated continuous wavelet transform in Euclidean spaceWavelet Analysis and Applications200618519810.1007/978-3-7643-7778-6_16 BrackxF.De SchepperN.SommenF.The Fourier transform in Clifford analysisAdv. Imaging Electron Phys.20091565520110.1016/S1076-5670(08)01402-X SteinE.M.WeissG.Introduction to Fourier Analysis on Euclidean Spaces1971PrincetonPrinceton University Press0232.42007 StrattonJ.A.MorseP.M.ChuL.J.LittleJ.D.C.CorbatoF.J.Spheroidal Wave Functions1956New YorkWiley10.1063/1.3060000 MichelV.Lectures on Constructive Approximation2013BaselBirkhäuser10.1007/978-0-8176-8403-7 De Bie, H., Xu, Y.: On the Clifford-Fourier transform. arXiv:1003.0689, December 2010, 30 pages CattaniC.KudreykoA.Harmonic wavelet method towards solution of the Fredholm type integral equations of the second kindAppl. Math. Comput.2010215124164417125960921186.65160 DelangheR.Clifford analysis: history and perspectiveComput. Methods Funct. Theory200111107153193160710.1007/BF03320981 Rizo-RodríguezD.Mendez-VazquezH.Garcia-ReyesE.Illumination invariant face recognition using quaternion-based correlation filtersJ. Math. Imaging Vis.201345164175301740510.1007/s10851-012-0352-0 Abreu-BlayaR.Bory-ReyesJ.BoschP.Extension theorem for complex Clifford algebras-valued functions on fractal domainsBound. Value Probl.20102010260891610.1155/2010/5131869 pages HeydariM.H.HooshmandaslM.R.CattaniC.LiM.Legendre wavelets method for solving fractional population growth model in a closed systemMath. Probl. Eng.20132013310798610.1155/2013/1610308 pages SauK.BasakaR.K.ChandaA.Image compression based on block truncation coding using Clifford algebraInternational Conference on Computational Intelligence: Modeling Techniques and Applications (CIMTA) 20132013699706 BrackxF.De SchepperN.SommenF.GürlebeckK.KönkeC.Clifford-Hermite and two-dimensional Clifford-Gabor filters for early vision(digital) Proceedings 17th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering2006Bauhaus-Universität Weimar ShiY.G.Orthogonal polynomials for Jacobi-exponential weightsActa Math. Hung.20131404363376308569110.1007/s10474-013-0338-4 Arfaoui, S.: New monogenic Gegenbauer Jacobi polynomials and associated spheroidal wavelets. Doctoral Thesis in Mathematics, University of Monastir, Tunisia, Faculty of Sciences, July 26, 2017 Van De VilleD.SageD.BalacK.UnserM.The Marr wavelet pyramid and multiscale directional image analysis16th European Signal Processing Conference (EUSIPCO 2008)20085 pages AntoineJ.-P.MurenziR.VandergheynstP.Two-dimensional directional wavelets in image processingInt. J. Imaging Syst. Technol.19967315216510.1002/(SICI)1098-1098(199623)7:3<152::AID-IMA1>3.0.CO;2-7 Lahar, S.: Clifford algebra: a visual introduction. A topnotch WordPress.com site, March 18, 2014 CarréP.BerthierM.Fernandez-MaloigneC.Color representation and processes with Clifford algebraAdvanced Color Image Processing and Analysis2013New YorkSpringer14717910.1007/978-1-4419-6190-7_6Chap. 6 ArfaouiS.Ben MabroukA.Some ultraspheroidal monogenic Clifford Gegenbauer Jacobi polynomials and associated waveletsAdv. Appl. Clifford