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Multi-resolution analysis with frontal decomposition

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Abstract

Use of the compactlyB-spline wavelet of Chui and Wang (1991); Chui (1992) is hindered by loss of accuracy on decomposition, through truncation of weight sequences which are countably infinite. Adaptations to finite intervals often encounter problems at boundaries. For multiresolution analysis on a finite interval employing the linearB-wavelet the present research provides a frontal approach to decomposition which avoids truncation of weight sequences, experiences no problems at boundaries, and which is exhibits a factor of three increase in computational efficiency. The boundary wavelets which complete the linearB-wavelet basis on a finite interval are constructed.

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References

  • Battle, G. (1988). A block-spin construction of ondelletes. Part I: Lemarie functions,Comm. Math. Phys. 15, 175–177.

    Google Scholar 

  • Battle, G. (1992). In Chui, Charles K. (ed.), Cardinal spline interpolation and the block-spin construction of wavelets,Wavelets: a tutorial in theory and applications, Academic Press, Inc., New York.

    Google Scholar 

  • Chui, Charles K., and Wang, J. Z. (1991). A cardinal spline approach to wavelets,Proc. Amer. Math. Soc. 113, 785–793.

    Google Scholar 

  • Chui, Charles K. (1992).An Introduction to Wavelets, Academic Press.

  • Strang, Gilbert (1989). Wavelets and dilation equations: a brief introduction,SIAM Review 31(4), 614–627.

    Google Scholar 

  • Daubechies, Ingrid (1992). Ten lectures on wavelets,CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 61, SIAM.

  • Mallat, Stephen (1989a). A theory for multiresolution signal decomposition: the wavelet representation,IEEE Trans. Pattern Analys. and Machine Intell. 11 674–693.

    Google Scholar 

  • Mallat, Stephen (1989b). Multiresolution approximations and wavelet orthonormal bases ofL 2(R),Trans. Amer. Math. Society.

  • Cohen, A., Daubechies, I., Jawerth, B., and Vial, P. (1992). Multiresolution analysis, wavelets, and fast algorithms on the interval,Comptes Rendus Acad. Sci. Paris (A).

  • Buhmen, G., and Michelli, C. (1992). Spline pre-wavelets for nonuniform knots,Numerische Mathematik 61, 455–474.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Old Dominion University, 23529, Norfolk, Virginia

    Charlie H. Cooke & Sang Kyu Yang

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  1. Charlie H. Cooke
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  2. Sang Kyu Yang
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Cooke, C.H., Yang, S.K. Multi-resolution analysis with frontal decomposition. J Sci Comput 9, 327–340 (1994). https://doi.org/10.1007/BF01575036

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  • DOI: https://doi.org/10.1007/BF01575036

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