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Irregularities and scaling in signal and Image processing: Multifractal analysis

Abstract : B. Mandelbrot gave a new birth to the notions of scale invariance, selfsimilarity and non-integer dimensions, gathering them as the founding corner-stones used to build up frac- tal geometry. The first purpose of the present contribution is to review and relate together these key notions, explore their interplay and show that they are different facets of a same intuition. Second, it will explain how these notions lead to the derivation of the mathe- matical tools underlying multifractal analysis. Third, it will reformulate these theoretical tools into a wavelet framework, hence enabling their better theoretical understanding as well as their efficient practical implementation. B. Mandelbrot used his concept of fractal geometry to analyze real-world applications of very different natures. As a tribute to his work, applications of various origins, and where multifractal analysis proved fruitful, are revisited to illustrate the theoretical developments proposed here.
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Submitted on : Friday, March 8, 2013 - 4:52:02 PM
Last modification on : Tuesday, September 8, 2020 - 10:52:06 AM
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  • HAL Id : hal-00798427, version 1

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Patrice Abry, Stéphane Jaffard, Herwig Wendt. Irregularities and scaling in signal and Image processing: Multifractal analysis. 2011. ⟨hal-00798427⟩

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