Skip to main content
SpringerLink
Log in

Optimization of Parameterized Compactly Supported Orthogonal Wavelets for Data Compression

  • Conference paper
Advances in Soft Computing (MICAI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7095))

Included in the following conference series:

Abstract

In this work we review the parameterization of filter coefficients of compactly supported orthogonal wavelets used to implement the discrete wavelet transform. We also present the design of wavelet based filters as a constrained optimization problem where a genetic algorithm can be used to improve the compression ratio on gray scale images by minimizing their entropy and we develop a quasi-perfect reconstruction scheme for images. Our experimental results report a significant improvement over previous works and they motivate us to explore other kinds of perfect reconstruction filters based on parameterized tight frames.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Mallat, S.G.: Multiresolution approximations and wavelet orthonormal bases of \({\mathbb{L}}^2({\mathbb{R}})\). Trans. Amer. Math. Soc. 315(1), 69–87 (1989)

    MathSciNet  MATH  Google Scholar 

  2. Mallat, S.G.: A theory for multiresolution signal decomposition: The wavelet representation. IEEE Trans. on Patt. Anal. Mach. Intell. 11(7), 674–693 (1989)

    Article  MATH  Google Scholar 

  3. Hereford, J.M., Roach, D.D.W., Pigford, R.: Image compression using parameterized wavelets with feedback. In: Proc. of SPIE, vol. 5102, pp. 267–277 (April 2003)

    Google Scholar 

  4. Daubechies, I.: Orthonormal bases of compactly supported wavelets. Commun. on Pure and Applied Math. 41(1), 909–996 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hehong, Z., Tewfik, A.: Parametrization of compactly supported orthonormal wavelets. IEEE Transactions on signal processing 41(3), 1428–1431 (1993)

    Article  MATH  Google Scholar 

  6. Pollen, D.: Su1(2f(z,1/z) for f a subfield of c. J. Amer. Math. Soc. 3, 611–624 (1990)

    MathSciNet  MATH  Google Scholar 

  7. Wells, R.O.: Parametrizing smooth compactly supported wavelets. Trans. Amer. Math. Soc. 338(2) (August 1993)

    Google Scholar 

  8. Schneid, J., Pittner, S.: On the parametrization of the coefficients of dilation equations for compactly supported wavelets. Computing 51, 165–173 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lina, J.M., Mayrand, M.: Parametrizations for daubechies wavelets. Ohys. Rev. E 48(6), R4160–R4163 (1993)

    MathSciNet  Google Scholar 

  10. Sherlock, B.G., Monro, D.M.: On the space of orthonormal wavelets. IEEE Transactions on Signal Processing 46(6), 1716–1720 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  11. Ming-Jun, L., Roach, W.: Parameterization of univariate orthogonal wavelets with short support. Aproximation theory X, Vanderbilt Univ. Press (2002)

    Google Scholar 

  12. Mallat, S.: A wavelet tour of signal processing. Academic Press Inc. (1998)

    Google Scholar 

  13. Walker, J.: A primer on wavelets and their scientific applications, 2nd edn. Chapman Hall/CRC, Taylor and Francis Group (2008)

    Google Scholar 

  14. Coello, C., Lamont, G., Van Velduizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, Heidelberg (2007)

    MATH  Google Scholar 

  15. Kuri, A.: A Comprehensive Approcah to Genetic Algorithms in Optimization and Learning. National Polytechnic Institute, Mexico (1999)

    Google Scholar 

  16. Shannon, C.: A mathematical theory of communication. Bell System Technical Journal 27, 379–423 (1948)

    Article  MathSciNet  MATH  Google Scholar 

  17. Herrera, O.: On the best evolutionary wavelet based filter to compress a specific signal. In: Sidorov, G., Hernández Aguirre, A., Reyes García, C.A. (eds.) MICAI 2010, Part II. LNCS (LNAI), vol. 6438, pp. 394–405. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  18. Wang, H., Peng, L.: Parameterizations of univariate wavelet tight frames with short support. Communications in Nonlinear Science and Numerical Simulation 11, 663–677 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Pennebaker, W., Mitchell, J.: JPEG: Still Image Data Compression Standard. Springer, Heidelberg (1992)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Sistemas, Universidad Autónoma Metropolitana Azcapotzalco, Av. San Pablo 180, Col. Reynosa Tamaulipas, 02200, México, D.F.

    Oscar Herrera Alcántara

  2. División de Ingeniería y Arquitectura, ITESM-CEM, Carretera al Lago de Guadalupe, Km 3.5, Atizapán, 52926, México, México

    Miguel González Mendoza

Authors
  1. Oscar Herrera Alcántara
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Miguel González Mendoza
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Mexican Petroleum Institute (IMP), Eje Central Lazaro Cardenas Norte, 152, Col. San Bartolo Atepehuacan, CP 07730, Mexico DF, Mexico

    Ildar Batyrshin

  2. National Polytechnic Institute (IPN), Center for Computing Research (CIC), Av. Juan Dios Bátiz, s/n, Col. Nueva Industrial Vallejo, CP 07738, Mexico D.F., Mexico

    Grigori Sidorov

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Herrera Alcántara, O., González Mendoza, M. (2011). Optimization of Parameterized Compactly Supported Orthogonal Wavelets for Data Compression. In: Batyrshin, I., Sidorov, G. (eds) Advances in Soft Computing. MICAI 2011. Lecture Notes in Computer Science(), vol 7095. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25330-0_45

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25330-0_45

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25329-4

  • Online ISBN: 978-3-642-25330-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation