On the construction of a class of bidimensional nonseparable compactly supported wavelets
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Abstract:
Chui and Wang discussed the construction of one-dimensional compactly supported wavelets under a general framework, and constructed one-dimensional compactly supported spline wavelets. In this paper, under a mild condition, the construction of $M=(\begin {smallmatrix} 1&11&-1\end {smallmatrix})$-wavelets is obtained.References
- Ingrid Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988), no. 7, 909–996. MR 951745, DOI 10.1002/cpa.3160410705
- Albert Cohen and Ingrid Daubechies, Nonseparable bidimensional wavelet bases, Rev. Mat. Iberoamericana 9 (1993), no. 1, 51–137. MR 1216125, DOI 10.4171/RMI/133
- Jelena Kovačević and Martin Vetterli, Nonseparable multidimensional perfect reconstruction filter banks and wavelet bases for ${\scr R}^n$, IEEE Trans. Inform. Theory 38 (1992), no. 2, 533–555. MR 1162213, DOI 10.1109/18.119722
- Gilbert Strang and Truong Nguyen, Wavelets and filter banks, Wellesley-Cambridge Press, Wellesley, MA, 1996. MR 1411910
- J. Kovačević and M. Vetterli, Perfect reconstruction filter banks for HDTV representation and coding, Image Comm., 2 (1990), 349–364.
- Eugene Belogay and Yang Wang, Arbitrarily smooth orthogonal nonseparable wavelets in $\mathbf R^2$, SIAM J. Math. Anal. 30 (1999), no. 3, 678–697. MR 1677949, DOI 10.1137/S0036141097327732
- K. Gröchenig and W. R. Madych, Multiresolution analysis, Haar bases, and self-similar tilings of $\textbf {R}^n$, IEEE Trans. Inform. Theory 38 (1992), no. 2, 556–568. MR 1162214, DOI 10.1109/18.119723
- Da Ren Huang, Yun Zhang Li, and Qi Huo Sun, Refinable functions and refinement masks with polynomial or exponential decay, Chinese Ann. Math. Ser. A 20 (1999), no. 4, 483–488 (Chinese, with Chinese summary); English transl., Chinese J. Contemp. Math. 20 (1999), no. 3, 393–400. MR 1752279
- Yun Zhang Li, An estimate of the regularity of a class of bidimensional nonseparable refinable functions, Acta Math. Sinica (Chinese Ser.) 42 (1999), no. 6, 1053–1064 (Chinese, with English and Chinese summaries). MR 1756029
- Ingrid Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992. MR 1162107, DOI 10.1137/1.9781611970104
- Charles K. Chui and Jian-zhong Wang, A cardinal spline approach to wavelets, Proc. Amer. Math. Soc. 113 (1991), no. 3, 785–793. MR 1077784, DOI 10.1090/S0002-9939-1991-1077784-X
- C. K. Chui and J. Z. Wang, A general framework of compactly supported splines and wavelets, CAT Report 219, July 1990.
- Charles K. Chui and Jian-zhong Wang, On compactly supported spline wavelets and a duality principle, Trans. Amer. Math. Soc. 330 (1992), no. 2, 903–915. MR 1076613, DOI 10.1090/S0002-9947-1992-1076613-3
- Charles K. Chui, An introduction to wavelets, Wavelet Analysis and its Applications, vol. 1, Academic Press, Inc., Boston, MA, 1992. MR 1150048
- Rong Qing Jia and Charles A. Micchelli, Using the refinement equations for the construction of pre-wavelets. II. Powers of two, Curves and surfaces (Chamonix-Mont-Blanc, 1990) Academic Press, Boston, MA, 1991, pp. 209–246. MR 1123739
- Ruilin Long, High dimensional wavelet analysis, World book publishing corporation, 1995 (Chinese edition).
- Carl de Boor, Ronald A. DeVore, and Amos Ron, On the construction of multivariate (pre)wavelets, Constr. Approx. 9 (1993), no. 2-3, 123–166. MR 1215767, DOI 10.1007/BF01198001
Additional Information
- Yun-Zhang Li
- Affiliation: Department of Applied Mathematics, Beijing University of Technology, Beijing, 100022, People’s Republic of China
- Email: yzlee@bjut.edu.cn
- Received by editor(s): October 9, 2001
- Received by editor(s) in revised form: July 2, 2004, and July 6, 2004
- Published electronically: June 7, 2005
- Additional Notes: This work was partially supported by the Natural Science Foundation of China and the Natural Science Foundation of Beijing.
- Communicated by: David R. Larson
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 3505-3513
- MSC (2000): Primary 42C40
- DOI: https://doi.org/10.1090/S0002-9939-05-07911-6
- MathSciNet review: 2163585