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Book Sections Year : 2006

Wavelet leaders in multifractal analysis

Abstract

The properties of several multifractal formalisms based on wavelet coefficients are compared from both mathematical and numerical points of view. When it is based directly on wavelet coefficients, the multifractal formalism is shown to yield, at best, the increasing part of the weak scaling exponent spectrum. The formalism has to be based on new multiresolution quantities, the wavelet leaders, in order to yield the entire and correct spectrum of Hölder singularities. The properties of this new multifractal formalism and of the alternative weak scaling exponent multifractal formalism are investigated. Examples based on known synthetic multifractal processes are illustrating its numerical implementation and abilities.
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Dates and versions

ensl-00195088 , version 1 (11-12-2007)

Identifiers

  • HAL Id : ensl-00195088 , version 1

Cite

Stéphane Jaffard, Bruno Lashermes, Patrice Abry. Wavelet leaders in multifractal analysis. T Qian, M. I; Vai, X. Yuesheng. Wavelet Analysis and Applications, Birkhäuser Verlag, pp.219--264, 2006, 978-3-7643-7777-9. ⟨ensl-00195088⟩
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