참고문헌
- I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math., 41(7)(1988), 909-996. https://doi.org/10.1002/cpa.3160410705
- I. Daubechies, Ten lectures on wavelets, volume 61 of CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992.
- S. Du and D. Yuan, The description of two-directional biorthogonal finitely supported wavelet packets with poly-scale dilation, Key Engineering Materials, 439-440(2010), 1171-1176. https://doi.org/10.4028/www.scientific.net/KEM.439-440.1171
- F. Keinert, Wavelets and multiwavelets, Studies in Advanced Mathematics. Chapman & Hall/CRC, Boca Raton, FL, 2004.
- S.-G. Kwon, Approximation order of two-direction multiscaling functions, Preprint.
- S.-G. Kwon, High order orthogonal two-direction scaling functions from orthogonal balanced multiscaling functions, In preparation.
- S.-G. Kwon, Characterization of orthonormal high-order balanced multiwavelets in terms of moments, Bull. Korean Math. Soc., 46(1)(2009), 183-198. https://doi.org/10.4134/BKMS.2009.46.1.183
- S.-G. Kwon, Two-direction multiwavelet moments, Appl. Math. Comput., 219(8)(2012), 3530-3540. https://doi.org/10.1016/j.amc.2012.09.034
- J. Lebrun and M. Vetterli. High order balanced multiwavelets, Proc. IEEE ICASSP, Seatle, WA, (1998), 1529-1532.
- J. Lebrun and M. Vetterli, High-order balanced multiwavelets: theory, factorization, and design, IEEE Trans. Signal Process., 49(9)(2001), 1918-1930. https://doi.org/10.1109/78.942621
- B. Lv and X. Wang, Design and properties of two-direction compactly supported wavelet packets with an integer dilation factor, In 2009 Third Inter. Symp. on Intel. Info. Tech. Appl.
-
J. Morawiec, On
$L^1$ -solution of a two-direction refinable equation, J. Math. Anal. Appl., 354(2)(2009), 648-656. https://doi.org/10.1016/j.jmaa.2009.01.041 - G. Plonka and V. Strela, From wavelets to multiwavelets, In Mathematical methods for curves and surfaces, II (Lillehammer, 1997), Innov. Appl. Math., pages 375-399. Vanderbilt Univ. Press, Nashville, TN, 1998.
- G. Wang, X. Zhou, and B. Wang, The construction of orthogonal two-direction multiwavelet from orthogonal two-direction wavelet, Preprint.
- C. Xie and S. Yang, Orthogonal two-direction multiscaling functions, Front. Math. China, 1(4)(2006), 604-611. https://doi.org/10.1007/s11464-006-0031-9
- S. Yang and Y. Li, Two-direction refinable functions and two-direction wavelets with dilation factor m, Appl. Math. Comput., 188(2)(2007), 1908-1920. https://doi.org/10.1016/j.amc.2006.11.078
- S. Yang and Y. Li, Two-direction refinable functions and two-direction wavelets with high approximation order and regularity, Sci. China Ser. A, 50(12)(2007), 1687-1704. https://doi.org/10.1007/s11425-007-0091-7
- S. Yang and C. Xie, A class of orthogonal two-direction refinable functions and two-direction wavelets, Int. J. Wavelets Multiresolut. Inf. Process., 6(6)(2008), 883-894. https://doi.org/10.1142/S0219691308002653