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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Published inEntropy (Basel, Switzerland) Vol. 22; no. 2; p. 196
Main Authors Nicolis, Orietta, Mateu, Jorge, Contreras-Reyes, Javier E
Format Journal Article
LanguageEnglish
Published Switzerland MDPI 07.02.2020
MDPI AG
Subjects
fractional brownian motion
rényi entropy
shannon entropy
tsallis entropy
wavelets
Shannon entropy
fractional Brownian motion
Rényi 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.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e22020196