Algebras201727322872306368882410.1007/s00006-017-0788-9 Pena, D.P.: Cauchy-Kowalevski extensions, Fueter’s theorems and boundary values of special systems in Clifford analysis. A PhD thesis, in Mathematics, Ghent University (2008) BrackxF.SommenF.The generalized Clifford-Hermite continuous wavelet transformAdv. Appl. Clifford Algebras20011151219231210672110.1007/BF03042219(Special Issue: Clifford Analysis, Proceedings of the Clifford Analysis Conference, Cetraro (Italy), October 1998) YangB.SukT.DaiM.FlusserJ.PapakostasG.A.2D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$2D$\end{document} and 3D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$3D$\end{document} image analysis by Gaussian-Hermite momentsMoments and Moment Invariants - Theory and Applications2014143173Science Gate Publishing, Chap. 7 AbramowitzM.StegunI.A.Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables1964WashingtonNational Bureau of Standards0171.38503 BrackxF.De SchepperN.SommenF.The Clifford-Gegenbauer polynomials and the associated continuous wavelet transformIntegral Transforms Spec. Funct.2004155387404208665110.1080/10652460410001727536 ArfaouiS.RezguiI.Ben MabroukA.Harmonic Wavelet Analysis on the Sphere, Spheroidal Wavelets2016Berlinde Gruyter1369.42026ISBN 978-11-048188-4 ColomboF.Sa BadiniI.SommenF.StruppaD.C.Analysis of Dirac Systems and Computational Algebra2004BostonBirkhäuser10.1007/978-0-8176-8166-1 StrattonJ.A.Spheroidal functionsPhysics19352151560010.35801 MoraisJ.KouK.I.SprößigW.Generalized holomorphic Szegö kernel in 3D spheroidsComput. Math. Appl.2013654576588301144210.1016/j.camwa.2012.10.011 LiL.-W.KangX.-K.LeongM.-S.Spheroidal Wave Functions in Electromagnetic Theory2002New YorkWiley Arfaoui, S., Ben Mabrouk, A.: Some generalized Clifford-Jacobi polynomials and associated spheroidal wavelets. arxiv:1704.03513, April 06, 2017, 24 pages. BrackxF.DelangheR.SommenF.Clifford Analysis1982LondonPitman Publication0529.30001 OsipovA.RokhlinV.XiaoH.Prolate spheroidal wave functions of order zero. Mathematical tools for bandlimited approximationApplied Mathematical Sciences2013BerlinSpringer BrackxF.De SchepperN.SommenF.The two-dimensional Clifford-Fourier transformJ. Math. Imaging Vis.200626518228386810.1007/s10851-006-3605-y HitzerE.MastorakisN.E.PardalosP.M.AgarwalR.P.KocinacL.New developments in Clifford Fourier transformsProceedings of the 2014 International Conference on Pure Mathematics, Applied Mathematics, Computational Methods (PMAMCM 2014)20141925 KindratenkoV.V.On using functions to describe the shapeJ. Math. Imaging Vis.200318225245197118010.1023/A:1022843426320 LevinE.LubinskyD.Orthogonal polynomials for exponential weights x2ρe−2Q(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$x^{2\rho }e^{-2\mathcal{Q}(x)}$\end{document} on [0,d)]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[0,d)]$\end{document}J. Approx. Theory2005134199256214229910.1016/j.jat.2005.02.006 BrackxF.De SchepperN.SommenF.The Clifford-Laguerre continuous wavelet transformBull. Belg. Math. Soc.2003102012151077.42026 De SchepperN.The generalized Clifford-Gegenbauer polynomials revisitedAdv. Appl. Clifford Algebras200919253268252466910.1007/s00006-009-0152-9 Moussa, M.