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2004 | 14 | 2 | 233-240
Tytuł artykułu

Ternary wavelets and their applications to signal compression

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
14
Numer
2
Strony
233-240
Opis fizyczny
Daty
wydano
2004
otrzymano
2003-12-25
Twórcy
  • Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
autor
  • Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
  • Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China
Bibliografia
  • 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.
  • Daubechies I. (1988): Orthogonal bases of compactly supported wavelets. - Comm. Pure Appl. Math., Vol. 41, No. 7, pp. 909-996.
  • 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.
  • Dubuc S. (1986): Interpolation through an iterative scheme. - J. Math. Anal. Appl., Vol. 114, No. 1, pp. 185-204.
  • 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.
  • 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
  • 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.
  • Liu Z., Gortler S.J. and Cohen M.F. (1994): Hierarchical spacetime control. -Computer Graphics Annual Conference Series, pp. 35-42.
  • 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.
  • 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.
  • Stollnitz E.J., DeRose T.D. and Salesin D.H. (1996). Wavelets for Computer Graphics: Theory and Applications. - San Francisco: Morgan Kaufmann.
  • Wei G. and Chen F. (2002): Four-point wavelets and their applications. - J. Comp. Sci. Tech., Vol. 17, No. 4, pp. 473-480.
  • Weissman A. (1990): A 6-point interpolatory subdivision scheme for curve design.- M. Sc. Thesis, Tel-Aviv University, Israel.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv14i2p233bwm
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