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Construction of multivariate compactly supported orthonormal wavelets

Ming-Jun Lai
2006 Advances in Computational Mathematics  
We propose a constructive method to find compactly supported orthonormal wavelets for any given compactly supported scaling function φ in the multivariate setting.  ...  Furthermore, the constructive method can be extended to construct compactly supported multi-wavelets for any given compactly supported orthonormal multi-scaling vector.  ...  Although many special multivariate nonseparable wavelets have been constructed, it is still an open problem how to construct multivariate compactly supported orthonormal wavelets for any given compactly  ... 
doi:10.1007/s10444-004-7643-y fatcat:lnwrzpffurgzrbobo2jgpkhwim

Page 1402 of Mathematical Reviews Vol. , Issue 93c [page]

1993 Mathematical Reviews  
Summary: “The general concept of multivariate wavelet bases is described with emphasis on the construction procedure.  ...  This scaling function is one of an infinite class of scaling functions introduced by Daubechies for the purpose of con- FOURIER ANALYSIS 1402 structing orthonormal bases of compactly supported wavelets  ... 

Page 5554 of Mathematical Reviews Vol. , Issue 2001H [page]

2001 Mathematical Reviews  
42C40 Karoui, Abderrazek A technique for the construction of compactly supported biorthogonal wavelets of L?  ...  To preserve such properties as self-duality while requiring compact support, the notion of tight frame is perhaps the only replacement for that of orthonormal wavelet.  ... 

Wavelet Analysis and Its Applications [chapter]

1998 Wavelet Analysis and Its Applications  
the Ml natdad. and correlating and ravwwing tn« couaction of information.  ...  Arlington, va, 22202-t)t)2. and to t»a Office of Managamam and lud9at.»aparworkKaduRion*roiact(07044ltl),\nratninaton. OC 20S0J 1. AGENCY USE ONLY (Itiv* blink)  ...  ;j «3 SUBJECT TERMS Time-frequency localization, symmetry for compactly supported orthonormal wavelets, multivariate wavelets with matrix dilations, interpolating wavelets and functional wavelet transform  ... 
doi:10.1016/s1874-608x(13)70006-2 fatcat:agt2ivyyd5ffvbmlzisw62iwzu

Wavelet Analysis and Its Applications [chapter]

1994 Wavelet Analysis and Its Applications  
the Ml natdad. and correlating and ravwwing tn« couaction of information.  ...  Arlington, va, 22202-t)t)2. and to t»a Office of Managamam and lud9at.»aparworkKaduRion*roiact(07044ltl),\nratninaton. OC 20S0J 1. AGENCY USE ONLY (Itiv* blink)  ...  ;j «3 SUBJECT TERMS Time-frequency localization, symmetry for compactly supported orthonormal wavelets, multivariate wavelets with matrix dilations, interpolating wavelets and functional wavelet transform  ... 
doi:10.1016/b978-0-08-052084-1.50001-6 fatcat:yocvxu4jafealc6li2frd6dvau

Wavelet Analysis and its Applications [chapter]

1997 Wavelet Analysis and Its Applications  
the Ml natdad. and correlating and ravwwing tn« couaction of information.  ...  Arlington, va, 22202-t)t)2. and to t»a Office of Managamam and lud9at.»aparworkKaduRion*roiact(07044ltl),\nratninaton. OC 20S0J 1. AGENCY USE ONLY (Itiv* blink)  ...  ;j «3 SUBJECT TERMS Time-frequency localization, symmetry for compactly supported orthonormal wavelets, multivariate wavelets with matrix dilations, interpolating wavelets and functional wavelet transform  ... 
doi:10.1016/s1874-608x(97)80020-9 fatcat:qfws3jrukvfmbkvltowh7olxam

Wavelet Analysis and Its Applications [chapter]

1994 Wavelet Analysis and Its Applications  
the Ml natdad. and correlating and ravwwing tn« couaction of information.  ...  Arlington, va, 22202-t)t)2. and to t»a Office of Managamam and lud9at.»aparworkKaduRion*roiact(07044ltl),\nratninaton. OC 20S0J 1. AGENCY USE ONLY (Itiv* blink)  ...  ;j «3 SUBJECT TERMS Time-frequency localization, symmetry for compactly supported orthonormal wavelets, multivariate wavelets with matrix dilations, interpolating wavelets and functional wavelet transform  ... 
doi:10.1016/b978-0-08-052087-2.50022-0 fatcat:gvlm3dbpjjhyhfq5qnutxbxxui

Wavelet Analysis and Its Applications [chapter]

1998 Wavelet Analysis and Its Applications  
the Ml natdad. and correlating and ravwwing tn« couaction of information.  ...  Arlington, va, 22202-t)t)2. and to t»a Office of Managamam and lud9at.»aparworkKaduRion*roiact(07044ltl),\nratninaton. OC 20S0J 1. AGENCY USE ONLY (Itiv* blink)  ...  ;j «3 SUBJECT TERMS Time-frequency localization, symmetry for compactly supported orthonormal wavelets, multivariate wavelets with matrix dilations, interpolating wavelets and functional wavelet transform  ... 
doi:10.1016/s1874-608x(98)80053-8 fatcat:c5xqfwsh4bcovdl4ztthbr45hi

