×
Lu, Da-Yong; Fan, Qi-Bin

A class of tight framelet packets. (English) Zbl 1249.42021

Czech. Math. J. 61, No. 3, 623-639 (2011).
Summary: This paper obtains a class of tight framelet packets on \(L^2(\mathbb {R}^d)\) from the extension principles and constructs the relationships between the basic framelet packets and the associated filters.

Cited in 2 Documents

MSC:

42C15 General harmonic expansions, frames
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems

Keywords:

wavelet frame; framelet packet; framelet; extension principle
Cite Review PDF
Full Text: DOI EuDML Link

References:

[1] B. Behera: Multiwavelet packets and frame packets of L 2(\(\mathbb{R}\)d). Proc. Ind. Acad. Sci., Math. Sci. 111 (2001), 439–463. · Zbl 1003.42019 · doi:10.1007/BF02829617
[2] J. J. Benedetto, O.M. Treiber: Wavelet frames: multiresolution analysis and extension principles. In: L. Debnath, ed., Wavelet Transforms and Time-Frequency Signal Analysis, Birkhäuser, 2001, pp. 3–36. · Zbl 1036.42032
[3] C. Boor, R.A. DeVore, A. Ron: On the construction of multivariate (pre) wavelets. Construct. Approx. 9 (1993), 123–166. · Zbl 0773.41013 · doi:10.1007/BF01198001
[4] D. Chen: On the splitting trick and wavelet frame packets. SIAM J. Math. Anal. 4 (2000), 726–739. · Zbl 0966.42024 · doi:10.1137/S0036141097323333
[5] Q. J. Chen, Z.X. Cheng: A study on compactly supported orthogonal vector-valued wavelets and wavelet packets. Chaos, Solitons and Fractals 31 (2007), 1024–1034. · Zbl 1142.42014 · doi:10.1016/j.chaos.2006.03.097
[6] O. Christensen: An Introduction to Frames and Riesz Bases. Birkhäuser, Boston, 2003. · Zbl 1017.42022
[7] C. R. Chui, C. Li: Non-orthogonal wavelet packets. SIAM J. Math. Anal. 24 (1993), 712–738. · Zbl 0770.41022 · doi:10.1137/0524044
[8] A. Cohen, I. Daubechies: On the instability of arbitrary biorthogonal wavelet packets. SIAM J. Math. Anal. 24 (1993), 1340–1354. · Zbl 0792.42020 · doi:10.1137/0524077
[9] R. R. Coifman, Y. Meyer, M. V. Wickerhauser: Size properties of wavelet packets. In: M. B. Ruskai et al., eds., Wavelets and Their Applications. Jones and Bartlett, Boston, 1992, pp. 453–470. · Zbl 0822.42019
[10] R. R. Coifman, Y. Meyer, M. V. Wickerhauser: Wavelet analysis and signal processing. In: M. B. Ruskai et al., eds., Wavelets and Their Applications. Jones and Bartlett, Boston, 1992, pp. 153–178. · Zbl 0792.94004
[11] I. Daubechies, B. Han: Pairs of dual wavelet frames from any two refinable functions. Constr. Approx. 20 (2004), 325–352. · Zbl 1055.42025 · doi:10.1007/s00365-004-0567-4
[12] I. Daubechies, B. Han, A. Ron, Z. Shen: Framelets: MRA-based constructions of wavelet frames. Appl. Comput. Harmon. Anal. 1 (2003), 1–46. · Zbl 1035.42031
[13] B. Han: Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix. J. Comput. Appl. Math. 155 (2003), 43–67. · Zbl 1021.42020 · doi:10.1016/S0377-0427(02)00891-9
[14] B. Han: Dual multiwavelet frames with high balancing order and compact fast frame transform. Appl. Comput. Harmon. Anal. 26 (2009), 14–42. · Zbl 1154.42007 · doi:10.1016/j.acha.2008.01.002
[15] B. Han: On dual wavelet tight frames. Appl. Comput. Harmon. Anal. 4 (1997), 380–413. · Zbl 0880.42017 · doi:10.1006/acha.1997.0217
[16] B. Han, Q. Mo: Symmetric MRA tight wavelet frames with three generators and high vanishing moments. Appl. Comput. Harmon. Anal. 18 (2005), 67–93. · Zbl 1057.42026 · doi:10.1016/j.acha.2004.09.001
[17] R. Long, W. Chen: Wavelet basis packets and wavelet frame packets. J. Fourier Anal. Appl. 3 (1997), 239–256. · Zbl 0882.42022 · doi:10.1007/BF02649111
[18] A. Ron, Z. Shen: Affine systems in L 2(\(\mathbb{R}\)d): the analysis of the analysis operator. J. Functional Anal. Appl. 148 (1997), 408–447. · Zbl 0891.42018 · doi:10.1006/jfan.1996.3079
[19] A. Ron, Z. Shen: Compactly supported tight affine spline frames in L 2(\(\mathbb{R}\)d). Math. Comput. 67 (1998), 191–207. · Zbl 0892.42018 · doi:10.1090/S0025-5718-98-00898-9
[20] I. W. Selesnick, A. F. Abdelnour: Symmetric wavelet tight frames with two generators. Appl. Comput. Harmon. Anal. 17 (2004), 211–225. · Zbl 1066.42027 · doi:10.1016/j.acha.2004.05.003
[21] Z. Shen: Nontensor product wavelet packets in L 2(\(\mathbb{R}\)s). SIAM J. Math. Anal. 26 (1995), 1061–1074. · Zbl 0826.42025 · doi:10.1137/S0036141093243642
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.