Fractal Approaches in Signal Processing

Abstract : We review some of the recent advances that have been made in the application of fractal tools for studying complex signals. The first part of the paper is devoted to a brief description of the theoretical methods used. These essentially consists in generalizations of previous well known techniques that allow to efficiently handle real signals. We present some general results dealing with the multifractal analysis of sequences of Choquet capacities, and the possibility of constructing such capacities with prescribed spectrum. Related results concerning the pointwise irregularity of a continuous function at each point are given in the frame of iterated functions systems. Finally, some results on a particular stochastic process are sketched: we define the multifractional Brownian motion, a generalization of the classical fractional Brownian motion, where the parameter H is replaced by a function verifying some regularity conditions. The second part consists in the description of selected applications of current interest, in the fields of image analysis, speech synthesis and road traffic modeling. In each case we try and show how a fractal approach provides new means to solve specific problems in signal processing, sometimes with greater success than classical methods.
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Chapitre d'ouvrage
C.J.G. Evertsz and H.-O. Peitgen and R.F. Voss. Fractal Geometry and Analysis : the Mandelbrot festschrift, World Scientific, 1996, 981-02-2434-6
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Jacques Lévy Véhel. Fractal Approaches in Signal Processing. C.J.G. Evertsz and H.-O. Peitgen and R.F. Voss. Fractal Geometry and Analysis : the Mandelbrot festschrift, World Scientific, 1996, 981-02-2434-6. 〈inria-00593322〉

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