Advertisement

Multiresolution Analysis with Pulses

  • Carl H. Rohwer
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 142)

Abstract

Multiresolution analysis has recently received considerable attention in relation to wavelets. The word “multiresolution” is appropriate in so far as wavelets are local in some sense, and therefore have exponentially decaying impulse response. In image processing it is clear that edges and impulses yield undesirable synthetic features in partially reconstructed images from linear multiscale decompositions. Median decompositions are regarded as better in practice, but computational complexity and lack of theory are problems. An alternative, from mathematical morphology is possible, yielding results demonstrably similar to the median decomposition, but computationally simpler, and having a strong theory for deriving qualitative and quantitative properties.

Keywords

Wavelet Decomposition Resolution Level Multiresolution Analysis Mathematical Morphology Impulsive Noise 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    A. Bijaoni, F. Murtagh, J.L. Starck, Image Processing and Data Analysis -The Multiscale Approach, Cambridge University Press, 1998.Google Scholar
  2. [2]
    C.K. Chui, Wavelets: A Mathematical Tool for Signal Analysis, SIAM, Philadelphia, 1997.zbMATHGoogle Scholar
  3. [3]
    C.L. Mallows, Some Theory of Nonlinear Smoothers, (Ann. Statist. 8, no. 4 (1980), 695–715 ).CrossRefGoogle Scholar
  4. [4]
    P. Maragos, R.W. Schafer, Morphological Filters–Part II: Their relations to Median, Order-Statistic, and Stack Filters, IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. ASSP-35 (1987), 1170–1184.MathSciNetGoogle Scholar
  5. [5]
    C.H. Rohwer, Idempotent One-Sided Approximation of Median Smoothers, Journal of Approximation Theory. Vol 58, No. 2 (1989).MathSciNetCrossRefGoogle Scholar
  6. [6]
    C.H. Rohwer, and L.M. Toerien, Locally Monotone Robust Approximation of Sequences, Journal of Computational and Applied Mathematics 36 (1991), 399–408.MathSciNetzbMATHCrossRefGoogle Scholar
  7. [7]
    C.H. Rohwer, Projections and Separators, Quaestiones Mathematicae 22 (1999), 219–230.MathSciNetzbMATHCrossRefGoogle Scholar
  8. [8]
    C.H. Rohwer, Fast Approximation with Locally Monotone Sequences. Proceedings 4th FAAT Conference, Maratea, (to appear).Google Scholar
  9. [9]
    H.L. Royden, Real Analysis, Macmillan, N.J., 1969.Google Scholar
  10. [10]
    J. Serra, Image Analysis and Mathematical Morphology, Acad. Press, London 1982.Google Scholar
  11. [11]
    P.F. Velleman, Robust nonlinear data smoothers: Definitions and recommendations, Proc. Natl. Acad. Sci. USA. 74, No. 2 (1977), 434–436.CrossRefGoogle Scholar
  12. [12]
    Zhou Xing-Wei, Yang De-Yun, Ding Run-Tao, Infinite length roots of median filters, Science in China, Ser. A, Vol. 35 (1992), 1496–1508.Google Scholar

Copyright information

© Birkhäuser Verlag Basel 2002

Authors and Affiliations

  • Carl H. Rohwer
    • 1
  1. 1.Department of MathematicsUniversity of StellenboschMatielandSouth Africa

Personalised recommendations