A Bayesian approach for the joint estimation of the multifractality parameter and integral scale based on the Whittle approximation

S. Combrexelle, H. Wendt, P. Abry, N. Dobigeon, S. McLaughlin, J. Y. Tourneret

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

Abstract

Multifractal analysis is a powerful tool used in signal processing. Multifractal models are essentially characterized by two parameters, the multifractality parameter c2 and the integral scale A (the time scale beyond which multifractal properties vanish). Yet, most applications concentrate on estimating c2 while the estimation of A is in general overlooked, despite the fact that A potentially conveys important information. Joint estimation of c2 and A is challenging due to the statistical nature of multifractal processes (i.e. the strong dependence and non-Gaussian nature), and has barely been considered. The present contribution addresses these limitations and proposes a Bayesian procedure for the joint estimation of (c2, A). Its originality resides, first, in the construction of a generic multivariate model for the statistics of wavelet leaders for multifractal multiplicative cascade processes, and second, in the use of a suitable Whittle approximation for the likelihood associated with the model. The resulting model enables Bayesian estimators for (c2, A) to also be computed for large sample size. Performance is assessed numerically for synthetic multifractal processes and illustrated for wind-tunnel turbulence data. The proposed procedure significantly improves estimation of c2 and yields, for the first time, reliable estimates for A.

Original languageEnglish
Title of host publicationAcoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on
PublisherIEEE
Pages3886-3890
Number of pages5
Volume2015-August
ISBN (Print)9781467369978
DOIs
Publication statusPublished - 4 Aug 2015
Event40th IEEE International Conference on Acoustics, Speech and Signal Processing 2015 - Brisbane, Australia
Duration: 19 Apr 201524 Apr 2015

Publication series

NameProceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing
PublisherIEEE
ISSN (Print)1520-6149

Conference

Conference40th IEEE International Conference on Acoustics, Speech and Signal Processing 2015
Abbreviated titleICASSP 2015
CountryAustralia
CityBrisbane
Period19/04/1524/04/15

Keywords

  • Bayesian Estimation
  • Integral Scale
  • Multifractal Analysis
  • Wavelet Leaders
  • Whittle Likelihood

ASJC Scopus subject areas

  • Signal Processing
  • Software
  • Electrical and Electronic Engineering

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