Skip to main content
SpringerLink
Log in

A Generalization of Average Interpolating Wavelets

  • Conference paper
  • First Online:
New Trends in Analysis and Interdisciplinary Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

  • 1046 Accesses

Abstract

We consider two-dimensional average interpolating wavelets, which are generated from the average interpolating lifting scheme on a two-dimensional triangular lattice. The resulting set of biorthogonal functions is the generalization of the one-dimensional Cohen–Daubechies–Feauveau (1, N) biorthogonal wavelet whose scaling function is an average interpolating function of the order N. Some properties of the biorthogonal bases and associated filters, such as the order of zeros, regularity, and decay will be described.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. D.L. Donoho, Interpolating wavelet transforms. Technical Report 408, Department of Statistics, Stanford University, pp. 1–54, 1992

    Google Scholar 

  2. D.L. Donoho, Smooth wavelet decompositions with blocky coefficient kernels, in Recent Advances in Wavelet Analysis (Academic, Boston, 1993), pp. 259–308

    MATH  Google Scholar 

  3. A. Cohen, I. Daubechies, J. Feauveau, Bi-orthogonal bases of compactly supported wavelets. Commun. Pure Appl. Math. 45, 486–560 (1992)

    Article  MATH  Google Scholar 

  4. K. Fujinoki, O.V. Vasilyev, Triangular wavelets: an isotropic image representation with hexagonal symmetry. EURASIP J. Image Video Process. 2009 (248581), 1–16 (2009)

    Article  Google Scholar 

  5. W. Sweldens, The lifting scheme: a custom-design construction of biorthogonal wavelets. J. Appl. Comput. Harmon. Anal. 3 (2), 186–200 (1996)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was partially supported by JSPS KAKENHI Grant Number 26730099.

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Tokai University, Kanagawa, 259-1292, Japan

    Kensuke Fujinoki

Authors
  1. Kensuke Fujinoki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kensuke Fujinoki .

Editor information

Editors and Affiliations

  1. Faculty of Information Technology, Macau University of Science and Technology, Taipa, Macao

    Pei Dang

  2. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Min Ku

  3. Faculty of Science and Technology, Department of Mathematics, University of Macau, Taipa, Macao

    Tao Qian

  4. Department of Mathematics, University of Torino, Torino, Italy

    Luigi G. Rodino

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Fujinoki, K. (2017). A Generalization of Average Interpolating Wavelets. In: Dang, P., Ku, M., Qian, T., Rodino, L. (eds) New Trends in Analysis and Interdisciplinary Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-48812-7_71

Download citation

Publish with us

Policies and ethics

Search

Navigation