Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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WAVELETS ON THE UNIT INTERVAL WITH BOUNDARY TREATMENT

  • Published : 1997.04.01
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Abstract

This paper concerns constructing wavelet bases on the unit interval, where a new boundary treatment is provided to overcome certain drawbacks of eariler constructions. Wavelet expansions on the unit interval usually suffer from artificial boundary effects and poor convergence at the boundaries. Many researchers have suggested a solution to the drawbacks. From a practical point of view, their solutions also have a common disadvantage. This paper provides a new solution using biorthogonality near the boundaries, that avoids the disadvantage while preserving their advantages.

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References

  1. IEEE Trans. on Image Processing v.1 Image coding using wavelet transform M. Antonini;M. Barlaud;P. Mathieu;I. Daubechies
  2. Numerical Methods of Approximation Theory Wavelets on a bounded interval C. K. Chui;E. Quak;D. Braess(ed);L. L. Schumacher(ed)
  3. Comm. Pure Appl. Math. v.45 Biorthogonal bases of compactly supported wavelets A. Cohen;I. Daubechies;J. Feauveau
  4. Appl. Comput. Harmonic Analysis v.1 Wavelets on the interval and fast wavelet transforms. A. Cohen;I. Daubechies;P. Vial
  5. Constr. Approx. v.9 Wavelet Galerkin methods;An adapted biorthogonal wavelet basis S. Dahlke;I. Weinreich
  6. Comm. Pure and Appl. Math. v.41 Orthonormal bases of compactly supported wavelets I. Daubechies
  7. Conf. Series in Appl. Math. v.61 Ten lectures on wavelets, CBMS-NSF Reg. I. Daubechies
  8. IEEE J. on Information Theory v.38 Image compression through wavelet transform coding R. DeVore;B. Jawerth;B. J. Lucier
  9. Constructive Aspects of Functional Analysis A Fourier analysis of the finite element variational method G. Fix;G. Strang;G. Geymonant(ed)
  10. SIAM Review v.46 Continuous and discrete wavelet transform C. E. Heil;D. F. Walnut
  11. Curves and Surfaces Using the refinement equations for the construction of pre-wavelets II: power of two R.-Q. Jia;C. Micchelli;P. J. Laurent;A. LeMehaute;L. L. Schumaker
  12. Technical Report #246, Purdue University(Submitted to Appl. Comput. Harmonic Analysis) Characterizations of Besov spaces by wavelets on the unit cube D.-G. Kim
  13. Wavelet bases on the interval and application to image compression D.-G. Kim
  14. Trans. Amer. Math. Soc. v.315 Multiresolution approximations and wavelet orthonormal bases of $L^2(R)$ S. Mallat
  15. Rev. Mat. Iberoamer v.7 Ondelettes sur l'intervalle Y. Meyler