A class of tight framelet packets

Da-Yong Lu; Qi-Bin Fan

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 3, page 623-639
  • ISSN: 0011-4642

Abstract

top
This paper obtains a class of tight framelet packets on L 2 ( ℝ d ) from the extension principles and constructs the relationships between the basic framelet packets and the associated filters.

How to cite

top

Lu, Da-Yong, and Fan, Qi-Bin. "A class of tight framelet packets." Czechoslovak Mathematical Journal 61.3 (2011): 623-639. <http://eudml.org/doc/196857>.

@article{Lu2011,
abstract = {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.},
author = {Lu, Da-Yong, Fan, Qi-Bin},
journal = {Czechoslovak Mathematical Journal},
keywords = {wavelet frames; framelet packets; framelets; extension principles; wavelet frame; framelet packet; framelet; extension principle},
language = {eng},
number = {3},
pages = {623-639},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A class of tight framelet packets},
url = {http://eudml.org/doc/196857},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Lu, Da-Yong
AU - Fan, Qi-Bin
TI - A class of tight framelet packets
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 3
SP - 623
EP - 639
AB - 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.
LA - eng
KW - wavelet frames; framelet packets; framelets; extension principles; wavelet frame; framelet packet; framelet; extension principle
UR - http://eudml.org/doc/196857
ER -

References

top
  1. Behera, B., 10.1007/BF02829617, Proc. Ind. Acad. Sci., Math. Sci. 111 (2001), 439-463. (2001) MR1923985DOI10.1007/BF02829617
  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. (2001) Zbl1036.42032MR1826007
  3. Boor, C., DeVore, R. A., Ron, A., 10.1007/BF01198001, Construct. Approx. 9 (1993), 123-166. (1993) Zbl0773.41013MR1215767DOI10.1007/BF01198001
  4. Chen, D., 10.1137/S0036141097323333, SIAM J. Math. Anal. 4 (2000), 726-739. (2000) Zbl0966.42024MR1745145DOI10.1137/S0036141097323333
  5. Chen, Q. J., Cheng, Z. X., 10.1016/j.chaos.2006.03.097, Chaos, Solitons and Fractals 31 (2007), 1024-1034. (2007) Zbl1142.42014MR2262193DOI10.1016/j.chaos.2006.03.097
  6. Christensen, O., An Introduction to Frames and Riesz Bases, Birkhäuser, Boston (2003). (2003) Zbl1017.42022MR1946982
  7. Chui, C. R., Li, C., 10.1137/0524044, SIAM J. Math. Anal. 24 (1993), 712-738. (1993) MR1215434DOI10.1137/0524044
  8. Cohen, A., Daubechies, I., 10.1137/0524077, SIAM J. Math. Anal. 24 (1993), 1340-1354. (1993) MR1234020DOI10.1137/0524077
  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. (1992) Zbl0822.42019MR1187353
  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. (1992) Zbl0792.94004MR1187341
  11. Daubechies, I., Han, B., 10.1007/s00365-004-0567-4, Constr. Approx. 20 (2004), 325-352. (2004) Zbl1055.42025MR2057532DOI10.1007/s00365-004-0567-4
  12. Daubechies, I., Han, B., Ron, A., Shen, Z., 10.1016/S1063-5203(02)00511-0, Appl. Comput. Harmon. Anal. 1 (2003), 1-46. (2003) Zbl1035.42031MR1971300DOI10.1016/S1063-5203(02)00511-0
  13. Han, B., 10.1016/S0377-0427(02)00891-9, J. Comput. Appl. Math. 155 (2003), 43-67. (2003) Zbl1021.42020MR1992289DOI10.1016/S0377-0427(02)00891-9
  14. Han, B., 10.1016/j.acha.2008.01.002, Appl. Comput. Harmon. Anal. 26 (2009), 14-42. (2009) Zbl1154.42007MR2467933DOI10.1016/j.acha.2008.01.002
  15. Han, B., 10.1006/acha.1997.0217, Appl. Comput. Harmon. Anal. 4 (1997), 380-413. (1997) Zbl0880.42017MR1474096DOI10.1006/acha.1997.0217
  16. Han, B., Mo, Q., 10.1016/j.acha.2004.09.001, Appl. Comput. Harmon. Anal. 18 (2005), 67-93. (2005) Zbl1057.42026MR2110513DOI10.1016/j.acha.2004.09.001
  17. Long, R., Chen, W., 10.1007/BF02649111, J. Fourier Anal. Appl. 3 (1997), 239-256. (1997) Zbl0882.42022MR1448338DOI10.1007/BF02649111
  18. Ron, A., Shen, Z., 10.1006/jfan.1996.3079, J. Functional Anal. Appl. 148 (1997), 408-447. (1997) MR1469348DOI10.1006/jfan.1996.3079
  19. Ron, A., Shen, Z., 10.1090/S0025-5718-98-00898-9, Math. Comput. 67 (1998), 191-207. (1998) MR1433269DOI10.1090/S0025-5718-98-00898-9
  20. Selesnick, I. W., Abdelnour, A. F., 10.1016/j.acha.2004.05.003, Appl. Comput. Harmon. Anal. 17 (2004), 211-225. (2004) Zbl1066.42027MR2082159DOI10.1016/j.acha.2004.05.003
  21. Shen, Z., 10.1137/S0036141093243642, SIAM J. Math. Anal. 26 (1995), 1061-1074. (1995) MR1338374DOI10.1137/S0036141093243642

NotesEmbed ?

top

You must be logged in to post comments.