Abstract
We address the problem of constructing multi-wavelets, that is, wavelets with more than one scaling and wavelet function. We generalize the algorithm, proposed by Alpert [1] for generating discrete Legendre multi-wavelets to the case of arbitrary, non-dyadic time interval splitting.
Preview
Unable to display preview. Download preview PDF.
References
Alpert, B.: A class of bases in L2 for the sparse representation of integral operators. SIAM J. Math. Anal. 24, 246–262 (1993)
Alpert, B., Beylkin, G., Coifman, R., Rochlin, V.: Wavelet bases for the fast solution of second-kind integral equations. SIAM Journal on Scientific Computing 14 (1), 159–184 (1993)
Egiazarian, K., Astola, J.: Tree-structured Haar transforms. Journal of Mathematical and Imaging Vision 16, 267–277 (2002)
Gotchev, A., Egiazarian, K., Astola, J.: On tree-structured legendre multi-wavelet bases. In: Proc. Int. Workshop on Spectral Methods and Multirate Signal Processing (SMMSP 2001), pp. 51–56 (2001)
Pogossova, E., Egiazarian, K., Astola, J.: Signal de-noising in tree-structured Haar basis. In: Guo, M. (ed.) ISPA 2003. LNCS, vol. 2745, pp. 736–739. Springer, Heidelberg (2003)
Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, San Diego (1999)
Resnikoff, H.L., Wells Jr., R.O.: Wavelet Analysis. Springer, New York (1998)
Strela, V., Heller, P.N., Strang, G., Topiwala, P., Heil, C.: The application of muti-wavelet filter banks to signal and image processing. IEEE Trans. on Image Proc. 8(4), 548–563 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pogossova, E., Egiazarian, K., Gotchev, A., Astola, J. (2005). Tree-Structured Legendre Multi-wavelets. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2005. EUROCAST 2005. Lecture Notes in Computer Science, vol 3643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556985_39
Download citation
DOI: https://doi.org/10.1007/11556985_39
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29002-5
Online ISBN: 978-3-540-31829-3
eBook Packages: Computer ScienceComputer Science (R0)