-M.: Calcul efficace et direct des représentations de maillages 3D utilisant les harmoniques sphériques. Thèse de Doctorat de l’université Claude Bernard, Lyon 1, France (2007) HeydariM.H.HooshmandaslM.R.ShakibaA.CattaniC.Legendre wavelets Galerkin method for solving nonlinear stochastic integral equationsNonlinear Dyn.20168511851202351143310.1007/s11071-016-2753-x CattaniC.Signorini cylindrical waves and Shannon waveletsAdv. Numer. Anal.2012201229483281329.7410524 pages BujackR.De BieH.De SchepperN.ScheuermannG.Convolution products for hypercomplex Fourier transformsJ. Math. Imaging Vis.201310.1007/s10851-013-0430-y1292.4200719 pages 322_CR7 F. Brackx (322_CR13) 2004; 15 M. Abramowitz (322_CR1) 1964 S. Arfaoui (322_CR8) 2016 F. Brackx (322_CR11) 1982 D. Rizo-Rodríguez (322_CR39) 2013; 45 Y.G. Shi (322_CR42) 2013; 140 322_CR4 V.V. Kindratenko (322_CR30) 2003; 18 S. Arfaoui (322_CR5) 2017; 27 E. Levin (322_CR32) 2005; 134 V. Michel (322_CR34) 2013 K. Sau (322_CR41) 2013 M.H. Heydari (322_CR27) 2013; 2013 J.A. Stratton (322_CR45) 1956 C. Cattani (322_CR21) 2010; 215 F. Brackx (322_CR10) 2001; 11 F. Brackx (322_CR15) 2006 J. Morais (322_CR35) 2013; 65 S. Arfaoui (322_CR6) 2017 E.M. Stein (322_CR43) 1971 322_CR31 C. Cattani (322_CR20) 2012; 2012 N. De Schepper (322_CR25) 2009; 19 P. Carré (322_CR19) 2013 B. Yang (322_CR47) 2014 F. Brackx (322_CR17) 2009; 156 322_CR36 F. Brackx (322_CR14) 2006; 26 322_CR38 M.H. Heydari (322_CR28) 2016; 85 R. Abreu-Blaya (322_CR2) 2010; 2010 F. Colombo (322_CR22) 2004 F. Brackx (322_CR16) 2006 R. Bujack (322_CR18) 2013 J.A. Stratton (322_CR44) 1935; 21 E. Hitzer (322_CR29) 2014 D. Van De Ville (322_CR46) 2008 R. Delanghe (322_CR26) 2001; 1 L.-W. Li (322_CR33) 2002 A. Osipov (322_CR37) 2013 322_CR40 J.-P. Antoine (322_CR3) 1996; 7 F. Brackx (322_CR9) 2000; 6 F. Brackx (322_CR12) 2003; 10 322_CR23 322_CR24 |
| References_xml | – reference: MichelV.Lectures on Constructive Approximation2013BaselBirkhäuser10.1007/978-0-8176-8403-7 – reference: SteinE.M.WeissG.Introduction to Fourier Analysis on Euclidean Spaces1971PrincetonPrinceton University Press0232.42007 – reference: StrattonJ.A.MorseP.M.ChuL.J.LittleJ.D.C.CorbatoF.J.Spheroidal Wave Functions1956New YorkWiley10.1063/1.3060000 – reference: LevinE.LubinskyD.Orthogonal polynomials for exponential weights x2ρe−2Q(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$x^{2\rho }e^{-2\mathcal{Q}(x)}$\end{document} on [0,d)]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[0,d)]$\end{document}J. Approx. Theory2005134199256214229910.1016/j.jat.2005.02.006 – reference: LiL.-W.KangX.-K.LeongM.