Abstract
Wavelets are just beginning to enter statistical theory and practice [2, 5, 7, 10, 12]. The pace of discovery is still swift, and except for orthogonal wavelets, the theory has yet to mature. However, the advantages of wavelets are already obvious in application areas such as image compression. Wavelets are more localized in space than the competing sines and cosines of Fourier series. They also use fewer coefficients in representing images, and they pick up edge effects better. The secret behind these successes is the capacity of wavelets to account for image variation on many different scales.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Antoniadis A, Oppenheim G (1995) Wavelets and Statistics. Springer, New York
Daubechies I (1992) Ten Lectures on Wavelets. SIAM, Philadelphia
Donoho DL, Johnstone IM (1995) Adapting to unknown smoothness via wavelet shrinkage. J Amer Stat Assoc 90:1200-1224
Hoffman K (1975) Analysis in Euclidean Space. Prentice-Hall, Engle-wood Cliffs, NJ
Jawerth B, Sweldens W (1994) An overview of wavelet based multiresolution analysis. SIAM Review 36:377-412
Kolaczyk ED (1996) A wavelet shrinkage approach to tomographic image reconstruction. J Amer Stat Assoc 91:1079-1090
Meyer Y (1993) Wavelets: Algorithms and Applications. Ryan RD, translator, SIAM, Philadelphia
Pollen D (1992) Daubechies’s scaling function on [0,3]. In Wavelets: A Tutorial in Theory and Applications, Chui CK, editor, Academic Press, New York, pp 3-13
Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. Cambridge University Press, Cambridge
Strang G (1989) Wavelets and dilation equations: a brief introduction. SIAM Review 31:614-627
Strichartz RS (1993) How to make wavelets. Amer Math Monthly 100:539-556
Walter GG (1994) Wavelets and Other Orthogonal Systems with Applications. CRC Press, Boca Raton, FL
Wickerhauser MV (1992) Acoustic signal compression with wavelet packets. In Wavelets: A Tutorial in Theory and Applications, Chui CK, editor, Academic Press, New York, pp 679-700
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer New York
About this chapter
Cite this chapter
Lange, K. (2010). Wavelets. In: Numerical Analysis for Statisticians. Statistics and Computing. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5945-4_21
Download citation
DOI: https://doi.org/10.1007/978-1-4419-5945-4_21
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-5944-7
Online ISBN: 978-1-4419-5945-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)