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Bayesian estimation for the multifractality parameter

Wendt, Herwig and Dobigeon, Nicolas and Tourneret, Jean-Yves and Abry, Patrice Bayesian estimation for the multifractality parameter. (2013) In: IEEE International Conference on Acoustics, Speech, and Signal Processing - ICASSP 2013, 26 May 2013 - 31 May 2013 (Vancouver, Canada).

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Official URL: http://dx.doi.org/10.1109/ICASSP.2013.6638929


Multifractal analysis has matured into a widely used signal and image processing tool. Due to the statistical nature of multifractal processes (strongly non-Gaussian and intricate dependence) the accurate estimation of multifractal parameters is very challenging in situations where the sample size is small (notably including a range of biomedical applications) and currently available estimators need to be improved. To overcome such limitations, the present contribution proposes a Bayesian estimation procedure for the multifractality (or intermittence) parameter. Its originality is threefold: First, the use of wavelet leaders, a recently introduced multiresolution quantity that has been shown to yield significant benefits for multifractal analysis; Second, the construction of a simple yet generic semi-parametric model for the marginals and covariance structure of wavelet leaders for the large class of multiplicative cascade based multifractal processes; Third, the construction of original Bayesian estimators associated with the model and the constraints imposed by multifractal theory. Performance are numerically assessed and illustrated for synthetic multifractal processes for a range of multifractal parameter values. The proposed procedure yields significantly improved estimation performance for small sample sizes.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6638929
HAL Id:hal-01151027
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)
Laboratory name:
Deposited On:06 May 2015 10:58

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