Skip to main content

Performance of a Wavelet Shrinking Method

  • Conference paper
  • First Online:
Book cover Numerical Methods and Applications (NMA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8962))

Included in the following conference series:

  • 1800 Accesses

Abstract

A concept for shrinking of wavelet coefficients has been presented and explored in a series of articles [24]. The theory and experiments so far suggest a strategy where the shrinking adapts to local smoothness properties of the original signal. From this strategy we employ partitioning of the global signal and local shrinking under smoothness constraints. Furthermore, we benchmark shrinking of local partitions’ wavelet coefficients utilizing a selection of wavelet basis functions. Then we present and benchmark an adaptive partition-based shrinking strategy where the best performing shrinkage is applied to individual partitions, one at a time. Finally, we compare the local and global benchmark results.

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

Access this chapter

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 EPUB and 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

References

  1. Daubechies, I.: Orthonormal bases of compactly supported wavelets. Commun. Pure Appl. Math. XLI, 909–966 (1988)

    Article  MathSciNet  Google Scholar 

  2. Dechevsky, L.T., Grip, N., Gundersen, J.: A new generation of wavelet shrinkage: adaptive strategies based on composition of Lorentz-type thresholding and Besov-type non-threshold shrinkage. In: Truchetet, F., Laligant, O. (eds.) Wavelet Applications in Industrial Processing V. Proceedings of SPIE, Boston, MA, USA, vol. 6763, pp. 1–14 (2007)

    Google Scholar 

  3. Dechevsky, L.T., Gundersen, J., Grip, N.: Wavelet compression, data fitting and approximation based on adaptive composition of Lorentz-type Thresholding and Besov-type non-threshold shrinkage. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2009. LNCS, vol. 5910, pp. 738–746. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  4. Dechevsky, L.T., Ramsay, J.O., Penev, S.I.: Penalized wavelet estimation with Besov regularity constraints. Mathematica Balkanica (N. S.) 13(3–4), 257–376 (1999)

    MATH  MathSciNet  Google Scholar 

  5. Donoho, D.L., Johnstone, I.M.: Ideal spatial adaptation by wavelet shrinkage. Biometrika 8(3), 425–455 (1994)

    Article  MathSciNet  Google Scholar 

  6. Donoho, D.L., Johnstone, I.M., Kerkyacharian, G., Picard, D.: Wavelet shrinkage: asymptopia? J. Roy. Stat. Soc. Ser. B 57(2), 301–369 (1995)

    MATH  MathSciNet  Google Scholar 

  7. Huffman, D.A.: A method for the construction of minimum-redundancy codes. In: Proceedings of the I.R.E., vol. 40, pp. 1098–1110 (1952)

    Google Scholar 

  8. Rose, A.: The sensitivity performance of the human eye on an absolute scale. J. Opt. Soc. Am. 38(2), 196–208 (1948)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rune Dalmo .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Dalmo, R., Bratlie, J., Bang, B. (2015). Performance of a Wavelet Shrinking Method. In: Dimov, I., Fidanova, S., Lirkov, I. (eds) Numerical Methods and Applications. NMA 2014. Lecture Notes in Computer Science(), vol 8962. Springer, Cham. https://doi.org/10.1007/978-3-319-15585-2_29

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-15585-2_29

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15584-5

  • Online ISBN: 978-3-319-15585-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics