Wavelet analysis of multifractal functions

Stephane Jaffard

doi:10.1117/12.217584

1 September 1995 Wavelet analysis of multifractal functions

Stephane Jaffard

Proceedings Volume 2569, Wavelet Applications in Signal and Image Processing III; (1995) https://doi.org/10.1117/12.217584
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

Multifractal signals are characterized by a local Holder exponent that may change completely from point to point. We show that wavelet methods are an extremely efficient tool for determining the exact Holder exponent of a function, or at least, for getting some information about this Holder exponent, such as the Spectrum of Singularities. We construct functions that have a given Holder exponent in a deterministic setting and also in a probabilistic setting (we then obtain the Multifractional Brownian Motion); we also study the Multifractal Formalism for Functions and give some results about its validity.

Citation Download Citation

Stephane Jaffard "Wavelet analysis of multifractal functions", Proc. SPIE 2569, Wavelet Applications in Signal and Image Processing III, (1 September 1995); https://doi.org/10.1117/12.217584

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