Wavelet-Based Entropy Measures to Characterize Two-Dimensional Fractional Brownian Fields

The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282-288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarith...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Switzerland), 2020-02, Vol.22 (2), p.196
Main Authors: Nicolis, Orietta, Mateu, Jorge, Contreras-Reyes, Javier E
Format: Article
Language:English
Subjects:
fractional brownian motion
rényi entropy
shannon entropy
tsallis entropy
wavelets
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Summary:The aim of this work was to extend the results of Perez et al. (Physica A (2006), 365 (2), 282-288) to the two-dimensional (2D) fractional Brownian field. In particular, we defined Shannon entropy using the wavelet spectrum from which the Hurst exponent is estimated by the regression of the logarithm of the square coefficients over the levels of resolutions. Using the same methodology. we also defined two other entropies in 2D: Tsallis and the Rényi entropies. A simulation study was performed for showing the ability of the method to characterize 2D (in this case, α = 2 ) self-similar processes.
ISSN:1099-4300
1099-4300
DOI:10.3390/e22020196