Positive Wavelet Representation of Fractal Signals and Images
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.
KeywordsAnalyse Wavelet Local Extremum Matched Filter Cascade Model Information Intensity
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