Abstract
An extrapolation procedure based on the vanishing moments property of the orthonormal wavelet family is associated to the à trous discrete wavelet transform with filters taken from the biorthogonal spline wavelets. This coupling avoids the construction of wavelets in the interval, enabling the confidence region increase of the transform when analyzing data. Simulations corroborate the efficiency of the proposed scheme.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Starck JL, Siebenmorgen R, Gredel R (1997) Spectral analysis using the wavelet transform. Astrophys J 482:1011–1020
Shensa MJ (1992) The discrete wavelet transform: wedding the ‘A Trous and Mallat algorithms. IEEE Trans Sig Proc 40(10):2464–2482
Grossmann A, Kronland-Martinet R, Morlet J (1987) Analysis of sound patterns through wavelet transforms. Int J Patt Recogn Artif Intell 1:99–126
Mallat S (1989) Multifrequency channel decompositions of images and wavelet models. IEEE Trans Acoustic Speech Signal Process 37:2091–2110
Williams JR, Amaratunga K (1997) A discrete wavelet transform without edge effects using wavelet extrapolation. J Fourier Anal Appl 3(4):435–449
Akay M (1997) Time-frequency and wavelets in biomedical signal processing, IEEE Press series on biomedical engineering. Wiley, Hardcover, 768 p
Brodie J, Daubechies I, De Mol C, Giannone D, Loris I (2009) Sparse and stable Markowitz portfolios. Proc Natl Acad Sci 106:12267–12272
Richard Johnson Jr C, Hendriks E, Berezhnoy IJ, Brevdo E, Hughes SM, Daubechies I, Li J, Postma E, Wang JZ (2008) Image processing for artist identification: computerized analysis of vincent van Gogh’s painting brushstrokes. Signal Process Magazine 25:37–48
Cohen A, Daubechies I, Vial P (1993) Wavelets on the interval and fast wavelet transforms. Appl Comp Harm Anal 1(1):54–81
Karabataka M, Cevdet Inceb M, Sengura A (2011) Wavelet domain association rules for efficient texture classification. Appl Soft Comput 11(1):32–38
Sheng-sheng Y, Xiao-cheng H, Jing-li Z, Jia-zhong C (2004) The boundary processing of wavelet based image compression. Wuhan Univ J Nat Sci 9(3):296–302. doi:10.1007/BF02907882
Lee WS, Kassim AA (2007) Signal and image approximation using interval wavelet transform. IEEE Trans Image Proc 16(1):46–56
Singh P, Singh P, Sharma RK (2011) JPEG image compression based on Biorthogonal, Coiflets and Daubechies Wavelet Families. Int J Comput Appl 13(1):1–7
Feil M, Uhl A (2001) Real-time image analysis using MIMD Parallel ‘a trous Wavelet algorithms. Real-Time Imaging 7(6):483–493
Acknowledgments
This work was supported by CNPq Grants 304854/2009-3, 476447/2010-0, and 201457/2010-5. Partial results described in this paper were previously presented in IntMath TDS at CNMAC 2010-SBMAC honoring Prof. Dalcidio Claudio and his leadership over more than 40 years of Interval Mathematics’ research in Brazil.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Renata Hax Reiser Sander.
Rights and permissions
About this article
Cite this article
Kozakevicius, A., Schmidt, A.A. Wavelet transform with special boundary treatment for 1D data. Comp. Appl. Math. 32, 447–457 (2013). https://doi.org/10.1007/s40314-013-0050-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40314-013-0050-6