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Wavelet Analysis and Applications Tao Qian, Mang I. Vai and Xu Yuesheng, Eds.

Summary: Wavelet Analysis and Applications
Tao Qian, Mang I. Vai and Xu Yuesheng, Eds.
Applied and Numerical Harmonic Analysis, 219­264
c 2006 Birkh¨auser Verlag Basel/Switzerland
Wavelet Leaders in Multifractal Analysis
St´ephane Jaffard, Bruno Lashermes and Patrice Abry
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 for-
malism 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 spec-
trum of H¨older singularities. The properties of this new multifractal formal-
ism 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.
1. Introduction
The purpose of multifractal analysis is to study functions or signals whose point-
wise H¨older regularity may change widely from point to point. In such situations,
the determination of the pointwise regularity at each point is numerically unsta-


Source: Abry, Patrice - Laboratoire de Physique, Ecole Normale Supérieure de Lyon


Collections: Engineering