Ternary wavelets and their applications to signal compression

Ghulam Mustafa; Falai Chen; Zhangjin Huang

International Journal of Applied Mathematics and Computer Science (2004)

  • Volume: 14, Issue: 2, page 233-240
  • ISSN: 1641-876X

Abstract

top
We introduce ternary wavelets, based on an interpolating 4-point C^2 ternary stationary subdivision scheme, for compressing fractal-like signals. These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals. The error in compressing fractal-like signals by ternary wavelets is at most half of that given by four-point wavelets (Wei and Chen, 2002). However, for compressing regular signals we further classify ternary wavelets into 'odd ternary' and 'even ternary' wavelets. Our odd ternary wavelets are better in part for compressing both regular and fractal-like signals than four-point wavelets. These ternary wavelets are locally supported, symmetric and stable. The analysis and synthesis algorithms have linear time complexity.

How to cite

top

Mustafa, Ghulam, Chen, Falai, and Huang, Zhangjin. "Ternary wavelets and their applications to signal compression." International Journal of Applied Mathematics and Computer Science 14.2 (2004): 233-240. <http://eudml.org/doc/207694>.

@article{Mustafa2004,
abstract = {We introduce ternary wavelets, based on an interpolating 4-point C^2 ternary stationary subdivision scheme, for compressing fractal-like signals. These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals. The error in compressing fractal-like signals by ternary wavelets is at most half of that given by four-point wavelets (Wei and Chen, 2002). However, for compressing regular signals we further classify ternary wavelets into 'odd ternary' and 'even ternary' wavelets. Our odd ternary wavelets are better in part for compressing both regular and fractal-like signals than four-point wavelets. These ternary wavelets are locally supported, symmetric and stable. The analysis and synthesis algorithms have linear time complexity.},
author = {Mustafa, Ghulam, Chen, Falai, Huang, Zhangjin},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {multiresolution; signal compression; wavelets; subdivision; multiresolution analysis; ternary wavelets},
language = {eng},
number = {2},
pages = {233-240},
title = {Ternary wavelets and their applications to signal compression},
url = {http://eudml.org/doc/207694},
volume = {14},
year = {2004},
}

TY - JOUR
AU - Mustafa, Ghulam
AU - Chen, Falai
AU - Huang, Zhangjin
TI - Ternary wavelets and their applications to signal compression
JO - International Journal of Applied Mathematics and Computer Science
PY - 2004
VL - 14
IS - 2
SP - 233
EP - 240
AB - We introduce ternary wavelets, based on an interpolating 4-point C^2 ternary stationary subdivision scheme, for compressing fractal-like signals. These wavelets are tightly squeezed and therefore they are more suitable for compressing fractal-like signals. The error in compressing fractal-like signals by ternary wavelets is at most half of that given by four-point wavelets (Wei and Chen, 2002). However, for compressing regular signals we further classify ternary wavelets into 'odd ternary' and 'even ternary' wavelets. Our odd ternary wavelets are better in part for compressing both regular and fractal-like signals than four-point wavelets. These ternary wavelets are locally supported, symmetric and stable. The analysis and synthesis algorithms have linear time complexity.
LA - eng
KW - multiresolution; signal compression; wavelets; subdivision; multiresolution analysis; ternary wavelets
UR - http://eudml.org/doc/207694
ER -

References

top
  1. Andersson L., Hall N., Jawerth B. and Peters G. (1993): Wavelets on closed subsets of the real line, In: Recent Advances in Wavelet Analysis (L.L. Shumaker and G. Webb, Eds.). -New York: Academic Press, pp. 1-61. Zbl0808.42019
  2. Daubechies I. (1988): Orthogonal bases of compactly supported wavelets. - Comm. Pure Appl. Math., Vol. 41, No. 7, pp. 909-996. Zbl0644.42026
  3. DeVore R., Jawerth B. and Lucier B. (1992): Image compression through wavelet transform coding. - IEEE Trans. Inf. Theory, Vol. 38, No. 2, pp. 719-746. Zbl0754.68118
  4. Dubuc S. (1986): Interpolation through an iterative scheme. - J. Math. Anal. Appl., Vol. 114, No. 1, pp. 185-204. Zbl0615.65005
  5. Dyn N., Levin D. and Gregory J. (1987): A four-point interpolatory subdivision scheme for curve design. - Comput. Aided Geom. Design, Vol. 4, No. 4, pp. 257-268. Zbl0638.65009
  6. Hassan M.F. and Dodgson N.A., (2001). Ternary and three-point univariate subdivision schemes. - Tech. Rep. No. 520, University of Cambridge, Computer Laboratory. Available at http://www.cl.cam.ac.uk/TechReports/UCAM-CL-TR-520.pdf Zbl1037.65024
  7. Hassan M.F., Ivrissimitzis I.P., Dodgson N.A. and Sabin M.A. (2002): An interpolating 4-point C^2 ternary stationary subdivision scheme.- Comput. Aided Geom. Design, Vol. 19, No. 1, pp. 1-18. Zbl0984.68167
  8. Liu Z., Gortler S.J. and Cohen M.F. (1994): Hierarchical spacetime control. -Computer Graphics Annual Conference Series, pp. 35-42. 
  9. Lounsbery M., DeRose T.D. and Warren J. (1997): Multiresolution analysis for surfaces of arbitrary topological type.- ACM Trans. Graphics, Vol. 16, No. 1, pp. 34-73. 
  10. Mallat S. (1989): A theory for multiresolution signal decomposition: The wavelet representation. - IEEE Trans. Pattern Anal. Mach. Intell., Vol. 11, No. 7, pp. 674-693. Zbl0709.94650
  11. Stollnitz E.J., DeRose T.D. and Salesin D.H. (1996). Wavelets for Computer Graphics: Theory and Applications. - San Francisco: Morgan Kaufmann. 
  12. Wei G. and Chen F. (2002): Four-point wavelets and their applications. - J. Comp. Sci. Tech., Vol. 17, No. 4, pp. 473-480. Zbl1017.94512
  13. Weissman A. (1990): A 6-point interpolatory subdivision scheme for curve design.- M. Sc. Thesis, Tel-Aviv University, Israel. 

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.