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 ( 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.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.