-S.Spheroidal Wave Functions in Electromagnetic Theory2002New YorkWiley – reference: BrackxF.SommenF.The generalized Clifford-Hermite continuous wavelet transformAdv. Appl. Clifford Algebras20011151219231210672110.1007/BF03042219(Special Issue: Clifford Analysis, Proceedings of the Clifford Analysis Conference, Cetraro (Italy), October 1998) – reference: ArfaouiS.Ben MabroukA.Some old orthogonal polynomials revisited and associated wavelets: two-parameters Clifford-Jacobi polynomials and associated spheroidal waveletsActa Appl. Math.201710.1007/s10440-017-0150-11407.42028 – reference: BujackR.De BieH.De SchepperN.ScheuermannG.Convolution products for hypercomplex Fourier transformsJ. Math. Imaging Vis.201310.1007/s10851-013-0430-y1292.4200719 pages – reference: HitzerE.MastorakisN.E.PardalosP.M.AgarwalR.P.KocinacL.New developments in Clifford Fourier transformsProceedings of the 2014 International Conference on Pure Mathematics, Applied Mathematics, Computational Methods (PMAMCM 2014)20141925 – reference: BrackxF.De SchepperN.SommenF.Clifford-Jacobi polynomials and the associated continuous wavelet transform in Euclidean spaceWavelet Analysis and Applications200618519810.1007/978-3-7643-7778-6_16 – reference: OsipovA.RokhlinV.XiaoH.Prolate spheroidal wave functions of order zero. Mathematical tools for bandlimited approximationApplied Mathematical Sciences2013BerlinSpringer – reference: BrackxF.DelangheR.SommenF.Clifford Analysis1982LondonPitman Publication0529.30001 – reference: AntoineJ.-P.MurenziR.VandergheynstP.Two-dimensional directional wavelets in image processingInt. J. Imaging Syst. Technol.19967315216510.1002/(SICI)1098-1098(199623)7:3<152::AID-IMA1>3.0.CO;2-7 – reference: CattaniC.KudreykoA.Harmonic wavelet method towards solution of the Fredholm type integral equations of the second kindAppl. Math. Comput.2010215124164417125960921186.65160 – reference: BrackxF.De SchepperN.SommenF.The Clifford-Laguerre continuous wavelet transformBull. Belg. Math. Soc.2003102012151077.42026 – reference: De Bie, H., Xu, Y.: On the Clifford-Fourier transform. arXiv:1003.0689, December 2010, 30 pages – reference: Arfaoui, S.: New monogenic Gegenbauer Jacobi polynomials and associated spheroidal wavelets. Doctoral Thesis in Mathematics, University of Monastir, Tunisia, Faculty of Sciences, July 26, 2017 – reference: CarréP.BerthierM.Fernandez-MaloigneC.Color representation and processes with Clifford algebraAdvanced Color Image Processing and Analysis2013New YorkSpringer14717910.1007/978-1-4419-6190-7_6Chap. 6 – reference: HeydariM.H.HooshmandaslM.R.CattaniC.LiM.Legendre wavelets method for solving fractional population growth model in a closed systemMath. Probl. Eng.20132013310798610.1155/2013/1610308 pages – reference: De SchepperN.The generalized Clifford-Gegenbauer polynomials revisitedAdv. Appl. Clifford Algebras200919253268252466910.1007/s00006-009-0152-9 – reference: ArfaouiS.Ben MabroukA.Some ultraspheroidal monogenic Clifford Gegenbauer Jacobi polynomials and associated waveletsAdv. Appl. Clifford Algebras201727322872306368882410.1007/s00006-017-0788-9 – reference: BrackxF.De SchepperN.SommenF.The two-dimensional Clifford-Fourier transformJ. Math. Imaging Vis.200626518228386810.1007/s10851-006-3605-y – reference: CattaniC.Signorini cylindrical waves and Shannon waveletsAdv. Numer. Anal.2012201229483281329.7410524 pages – reference: KindratenkoV.V.On using functions to describe the