Advertisement

Construction of Wavelet Frames Generated by MEP

  • Aleksandr Krivoshein
  • Vladimir Protasov
  • Maria SkopinaEmail author
Chapter
  • 656 Downloads
Part of the Industrial and Applied Mathematics book series (INAMA)

Abstract

Sufficient conditions for a dual wavelet system to be a dual wavelet frame are studied. Algorithmic methods for the construction of tight and dual compactly supported wavelet frames, providing an arbitrary approximation order and other important features, are discussed.

Keywords

Tight Wavelet Frames Wavelet System Dilation Matrix Vanishing Moments Polyphase Components 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Sadovnichii, V.A.: Theory of Operators. Roger Cooke Publisher, New York, Consultants Bureau (1991)Google Scholar
  2. 2.
    Novikov, I.Y., Protasov, V.Y., Skopina, M.A.: Wavelet Theory, vol. 239. AMS, Providence, RI, Translations Mathematical Monographs (2011)Google Scholar
  3. 3.
    Scheiderer, C.: Sums of squares on real algebraic surfaces. Manuscripta Math. 119(4), 395–410 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Charina, M., Putinar, M., Scheiderer, C., Stöckler, J.: An algebraic perspective on multivariate tight wavelet frames. Constr. Approx. 38, 253–276 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Charina, M., Putinar, M., Scheiderer, C., Stöckler, J.: An algebraic perspective on multivariate tight wavelet frames II. Appl. Comput. Harmon. Anal. 11, 185–213 (2006)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Dritschel, M.A.: On factorization of trigonometric polynomials. Integr. Eqn. Oper. Theory 49, 11–42 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Geronimo, J., Lai, M.J.: Factorization of multivariate positive laurent polynomials. J. Approx. Theory 139(1–2), 327–345 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Lawton, W., Lee, S.L., Shen, Z.: An algorithm for matrix extension and wavelet construction. Math. Comp. 37, 271–300 (1996)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Ron, A., Shen, Z.: Compactly supported tight affine spline frames in \({L_2(R^d)}\). Math. Comp. 67, 191–207 (1998)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2016

Authors and Affiliations

  • Aleksandr Krivoshein
    • 1
  • Vladimir Protasov
    • 2
  • Maria Skopina
    • 1
    Email author
  1. 1.Department of Applied Mathematics and Control ProcessesSaint Petersburg State UniversitySaint PetersburgRussia
  2. 2.Department of Mechanics and MathematicsLomonosov Moscow State UniversityMoscowRussia

Personalised recommendations