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Bayesian estimation for the multifractality parameter

Abstract : 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.
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  • HAL Id : hal-01151027, version 1
  • OATAO : 12435

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Herwig Wendt, Nicolas Dobigeon, Jean-Yves Tourneret, Patrice Abry. Bayesian estimation for the multifractality parameter. IEEE International Conference on Acoustics, Speech, and Signal Processing - ICASSP 2013, May 2013, Vancouver, Canada. pp. 6556-6560. ⟨hal-01151027⟩

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