shapeJ. Math. Imaging Vis.200318225245197118010.1023/A:1022843426320 – reference: Pena, D.P.: Cauchy-Kowalevski extensions, Fueter’s theorems and boundary values of special systems in Clifford analysis. A PhD thesis, in Mathematics, Ghent University (2008) – reference: Abreu-BlayaR.Bory-ReyesJ.BoschP.Extension theorem for complex Clifford algebras-valued functions on fractal domainsBound. Value Probl.20102010260891610.1155/2010/5131869 pages – reference: BrackxF.De SchepperN.SommenF.The Clifford-Gegenbauer polynomials and the associated continuous wavelet transformIntegral Transforms Spec. Funct.2004155387404208665110.1080/10652460410001727536 – reference: SauK.BasakaR.K.ChandaA.Image compression based on block truncation coding using Clifford algebraInternational Conference on Computational Intelligence: Modeling Techniques and Applications (CIMTA) 20132013699706 – reference: Moussa, M.-M.: Calcul efficace et direct des représentations de maillages 3D utilisant les harmoniques sphériques. Thèse de Doctorat de l’université Claude Bernard, Lyon 1, France (2007) – reference: Rizo-RodríguezD.Mendez-VazquezH.Garcia-ReyesE.Illumination invariant face recognition using quaternion-based correlation filtersJ. Math. Imaging Vis.201345164175301740510.1007/s10851-012-0352-0 – reference: BrackxF.De SchepperN.SommenF.GürlebeckK.KönkeC.Clifford-Hermite and two-dimensional Clifford-Gabor filters for early vision(digital) Proceedings 17th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering2006Bauhaus-Universität Weimar – reference: YangB.SukT.DaiM.FlusserJ.PapakostasG.A.2D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$2D$\end{document} and 3D\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$3D$\end{document} image analysis by Gaussian-Hermite momentsMoments and Moment Invariants - Theory and Applications2014143173Science Gate Publishing, Chap. 7 – reference: Arfaoui, S., Ben Mabrouk, A.: Some generalized Clifford-Jacobi polynomials and associated spheroidal wavelets. arxiv:1704.03513, April 06, 2017, 24 pages. – reference: De Bie, H.: Clifford algebras, Fourier transforms and quantum mechanics. arXiv:1209.6434v1, September 2012, 39 pages – reference: Lahar, S.: Clifford algebra: a visual introduction. A topnotch WordPress.com site, March 18, 2014 – reference: BrackxF.SommenF.Clifford-Hermite wavelets in Euclidean spaceJ. Fourier Anal. Appl.200063299310175514510.1007/BF02511157 – reference: ColomboF.Sa BadiniI.SommenF.StruppaD.C.Analysis of Dirac Systems and Computational Algebra2004BostonBirkhäuser10.1007/978-0-8176-8166-1 – reference: Van De VilleD.SageD.BalacK.UnserM.The Marr wavelet pyramid and multiscale directional image analysis16th European Signal Processing Conference (EUSIPCO 2008)20085 pages – reference: BrackxF.De SchepperN.SommenF.The Fourier transform in Clifford analysisAdv. Imaging Electron Phys.20091565520110.1016/S1076-5670(08)01402-X – reference: DelangheR.Clifford analysis: history and perspectiveComput. Methods Funct. Theory200111107153193160710.1007/BF03320981 – reference: HeydariM.H.HooshmandaslM.R.ShakibaA.CattaniC.Legendre wavelets Galerkin method for solving nonlinear stochastic integral equationsNonlinear Dyn.20168511851202351143310.1007/s11071-016-2753-x – reference: AbramowitzM.StegunI.A.Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables1964WashingtonNational Bureau of Standards0171.38503 – reference: MoraisJ.KouK.I.SprößigW.Generalized holomorphic Szegö kernel in 3D spheroidsComput. Math. Appl.2013654576588301144210.1016/j.camwa.2012.10.011 – reference: Saillard, J., Bunel, G.: Apport des fonctions sphéroidales pour l’estimation des paramètres d’une cible radar. 12ème Colloque Gretsi-Juan-Les-Pins, 12-19 Juin 1989, 4 pages – reference: ShiY.G.Orthogonal polynomials for Jacobi-exponential weightsActa Math. Hung.20131404363376308569110.1007/s10474-013-0338-4 – reference: ArfaouiS.RezguiI.Ben MabroukA.Harmonic Wavelet Analysis on the Sphere, Spheroidal Wavelets2016Berlinde Gruyter1369.42026ISBN 978-11-048188-4 – reference: StrattonJ.A.Spheroidal functionsPhysics19352151560010.35801 – volume: 18 start-page: 225 year: 2003 ident: 322_CR30 publication-title: J. Math. Imaging Vis. doi: 10.1023/A:1022843426320 – ident: 322_CR4 – volume-title: Spheroidal Wave Functions year: 1956 ident: 322_CR45 doi: 10.1063/1.3060000 – volume-title: Lectures on Constructive Approximation year: 2013 ident: 322_CR34 doi: 10.1007/978-0-8176-8403-7 – volume: 1 start-page: 107 issue: 1 year: 2001 ident: 322_CR26 publication-title: Comput. Methods Funct. Theory doi: 10.1007/BF03320981 – volume: 15 start-page: 387 issue: 5 year: 2004 ident: 322_CR13 publication-title: Integral Transforms Spec. Funct. doi: 10.1080/10652460410001727536 – volume-title: Introduction to Fourier Analysis on Euclidean Spaces year: 1971 ident: 322_CR43 – volume: 6 start-page: 299 issue: 3 year: 2000 ident: 322_CR9 publication-title: J. Fourier Anal. Appl. doi: 10.1007/BF02511157 – volume-title: Spheroidal Wave Functions in Electromagnetic Theory year: 2002 ident: 322_CR33 – volume: 7 start-page: 152 issue: 3 year: 1996 ident: 322_CR3 publication-title: Int. J. Imaging Syst. Technol. doi: 10.1002/(SICI)1098-1098(199623)7:3<152::AID-IMA1>3.0.CO;2-7 – start-page: 19 volume-title: Proceedings of the 2014 International Conference on Pure Mathematics, Applied Mathematics, Computational Methods (PMAMCM 2014) year: 2014 ident: 322_CR29 – volume: 27 start-page: 2287 issue: 3 year: 2017 ident: 322_CR5 publication-title: Adv. Appl. Clifford Algebras doi: 10.1007/s00006-017-0788-9 – volume-title: (digital) Proceedings 17th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering year: 2006 ident: 322_CR16 – volume-title: Analysis of Dirac Systems and Computational Algebra year: 2004 ident: 322_CR22 doi: 10.1007/978-0-8176-8166-1 – volume: 65 start-page: 576 issue: 4 year: 2013 ident: 322_CR35 publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2012.10.011 – ident: 322_CR23 – ident: 322_CR40 – ident: 322_CR7 – volume: 45 start-page: 164 year: 2013 ident: 322_CR39 publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-012-0352-0 – start-page: 699 volume-title: International Conference