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Signal Enhancement Based on Hölder Regularity Analysis

  • J. Lévy Véhel
Part of the The IMA Volumes in Mathematics and its Application book series (IMA, volume 132)

Abstract

We present an approach for signal enhancement based on the analysis of the local Hölder regularity. The method does not make explicit assumptions on the type of noise or on the global smoothness of the original data, but rather supposes that signal enhancement is equivalent to increasing the Hölder regularity at each point. Such a scheme is well adapted to the case where the signal to be recovered is itself very irregular, e.g. nowhere differentiate with rapidly varying local regularity. In particular, we show an application to SAR image denoising where this technique yields good results compared to other algorithms.

Keywords

Original Signal Wavelet Coefficient Synthetic Aperture Radar Synthetic Aperture Radar Image Local Regularity 
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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References

  1. [1]
    R.A. Devore and B. Lucier, Fast wavelet techniques for near optimal image processing, in IEEE Military Communications Conference, 2–12 (1992).Google Scholar
  2. [2]
    K. Daoudi, J. Lévy Véhel, and Y. Meyer, Construction of functions with prescribed local regularity, Constructive Approximation, 14(03) (1998), 349–385.MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    L. Gagnon and F. Drissi Smaili, Speckle noise reduction of airborne SAR images with symétrie Daubechies wavelets, in Signal and Data Processing of Small Targerts, Proc. SPIE 2759 (1996).Google Scholar
  4. [4]
    D.L. Donoho, De-noising by soft-thresholding, IEEE Trans. Inf. Theory 41, 3 (1994), 613–627.MathSciNetCrossRefGoogle Scholar
  5. [5]
    B. Guiheneuf and J. Levy Véhel, 2 micro-local analysis and applications in signal processing, in Int. Conf. on Wavelet, Tangier, 1997.Google Scholar
  6. [6]
    Y. Meyer, Wavelets, Vibrations and Scalings, American Mathematicel Society, 9 (1997), CRM Monograph Series.Google Scholar
  7. [7]
    C.J. Oliver, Information from SAR images, J. Phys. D, 24 (1991), 1493–15144.CrossRefGoogle Scholar
  8. [8]
    J. Levy Véhel, Fractal Approaches in Signal Processing, Fractals, 3(4) (1995), 755–775.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    P. Legrand and J. LEVY VÉHEL, Statistical denoising of irregular signals, Preprint.Google Scholar
  10. [10]
    J. LÉVY VÉHEL AND B. Guiheneuf, Multifractal Image Denoising, in SCIA, 1997.Google Scholar
  11. [11]
    S. Seuret and J. Levy Véhel, The local Holder function of a continuous function, Preprint.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 2002

Authors and Affiliations

  • J. Lévy Véhel
    • 1
  1. 1.Projet FractalesInriaLe Chesnay CedexFrance

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