Construction of Orthogonal and Symmetric Multi-Wavelets with Vanishing Moments

Abstract:

It is a classical result that there is no compactly supported, symmetric, orthogonal univariate scalar wavelet. In this paper, the author aims to obtain multi-wavelets with several good properties. That is, the multi-wavelets are compactly supported, symmetric, orthogonal and have suitable vanishing moments. Firstly, we point out that the orthogonality and symmetry of the multi-wavelets can be obtained if the filter banks are constructed by matrix factorization. Secondly, it is presented how the choices of 2-th real orthogonal matrices matters in the construction. In the end, this paper discusses how the parameters are chosen so that the multi-wavelets will have suitable vanishing moments.

• Periodical: Applied Mechanics and Materials (Volumes 16-19)
• Pages: 618-622
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.16-19.618
• Online since: October 2009
• Authors: Hong Ying Xiao
• Keywords: Linear Phase, Multi Wavelet, PR Condition, Vanishing Moment

References

[1] I. Daubechies: Ten Lectures on Wavelets (CBMS, 61, SIAM, Philadelphia 1992), pp.167-174.

[2] Q.H. Chen, C.A. Micchelli, S.L. Peng and Y. Xu: SIAM J. Matrix Anal. Appl., Vol. 26 (2003), pp.517-531.

[3] C. Heil, G. Strang and V. Strela: Numerische Math., Vol. 73 (1996), pp.75-94.

[4] H.Y. Xiao: Piecewise Linear Spectral Sequences and Wavelet Filter Banks (Ph.D., Chinese Academy of Sciences, China 2005), pp.41-49.