on Computational Intelligence: Modeling Techniques and Applications (CIMTA) 2013 year: 2013 ident: 322_CR41 – year: 2013 ident: 322_CR18 publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-013-0430-y – start-page: 185 volume-title: Wavelet Analysis and Applications year: 2006 ident: 322_CR15 doi: 10.1007/978-3-7643-7778-6_16 – volume: 134 start-page: 199 year: 2005 ident: 322_CR32 publication-title: J. Approx. Theory doi: 10.1016/j.jat.2005.02.006 – volume: 19 start-page: 253 year: 2009 ident: 322_CR25 publication-title: Adv. Appl. Clifford Algebras doi: 10.1007/s00006-009-0152-9 – volume-title: Harmonic Wavelet Analysis on the Sphere, Spheroidal Wavelets year: 2016 ident: 322_CR8 – volume: 26 start-page: 5 year: 2006 ident: 322_CR14 publication-title: J. Math. Imaging Vis. doi: 10.1007/s10851-006-3605-y – volume: 2012 year: 2012 ident: 322_CR20 publication-title: Adv. Numer. Anal. – volume-title: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables year: 1964 ident: 322_CR1 – volume: 2010 year: 2010 ident: 322_CR2 publication-title: Bound. Value Probl. doi: 10.1155/2010/513186 – volume: 2013 year: 2013 ident: 322_CR27 publication-title: Math. Probl. Eng. doi: 10.1155/2013/161030 – volume: 10 start-page: 201 year: 2003 ident: 322_CR12 publication-title: Bull. Belg. Math. Soc. – volume: 11 start-page: 219 issue: 51 year: 2001 ident: 322_CR10 publication-title: Adv. Appl. Clifford Algebras doi: 10.1007/BF03042219 – volume: 21 start-page: 51 year: 1935 ident: 322_CR44 publication-title: Physics – volume: 215 start-page: 4164 issue: 12 year: 2010 ident: 322_CR21 publication-title: Appl. Math. Comput. – start-page: 143 volume-title: Moments and Moment Invariants - Theory and Applications year: 2014 ident: 322_CR47 – volume: 140 start-page: 363 issue: 4 year: 2013 ident: 322_CR42 publication-title: Acta Math. Hung. doi: 10.1007/s10474-013-0338-4 – volume: 156 start-page: 55 year: 2009 ident: 322_CR17 publication-title: Adv. Imaging Electron Phys. doi: 10.1016/S1076-5670(08)01402-X – start-page: 147 volume-title: Advanced Color Image Processing and Analysis year: 2013 ident: 322_CR19 doi: 10.1007/978-1-4419-6190-7_6 – volume-title: Applied Mathematical Sciences year: 2013 ident: 322_CR37 – volume-title: Clifford Analysis year: 1982 ident: 322_CR11 – ident: 322_CR31 doi: 10.1201/b18273-5 – ident: 322_CR24 doi: 10.1093/imrn/rnq288 – ident: 322_CR36 – ident: 322_CR38 – volume-title: 16th European Signal Processing Conference (EUSIPCO 2008) year: 2008 ident: 322_CR46 – volume: 85 start-page: 1185 year: 2016 ident: 322_CR28 publication-title: Nonlinear Dyn. doi: 10.1007/s11071-016-2753-x – year: 2017 ident: 322_CR6 publication-title: Acta Appl. Math. doi: 10.1007/s10440-017-0150-1 |
| SSID | ssj0003966 |
| Score | 2.2784855 |
| Snippet | Recently 3D image processing has interested researchers in both theoretical and applied fields and thus has constituted a challenging subject. Theoretically,... |
| SourceID | crossref springer |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 1 |
