A class of tight framelet packets
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 623-639
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
DOI : 10.1007/s10587-011-0035-9
Classification : 42C15, 42C40
Keywords: wavelet frames; framelet packets; framelets; extension principles
@article{10_1007_s10587_011_0035_9,
     author = {Lu, Da-Yong and Fan, Qi-Bin},
     title = {A class of tight framelet packets},
     journal = {Czechoslovak Mathematical Journal},
     pages = {623--639},
     year = {2011},
     volume = {61},
     number = {3},
     doi = {10.1007/s10587-011-0035-9},
     mrnumber = {2853079},
     zbl = {1249.42021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0035-9/}
}
TY  - JOUR
AU  - Lu, Da-Yong
AU  - Fan, Qi-Bin
TI  - A class of tight framelet packets
JO  - Czechoslovak Mathematical Journal
PY  - 2011
SP  - 623
EP  - 639
VL  - 61
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0035-9/
DO  - 10.1007/s10587-011-0035-9
LA  - en
ID  - 10_1007_s10587_011_0035_9
ER  - 
%0 Journal Article
%A Lu, Da-Yong
%A Fan, Qi-Bin
%T A class of tight framelet packets
%J Czechoslovak Mathematical Journal
%D 2011
%P 623-639
%V 61
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0035-9/
%R 10.1007/s10587-011-0035-9
%G en
%F 10_1007_s10587_011_0035_9
Lu, Da-Yong; Fan, Qi-Bin. A class of tight framelet packets. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 623-639. doi: 10.1007/s10587-011-0035-9

[1] Behera, B.: Multiwavelet packets and frame packets of $L^2(\mathbb R^d)$. Proc. Ind. Acad. Sci., Math. Sci. 111 (2001), 439-463. | DOI | MR

[2] Benedetto, J. J., Treiber, O. M.: Wavelet frames: multiresolution analysis and extension principles. In: L. Debnath, ed., Wavelet Transforms and Time-Frequency Signal Analysis, Birkhäuser (2001), 3-36. | MR | Zbl

[3] Boor, C., DeVore, R. A., Ron, A.: On the construction of multivariate (pre) wavelets. Construct. Approx. 9 (1993), 123-166. | DOI | MR | Zbl

[4] Chen, D.: On the splitting trick and wavelet frame packets. SIAM J. Math. Anal. 4 (2000), 726-739. | DOI | MR | Zbl

[5] Chen, Q. J., Cheng, Z. X.: A study on compactly supported orthogonal vector-valued wavelets and wavelet packets. Chaos, Solitons and Fractals 31 (2007), 1024-1034. | DOI | MR | Zbl

[6] Christensen, O.: An Introduction to Frames and Riesz Bases. Birkhäuser, Boston (2003). | MR | Zbl

[7] Chui, C. R., Li, C.: Non-orthogonal wavelet packets. SIAM J. Math. Anal. 24 (1993), 712-738. | DOI | MR

[8] Cohen, A., Daubechies, I.: On the instability of arbitrary biorthogonal wavelet packets. SIAM J. Math. Anal. 24 (1993), 1340-1354. | DOI | MR

[9] Coifman, R. R., Meyer, Y., Wickerhauser, M. V.: Size properties of wavelet packets. In: M. B. Ruskai et al., eds., Wavelets and Their Applications. Jones and Bartlett, Boston (1992), 453-470. | MR | Zbl

[10] Coifman, R. R., Meyer, Y., Wickerhauser, M. V.: Wavelet analysis and signal processing. In: M. B. Ruskai et al., eds., Wavelets and Their Applications. Jones and Bartlett, Boston (1992), 153-178. | MR | Zbl

[11] Daubechies, I., Han, B.: Pairs of dual wavelet frames from any two refinable functions. Constr. Approx. 20 (2004), 325-352. | DOI | MR | Zbl

[12] Daubechies, I., Han, B., Ron, A., Shen, Z.: Framelets: MRA-based constructions of wavelet frames. Appl. Comput. Harmon. Anal. 1 (2003), 1-46. | DOI | MR | Zbl

[13] Han, B.: Compactly supported tight wavelet frames and orthonormal wavelets of exponential decay with a general dilation matrix. J. Comput. Appl. Math. 155 (2003), 43-67. | DOI | MR | Zbl

[14] Han, B.: Dual multiwavelet frames with high balancing order and compact fast frame transform. Appl. Comput. Harmon. Anal. 26 (2009), 14-42. | DOI | MR | Zbl

[15] Han, B.: On dual wavelet tight frames. Appl. Comput. Harmon. Anal. 4 (1997), 380-413. | DOI | MR | Zbl

[16] Han, B., Mo, Q.: Symmetric MRA tight wavelet frames with three generators and high vanishing moments. Appl. Comput. Harmon. Anal. 18 (2005), 67-93. | DOI | MR | Zbl

[17] Long, R., Chen, W.: Wavelet basis packets and wavelet frame packets. J. Fourier Anal. Appl. 3 (1997), 239-256. | DOI | MR | Zbl

[18] Ron, A., Shen, Z.: Affine systems in $L_2(\mathbb R^d)$: the analysis of the analysis operator. J. Functional Anal. Appl. 148 (1997), 408-447. | DOI | MR

[19] Ron, A., Shen, Z.: Compactly supported tight affine spline frames in $L_2(\mathbb R^d)$. Math. Comput. 67 (1998), 191-207. | DOI | MR

[20] Selesnick, I. W., Abdelnour, A. F.: Symmetric wavelet tight frames with two generators. Appl. Comput. Harmon. Anal. 17 (2004), 211-225. | DOI | MR | Zbl

[21] Shen, Z.: Nontensor product wavelet packets in $L^2(\mathbb R^s)$. SIAM J. Math. Anal. 26 (1995), 1061-1074. | DOI | MR

Cité par Sources :