Abstract
This paper studies the mathematical, mechanism of the generalized interpolating filters and gives the corresponding parametric representations. On the basis of the parametric representations, a novel criterion and algorithm are proposed to design interval interpolating wavelets with robust boundary filters. Furthermore, some examples are designed and their performances in data compression are investigated. Both the theoretical analysis and the experimental results show that such an interval interpolating wavelet can effectively suppress the boundary effect.
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References
Donoho, D. L., Interpolating wavelet transform, Technical Report, Stanford: Dept. of Statistics of Stanford Univ., 1992, 10.
Dubue, S., Interpolation throught an iterative scheme, J. Math. Anal. and Appl., 1986, 144: 185.
Deslauriers, G., Dubue, S., Symmetric iterative interpolation processes, Constr. Approx., 1989, 5(1): 49.
Sweldens, W., The lifting scheme: a custom-design construction of biorthogonal wavelets, Appl. Comput. Harmon. Anal., 1996, 3(2): 186.
Sweldens, W., The lifting scheme: a construction of second generation wavelets SIAM J. Math. Anal., 1997, 29: 511.
Shui Penglang, Bao Zheng, Biothogonal interpolating wavelets with compactly supported duals, Electron. Lett., 1998, 34(12): 1185.
Shui Penglang, Bao Zheng, Signal-adapted biorthogonal interpolating recursive wavelets, Electron. Lett., 1998, 34(20): 1920.
Daubechies, I., Orthonormal bases of compactly supported wavelets II: Variations on a theme, SIAM J. Math. Anal., 1993, 24 (2): 499–519.
Andersson, L., Hall, H., Jawerth, B., et al., Wavelets on closed subsets of the real line. Recent Advances in Wavelet Analysis, 1993, 1: 61.
Cohen, A., Daubechies, I., Vial, P., Wavelets on the interval and fast wavelet transforms, Applied and Computational Harmonic Analysis, 1993, 1: 54.
Wang Hongyu, The Special on Digital Signal Processing (in Chinese), Beijing: National Defense Industry Press, 1995.
Devore, R. A., Jawerth, B., Lucier, B. J., Image compression throught wavelet transform coding, IEEE Trans. on Information Theory, 1992, 38 (2): 719.
Shapiro, J. M., Embedded image coding using zerotrees of wavelet coefficients, IEEE Trans. on SP, 1993, 41(12): 3445.
Mallat, S., Falzon, F., Analysis of low bit rate image transform coding, IEEE. Trans. on SP, 1998, 46(4): 1027.
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Shui, P., Bao, Z. Interval interpolating wavelets with robust boundary filters. Sci. China Ser. E-Technol. Sci. 43, 287–296 (2000). https://doi.org/10.1007/BF02916833
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DOI: https://doi.org/10.1007/BF02916833