| SubjectTerms | Applications of Mathematics Calculus of Variations and Optimal Control; Optimization Computational Mathematics and Numerical Analysis Mathematics Mathematics and Statistics Partial Differential Equations Probability Theory and Stochastic Processes |
| Subtitle | Some Monogenic Clifford Polynomials and Associated Wavelets |
| Title | New Type of Gegenbauer-Jacobi-Hermite Monogenic Polynomials and Associated Continuous Clifford Wavelet Transform |
| URI | https://link.springer.com/article/10.1007/s10440-020-00322-0 |
| Volume | 170 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1La8MwDDZbe9kOY0_WPYoPu22GxG7S-FjK2tKxsUPLulOwHRsCJSlteti_n5Qm3QqjsHMUH2RZ0oekT4Q8dJGAxCjFksA4BhYSMI1MmJAbSBsJw6Uruy3ewtG0M54Fs2oobFV3u9clydJT_xp2wzokwh2wRIBQANSbAWJ3sOIp7239r5CbCiUyeoP_ldWozN9n7Iaj3VpoGWIGp-Skyg1pb3OZZ-TAZufk-HVLrLq6IAtwShSxI80dHQLiz7Ra2yUbg2PTKRtha0thKbzUHL6lhr7n8y-cPAYroypLaH0dNqFITJVma4D-tD9PHXa50w-FiygKOqnz2UsyHTxP-iNWLU1goFe_YBbyEW4A5RgIQ6F1ETeaO-GMtKbTTXwtfOdEAELdJAl5x3mAUYQ0MtCQ3SVaXJFGlmf2mtDIGE8h4Z2QgKINVyEICR15QsH5LmoRv9ZdbCpGcVxsMY9_uJBR3zHoOy71HXst8rj9Z7Hh09gr_VRfSVy9rdUe8Zv_id-SI46mUDan3JFGsVzbe0gxCt0mh9Fg2CbN3vDz5bld2tc32JLITw |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV09T8MwELVQGYAB8SnKpwc2sJTETRqPVUUJpa0YWtEtsh1bilQlVZsO_Hvu0qRQCVVizsXD-Xx-T3f3TMhjGwVItJQs8bVlECE-U6iECdhAmJBrT9iy22IURJNWf-pPq6GwZd3tXpcky0z9a9gN65BIdyASgUIBUd8HMBBiI9fE62zyLxfrCiUqekP-FdWozN9rbF9H27XQ8orpnZDjChvSznozT8meyc7I0XAjrLo8J3NIShS5I80tfQXGnym5MgvWh8SmUhZha0thKJzUHL6lmn7ksy-cPIYoozJLaL0dJqEoTJVmK6D-tDtLLXa500-JD1EUdFzj2Qsy6b2MuxGrHk1g4Fe3YAbwiKeB5Wi4hgJjQ08rz3KrhdGtduIq7lrLfTBqJ0ngtawDHIULLXwF6C5R_JI0sjwzV4SGWjsSBe-4ABatPRmAEVehwyWsb8MmcWvfxbpSFMeHLWbxjxYy-jsGf8elv2OnSZ42_8zXeho7rZ_rLYmrs7XcYX79P_MHchCNh4N48DZ6vyGHHoZF2ahySxrFYmXuAG4U6r6Mrm9zssjI |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LT8MwDI4QSAgOiKcYzxy4QbS2WbvmOA3GGDDtsIndqiZNpEpTO23tgX-P3cfYJDSJc90cHMf2J9ufCXloIwGJCkMWucowsBCXSWTChNxAaJ8rR5ii22Lo9SetwdSdrk3xF93udUmynGlAlqYka84j01wbfMOaJEIfsEqAUwDa98Ad22jXE6ez8sVclNVKZPcGXyyqsZm_z9gMTZt10SLc9I7JUZUn0k55sSdkRyen5PBzRbK6PCNzcFAUcSRNDX0F9J_IMNcLNgAnJ2PWxzaXTFN4tSl8ixUdpbNvnEIGi6NhEtH6anREkaQqTvI0X9LuLDbY8U6_QlxKkdFxnduek0nvZdzts2qBAgMd2xnTkJs4ChCPgpDkaeM7SjqGGyW0arUjW3LbGO6CUDuKPKdlLMArXCjhSsj0IskvyG6SJvqSUF8pK0TyOy4AUSsn9ECIS9_iIZxv_Aaxa90FqmIXxyUXs-CXFxn1HYC-g0LfgdUgj6t_5iW3xlbpp_pKguqdLbeIX_1P_J7sj557wcfb8P2aHDhoFUXPyg3ZzRa5voXMI5N3hXH9AGNpzQQ |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=New+Type+of+Gegenbauer-Jacobi-Hermite+Monogenic+Polynomials+and+Associated+Continuous+Clifford+Wavelet+Transform&rft.jtitle=Acta+applicandae+mathematicae&rft.au=Arfaoui%2C+Sabrine&rft.au=Ben+Mabrouk%2C+Anouar&rft.au=Cattani%2C+Carlo&rft.date=2020-12-01&rft.pub=Springer+Netherlands&rft.issn=0167-8019&rft.eissn=1572-9036&rft.volume=170&rft.issue=1&rft.spage=1&rft.epage=35&rft_id=info:doi/10.1007%2Fs10440-020-00322-0&rft.externalDocID=10_1007_s10440_020_00322_0 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0167-8019&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0167-8019&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0167-8019&client=summon |