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

Combrexelle, Sébastien and Wendt, Herwig and Abry, Patrice and Dobigeon, Nicolas and Tourneret, Jean-Yves and Mc Laughlin, Stephen A Bayesian approach for the joint estimation of the multifractality parameter and integral scale based on the Whittle approximation. (2015) In: 40th IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2015), 19 April 2015 - 24 April 2015 (Brisbane, Australia).

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Official URL: http://dx.doi.org/10.1109/ICASSP.2015.7178699

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.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org This papers appears in Proceedings of ICASSP 2015. Electronic ISBN: 978-1-4673-6997-8 The original PDF of the article can be found at: http://ieeexplore.ieee.org/document/7178699/?reload=true&arnumber=7178699 Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
HAL Id:hal-01387798
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > Ecole Normale Supérieure de Lyon - ENS de Lyon (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Heriot-Watt University (UNITED KINGDOM)
Laboratory name:
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Deposited By: IRIT IRIT
Deposited On:06 Oct 2016 07:56

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