WAVELET ANALYSIS AND ITS APPLICATIONS [chapter]

CHARLESK CHUI
1992 Wavelets  
SECURITY CLASSIFICATION OF REPORT UNCLASSIFIED NSN 7540-01 -280-5500 18. SECURITY CLASSIFICATION UNCLASSIFIED 19. SECURITY CLASSIFICATION OF ABSTRACT UNCLASSIFIED 15. NUMBER OF PAGES 6 16.  ...  the data nttata. and corseting and reviewing the collection of information, tend comments regarding this burden estimate or any otner asoect of tnu collection of information, including suggestions for  ...  DTIC QUALITY INSPECTED 8 SUBJECT TERMS Time-frequency localization, symmetry for compactly supported orthonormal wavelets, multivariate wavelets with matrix dilations, interpolating wavelets and functional  ... 
doi:10.1016/b978-0-12-174590-5.50029-0 fatcat:jf5kqafy65fdxek3h4mosccnlq

Wavelet Analysis and Its Applications [chapter]

1994 Wavelet Analysis and Its Applications  
the Ml natdad. and correlating and ravwwing tn« couaction of information.  ...  Arlington, va, 22202-t)t)2. and to t»a Office of Managamam and lud9at.»aparworkKaduRion*roiact(07044ltl),\nratninaton. OC 20S0J 1. AGENCY USE ONLY (Itiv* blink)  ...  ;j «3 SUBJECT TERMS Time-frequency localization, symmetry for compactly supported orthonormal wavelets, multivariate wavelets with matrix dilations, interpolating wavelets and functional wavelet transform  ... 
doi:10.1016/b978-0-08-052087-2.50001-3 fatcat:bokonfkoovhs3pnwco27u5z4em

Wavelet Analysis and Its Applications [chapter]

1994 Wavelet Analysis and Its Applications  
the Ml natdad. and correlating and ravwwing tn« couaction of information.  ...  Arlington, va, 22202-t)t)2. and to t»a Office of Managamam and lud9at.»aparworkKaduRion*roiact(07044ltl),\nratninaton. OC 20S0J 1. AGENCY USE ONLY (Itiv* blink)  ...  ;j «3 SUBJECT TERMS Time-frequency localization, symmetry for compactly supported orthonormal wavelets, multivariate wavelets with matrix dilations, interpolating wavelets and functional wavelet transform  ... 
doi:10.1016/b978-0-08-052084-1.50035-1 fatcat:4kbmfhne25d3bfweaynfigftr4

Wavelet Analysis and Its Applications [chapter]

1992 Wavelet Analysis and Its Applications  
the Ml natdad. and correlating and ravwwing tn« couaction of information.  ...  Arlington, va, 22202-t)t)2. and to t»a Office of Managamam and lud9at.»aparworkKaduRion*roiact(07044ltl),\nratninaton. OC 20S0J 1. AGENCY USE ONLY (Itiv* blink)  ...  ;j «3 SUBJECT TERMS Time-frequency localization, symmetry for compactly supported orthonormal wavelets, multivariate wavelets with matrix dilations, interpolating wavelets and functional wavelet transform  ... 
doi:10.1016/b978-0-12-174584-4.50001-3 fatcat:fjusdwuxnzcj5mmspnaa5ogc6i

Wavelet Analysis and its Applications [chapter]

1998 Wavelet Analysis and Its Applications  
the Ml natdad. and correlating and ravwwing tn« couaction of information.  ...  Arlington, va, 22202-t)t)2. and to t»a Office of Managamam and lud9at.»aparworkKaduRion*roiact(07044ltl),\nratninaton. OC 20S0J 1. AGENCY USE ONLY (Itiv* blink)  ...  ;j «3 SUBJECT TERMS Time-frequency localization, symmetry for compactly supported orthonormal wavelets, multivariate wavelets with matrix dilations, interpolating wavelets and functional wavelet transform  ... 
doi:10.1016/s1874-608x(98)80056-3 fatcat:bavw6co2fjcare7lsxgamajife

Wavelet Analysis and Its Applications [chapter]

1992 Wavelets  
the Ml natdad. and correlating and ravwwing tn« couaction of information.  ...  Arlington, va, 22202-t)t)2. and to t»a Office of Managamam and lud9at.»aparworkKaduRion*roiact(07044ltl),\nratninaton. OC 20S0J 1. AGENCY USE ONLY (Itiv* blink)  ...  ;j «3 SUBJECT TERMS Time-frequency localization, symmetry for compactly supported orthonormal wavelets, multivariate wavelets with matrix dilations, interpolating wavelets and functional wavelet transform  ... 
doi:10.1016/b978-0-12-174590-5.50001-0 fatcat:iqs2jgt3gverhkte7b5ajczfm4

Page 8500 of Mathematical Reviews Vol. , Issue 99m [page]

1999 Mathematical Reviews  
Shen, “Construction of compactly supported biorthogonal wavelets in L,(R°)”, Preprint, 1997; per bibl.], we are able to obtain sym- metrical compactly supported multivariate biorthogonal wavelets which  ...  The subse- quent construction of compactly supported biorthogonal wavelets is based on the concept of stable completions.  ... 
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