Positive Wavelet Representation of Fractal Signals and Images

  • Graham H. Watson
  • J. Glynn Jones


With appropriate choice of an analysing wavelet in the form of a positive pulse, information concerning the structure of a signal is concentrated economically in the local maxima and minima of the function of two variables, position and scale, given by the wavelet transformation. This information is extracted by a process of correlation detection, in which the analysing wavelet is regarded as a multiple-scale matched filter. Identification of local extrema corresponds to the detection of signal wavelets. The ensemble of such signal wavelets provides a discrete feature-based representation of the given function. In contrast to the standard method of reconstruction by means of the linear inverse wavelet transform, an alternative method of reconstruction from the feature-based representation is demonstrated. Applications of the positive wavelet representation to an elucidation of the fractal structure of measured and simulated turbulence are illustrated. The method extends in a straightforward manner to two dimensions. An application which demonstrates the multiple-scale feature-based representation of a two-dimensional image is presented.


Analyse Wavelet Local Extremum Matched Filter Cascade Model Information Intensity 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Graham H. Watson
  • J. Glynn Jones

There are no affiliations available

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