Multiwavelets and Image Processing

  • M. Cotronei
  • L. Puccio
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 1)


This work contains a brief overview of the researches carried on by the authors on multiwavelet theory and applications. In particular, the effectiveness of multiwavelet techniques in image processing is shown and some evolutions of the theory are mentioned.


Decomposition Scheme Lift Scheme Multiscaling Function Barbara Image Refinable Function Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Bacchelli S., Cotronei M., and Lazzaro D. (2000) An algebraic construction of k-balanced multiwavelets via the lifting scheme. Num. Alg., 23 n. 4, 329–356.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bacchelli S., Cotronei M., and Lazzaro D. (2000) A recursive approach to the construction of k-balanced biorthogonal multifilters. In: Curve and Surface Fitting: Saint Malo 99, ( A. Cohen, C. Rabut, and L.L. Schumacker eds. ), Vanderbilt University Press, 27–36.Google Scholar
  3. 3.
    Bacchelli S., Cotronei M., Lazzaro D., Puccio L. (2000) Multiwavelets and construction of biorthogonal k-balanced multifilters. In: Recent Trends in Numerical Analysis, serie: Advances in Computation: Theory and Practice, ( L. Brugnano and D. Trigiante, eds.), Nova Science Publishers, Inc.Google Scholar
  4. 4.
    Cotronei M., Bacchelli S., and Sauer T. (2000) Multifilters with and without prefilters, submitted.Google Scholar
  5. 5.
    Barnabei M. and Montefusco L.B., Recursive Properties of Toeplitz and Hurwitz Matrices (1998) Linear Algebra and its Applications, 274, 367–388.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Chui C.K. and Lian J. (1996) A study of orthonormal multi-wavelets, Appl. Numer. Math., 20, 273–298.MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Chui C.K. (1992) An introduction to wavelets, Academic Press.Google Scholar
  8. 8.
    Cotronei M. (1996) Multiwavelets: analisi teorica ed algoritmi, Ph.D. Dissertation.Google Scholar
  9. 9.
    Cotronei M., Lazzaro D., Montefusco L.B., and Puccio L. (2000) Image compression through embedded multiwavelet transform coding, IEEE Trans. on Image Process., 9 n. 2, 184–189.MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Cotronei M., Lazzaro D., Montefusco L.B., and Puccio L., Some experiments on image compression by means of multiwavelet transform, Atti Accademia Pelori-tana dei Pericolanti, Classe I di Sc. Mat. Fis. e Natur., vol. LXXVI, to appear.Google Scholar
  11. 11.
    Cotronei M., Montefusco L.B., and Puccio L. (1998) Multiwavelet analysis and signal processing, IEEE Trans. on Circuits and Systems II: Analog and Digital Signal Processing, 45, 970–987.Google Scholar
  12. 12.
    Cotronei M. and Puccio L. (2000) Effectiveness of multiwavelets in signal and image processing. In: Ann. Univ. Ferrara–Sez. VII–Sc. Mat., Supplemento al Vol. XLV., 19–32.Google Scholar
  13. 13.
    Davis G., Strela V., and Turcajova R. (1999) Multiwavelet construction via the lifting scheme. In: Wavelet Analysis and Multiresolution Methods, T.-X. He (ed.), Lecture Notes in Pure and Applied Mathematics, Marcel Dekker.Google Scholar
  14. 14.
    Geronimo J.S., Hardin D.P., and Massopust P.R. (1994) Fractal functions and wavelet expansions based on several scaling functions, J. Approx. Theory, 78 n. 3, 373–401.MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Goh S.S., Jiang Q., and Xia T., Construction of biorthogonal multiwavelets using the lifting scheme, preprint.Google Scholar
  16. 16.
    Goodman T N T and Lee S.L. (1994) Wavelets of multiplicity r, Trans. Amer. Math. Soc., 342 (1): 307–324.MathSciNetzbMATHGoogle Scholar
  17. 17.
    Hardin D.P. and Roach D.W. (1998) Multiwavelet prefilters I: orthogonal pre-filters preserving approximation order p 2, IEEE Trans. on Circuits and Systems II: Analog and Digital Signal Processing, 45, 1106–1112.zbMATHGoogle Scholar
  18. 18.
    Jiang Q., On the construction of biorthogonal multiwavelet bases, preprint.Google Scholar
  19. 19.
    Lebrun J. and Vetterli M. (1998) Balanced multiwavelets: theory and design, IEEE Trans. on Signal Process., 46.Google Scholar
  20. 20.
    Lebrun J. and Vetterli M. (1998) High order balanced multiwavelets: theory, factorization and design, Proc. IEEE ICASSP., IEEE Press.Google Scholar
  21. 21.
    Micchelli C. and Sauer T. (1997) Regularity of multiwavelets, Adv. Comput. Math., 7 n. 4, 455–545.MathSciNetzbMATHGoogle Scholar
  22. 22.
    Plonka G. (1997) Approximation order provided by refinable function vectors, Constructive Approximation, 13, 221–244.MathSciNetzbMATHGoogle Scholar
  23. 23.
    Plonka G. and Strela V. (1998) Construction of multiscaling functions with approximation and symmetry, SIAM J. Math. Anal. 29, 481–510.MathSciNetzbMATHGoogle Scholar
  24. 24.
    Plonka G. and Strela V. (1998) From wavelets to multiwavelets. In: Mathematical Methods of Curves and Surfaces II ( M. Daehlen, T. Lyche, and L.L. Schumaker, eds.), Vanderbilt University Press, Nashville, 1–25.Google Scholar
  25. 25.
    Selesnick I. (1998) Multiwavelet bases with extra approximation properties, IEEE Trans. on Signal Process., 46, 2898–2908.MathSciNetCrossRefGoogle Scholar
  26. 26.
    Strang G. and Strela V. (1995) Short wavelets and matrix dilation equations, IEEE Trans. on Signal Process., 43., 108–115.Google Scholar
  27. 27.
    Strela V., Heller P.N., Strang G., Topiwala P., and Heil C. (1999) The application of multiwavelet filter banks to signal and image processing, IEEE Trans. on Image Process., 8, 548–563.CrossRefGoogle Scholar
  28. 28.
    Sweldens W. (1996) The lifting scheme: a custom-design construction of biorthogonal wavelets, ACHA, vol. 3, 186–200.MathSciNetzbMATHGoogle Scholar
  29. 29.
    Xia X.G., Geronimo J.S., Hardin D.P., and Suter B.W. (1996) Design of pre-filters for discrete multiwavelet transforms, IEEE Trans. on Signal Process., 44, 25–35.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • M. Cotronei
    • 1
  • L. Puccio
    • 1
  1. 1.Department of MathematicsUniversity of MessinaMessinaItaly

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