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A Bayesian Approach for the Multifractal Analysis of Spatio-Temporal Data

Combrexelle, Sébastien and Wendt, Herwig and Tourneret, Jean-Yves and Altmann, Yoann and Mclaughlin, Stephen and Abry, Patrice A Bayesian Approach for the Multifractal Analysis of Spatio-Temporal Data. (2016) In: 23rd International Conference on Systems, Signals and Image Processing (IWSSIP 2016), 23 May 2016 - 25 May 2016 (Bratislava, Slovakia).

(Document in English)

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Official URL: http://dx.doi.org/10.1109/IWSSIP.2016.7502769


Multifractal (MF) analysis enables the theoretical study of scale invariance models and their practical assessment via wavelet leaders. Yet, the accurate estimation of MF parameters remains a challenging task. For a range of applications, notably biomedical, the performance can potentially be improved by taking advantage of the multivariate nature of data. However, this has barely been considered in the context of MF analysis. This paper proposes a Bayesian model that enables the joint estimation of MF parameters for multivariate time series. It builds on a recently introduced statistical model for leaders and is formulated using a 3D gamma Markov random field joint prior for the MF parameters of the voxels of spatio-temporal data, represented as a multivariate time series, that counteracts the statistical variability induced by small sample size. Numerical simulations indicate that the proposed Bayesian estimator significantly outperforms current state-of-the-art algorithms.

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 IWSSIP 2016. Electronic ISBN: 978-1-4673-9555-7 ISSN: 2157-8702 The original PDF of the article can be found at: http://ieeexplore.ieee.org/document/7502769/ 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-01511895
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 - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Université Claude Bernard-Lyon I - UCBL (FRANCE)
Other partners > Heriot-Watt University (UNITED KINGDOM)
Laboratory name:
Deposited On:22 Mar 2017 13:23

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